Class 12 • Electrostatics

Electric Charges & Fields

NEET & CBSE oriented theory with formulas, examples and diagrams

1. Electric Charge

Electric charge is a fundamental property of matter responsible for electric force. Charges can be positive or negative.

Like charges repel each other
Unlike charges attract each other
Charge is conserved

2. Coulomb’s Law

Force between two charges:

\( F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2} \)

The force between two point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them.

Figure: Force between two point charges

Example 1

Two charges of \(2\mu C\) and \(3\mu C\) are separated by a distance of 0.5 m. Find the force between them.

Solution:
Using Coulomb’s law, \( F = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2} \)

3. Electric Field

Electric Field:

\( E = \frac{F}{q} = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2} \)

Electric field is defined as force per unit positive test charge.

Quick Summary

Charge is conserved and quantized
Coulomb’s law governs electrostatic force
Electric field represents effect of charge

4. Electric Flux

Electric flux gives a measure of the total electric field passing through a given surface.

Electric Flux:

\( \Phi_E = \vec{E} \cdot \vec{A} = EA\cos\theta \)

SI unit: \( N\,m^2/C \)
Maximum flux when \( \theta = 0^\circ \)
Zero flux when \( \theta = 90^\circ \)

5. Gauss’s Law

Gauss’s law relates the electric flux through a closed surface to the total charge enclosed by that surface.

Gauss’s Law:

\( \oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enclosed}}}{\varepsilon_0} \)

Gauss’s law is valid for any closed surface irrespective of its shape.

6. Applications of Gauss’s Law

Electric field due to infinite line charge
Electric field due to infinite plane sheet
Electric field due to uniformly charged spherical shell

Electric Field due to Infinite Line Charge

\( E = \frac{\lambda}{2\pi\varepsilon_0 r} \)

The electric field is inversely proportional to distance from the line charge and directed radially outward.

7. Conductors in Electrostatic Equilibrium

Electric field inside a conductor is zero
Excess charge resides on the surface
Electric field is normal to the surface
Potential remains constant throughout the conductor

Key Result:

\( E_{\text{inside conductor}} = 0 \)

8. Methods of Charging

Charging by friction
Charging by conduction
Charging by induction

Charging by induction does not require direct contact between bodies.

9. Earthing

Earthing is the process of transferring excess charge from a conductor to the earth to neutralize it.

Earth acts as a charge reservoir
Prevents electric shock
Used in buildings and electrical devices

Electrostatics – Final Key Points

Electric flux links field and surface area
Gauss’s law simplifies electric field calculations
Electric field inside conductor is zero
Earthing ensures safety

10. Electric Potential

Electric potential at a point is defined as the work done per unit positive charge in bringing the charge from infinity to that point against the electric field.

Electric Potential:

\( V = \frac{W}{q} \)

SI unit: Volt (V)
Scalar quantity
Depends only on position, not on path

11. Electric Potential due to a Point Charge

\( V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r} \)

Electric potential decreases with increase in distance from the charge.

12. Relation between Electric Field and Potential

Electric field is the negative gradient of electric potential.

\( \vec{E} = -\frac{dV}{dr} \)

Electric field points in the direction of decreasing potential
Greater the potential gradient, stronger the electric field

13. Equipotential Surfaces

An equipotential surface is a surface on which the electric potential is the same at every point.

No work is done in moving a charge on an equipotential surface
Electric field is always perpendicular to equipotential surfaces
Equipotential surfaces never intersect

Examples of Equipotential Surfaces

Concentric spheres around a point charge
Parallel planes in a uniform electric field

14. Electric Potential Energy

Electric potential energy is the work done in assembling a system of charges.

Potential Energy of Two Charges:

\( U = \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r} \)

Like charges → Positive potential energy
Unlike charges → Negative potential energy

15. Potential Energy of a System of Charges

The total potential energy of a system is the sum of potential energies of all pairs of charges.

\( U = \sum \frac{1}{4\pi\varepsilon_0}\frac{q_i q_j}{r_{ij}} \)

16. Capacitor (Introduction)

A capacitor is a device used to store electric charge and electrical energy.

Consists of two conductors separated by an insulator
Common example: Parallel plate capacitor

Capacitance:

\( C = \frac{Q}{V} \)

SI unit: Farad (F)
Depends on geometry and medium

10. Electric Potential

Electric potential at a point is defined as the work done per unit positive charge in bringing the charge from infinity to that point against the electric field.

Electric Potential:

\( V = \frac{W}{q} \)

SI unit: Volt (V)
Scalar quantity
Depends only on position, not on path

11. Electric Potential due to a Point Charge

\( V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r} \)

Electric potential decreases with increase in distance from the charge.

12. Relation between Electric Field and Potential

Electric field is the negative gradient of electric potential.

\( \vec{E} = -\frac{dV}{dr} \)

Electric field points in the direction of decreasing potential
Greater the potential gradient, stronger the electric field

13. Equipotential Surfaces

An equipotential surface is a surface on which the electric potential is the same at every point.

No work is done in moving a charge on an equipotential surface
Electric field is always perpendicular to equipotential surfaces
Equipotential surfaces never intersect

Examples of Equipotential Surfaces

Concentric spheres around a point charge
Parallel planes in a uniform electric field

14. Electric Potential Energy

Electric potential energy is the work done in assembling a system of charges.

Potential Energy of Two Charges:

\( U = \frac{1}{4\pi\varepsilon_0}\frac{q_1q_2}{r} \)

Like charges → Positive potential energy
Unlike charges → Negative potential energy

15. Potential Energy of a System of Charges

The total potential energy of a system is the sum of potential energies of all pairs of charges.

\( U = \sum \frac{1}{4\pi\varepsilon_0}\frac{q_i q_j}{r_{ij}} \)

16. Capacitor (Introduction)

A capacitor is a device used to store electric charge and electrical energy.

Consists of two conductors separated by an insulator
Common example: Parallel plate capacitor

Capacitance:

\( C = \frac{Q}{V} \)

SI unit: Farad (F)
Depends on geometry and medium

17. Parallel Plate Capacitor

A parallel plate capacitor consists of two large parallel conducting plates separated by a small distance. One plate is positively charged and the other negatively charged.

Plates are very close compared to their size
Electric field between plates is uniform

18. Capacitance of Parallel Plate Capacitor (Derivation)

Let area of each plate = A
Distance between plates = d
Charge on plates = ±Q

Electric field between plates:

\( E = \frac{\sigma}{\varepsilon_0} = \frac{Q}{\varepsilon_0 A} \)

Potential difference between plates:

\( V = Ed = \frac{Qd}{\varepsilon_0 A} \)

Capacitance:

\( C = \frac{Q}{V} = \frac{\varepsilon_0 A}{d} \)

Capacitance increases with area
Capacitance decreases with distance

19. Capacitor with Dielectric

When a dielectric material is placed between the plates of a capacitor, its capacitance increases.

\( C = K \varepsilon_0 \frac{A}{d} \)

K = dielectric constant
Dielectric reduces effective electric field
Examples: Glass, mica, plastic

Important Effects of Dielectric

Capacitance increases by factor K
Electric field reduces to \( E/K \)
Stored energy changes

20. Energy Stored in a Capacitor

Energy stored in a capacitor is equal to the work done in charging it.

Energy Stored:

\( U = \frac{1}{2}CV^2 \)

Alternative Forms:

\( U = \frac{1}{2}QV = \frac{Q^2}{2C} \)

Energy is stored in the electric field
Unit of energy: Joule (J)

21. Energy Density of Electric Field

Energy stored per unit volume of electric field is called energy density.

\( u = \frac{1}{2} \varepsilon_0 E^2 \)

Valid for vacuum
For dielectric, replace \( \varepsilon_0 \) by \( \varepsilon \)

22. Force between Plates of a Capacitor

The plates of a charged capacitor attract each other due to electric forces.

Force per unit area (Pressure):

\( P = \frac{1}{2} \varepsilon_0 E^2 \)

Force is always attractive
Independent of charge sign

23. Capacitors in Series

When capacitors are connected end-to-end so that the same charge flows through each capacitor, they are said to be connected in series.

Charge on each capacitor is same
Total potential difference is sum of individual voltages

Derivation

Let three capacitors C₁, C₂, C₃ be connected in series.

Total voltage:

\( V = V_1 + V_2 + V_3 \)

Since \( V = \frac{Q}{C} \):

\( \frac{Q}{C_{eq}} = \frac{Q}{C_1} + \frac{Q}{C_2} + \frac{Q}{C_3} \)

Equivalent capacitance:

\( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3} \)

Equivalent capacitance is always less than the smallest capacitor
Used when high voltage rating is required

24. Capacitors in Parallel

When capacitors are connected across the same potential difference, they are said to be connected in parallel.

Potential difference across each capacitor is same
Total charge is sum of individual charges

Derivation

Let capacitors C₁, C₂, C₃ be connected in parallel.

Total charge:

\( Q = Q_1 + Q_2 + Q_3 \)

Using \( Q = CV \):

\( C_{eq}V = C_1V + C_2V + C_3V \)

Equivalent capacitance:

\( C_{eq} = C_1 + C_2 + C_3 \)

Equivalent capacitance is greater than the largest capacitor
Used when large charge storage is needed

Series vs Parallel (Quick Comparison)

Series: Same charge, voltage divides
Parallel: Same voltage, charge divides
Series: Capacitance decreases
Parallel: Capacitance increases

25. Capacitor with Dielectric

A dielectric is an insulating material which, when placed between the plates of a capacitor, increases its capacitance.

Dielectric constant (relative permittivity) = K
For vacuum or air, \( K = 1 \)
For all dielectrics, \( K > 1 \)

Capacitor Completely Filled with Dielectric

Consider a parallel plate capacitor of plate area A and separation d.

Capacitance without dielectric:

\( C_0 = \frac{\varepsilon_0 A}{d} \)

Capacitance with dielectric fully filled:

\( C = K C_0 = \frac{K \varepsilon_0 A}{d} \)

Capacitance increases by factor K
Electric field inside dielectric reduces

Effect on Electric Field

Original electric field:

\( E_0 = \frac{\sigma}{\varepsilon_0} \)

Electric field with dielectric:

\( E = \frac{E_0}{K} \)

Dielectric reduces the electric field by a factor K.

26. Energy Stored in a Capacitor

Energy stored:

\( U = \frac{1}{2} C V^2 \)

Alternate forms:

\( U = \frac{Q^2}{2C} = \frac{1}{2}QV \)

Energy Change on Inserting Dielectric

Case 1: Battery connected (V constant)

New energy:

\( U' = \frac{1}{2} (KC) V^2 = K U \)

Energy increases
Extra energy comes from battery

Case 2: Battery disconnected (Q constant)

New energy:

\( U' = \frac{U}{K} \)

Energy decreases
Energy used to polarize dielectric

27. Capacitor Partially Filled with Dielectric

If a dielectric slab of thickness t is inserted between the plates of separation d, the effective capacitance becomes:

\( C = \frac{\varepsilon_0 A}{(d - t) + \frac{t}{K}} \)

This is equivalent to two capacitors in series
Important for NEET numerical problems

NEET Exam Tips

Always check whether battery is connected or not
Capacitance depends only on geometry and dielectric
Energy depends on external conditions (Q or V)

28. Force on a Dielectric Slab

When a dielectric slab is partially inserted between the plates of a charged capacitor, a force acts on the slab pulling it inside the capacitor.

Force always acts to increase capacitance
Direction: slab pulled into region of stronger electric field
Very important for NEET numericals

Case 1: Battery Connected (Voltage Constant)

When the capacitor remains connected to a battery:

Potential difference \(V\) = constant
Charge on capacitor changes

Force on dielectric slab:

\( F = \frac{1}{2} \varepsilon_0 A E^2 (K - 1) \)

Since \( E = \frac{V}{d} \):

\( F = \frac{1}{2} \varepsilon_0 A \left(\frac{V}{d}\right)^2 (K - 1) \)

👉 Force is independent of length inserted

Case 2: Battery Disconnected (Charge Constant)

When battery is disconnected:

Total charge \(Q\) remains constant
Potential difference decreases

Force on dielectric slab:

\( F = \frac{Q^2}{2 \varepsilon_0 A} \left(\frac{K - 1}{K}\right) \)

👉 Force is smaller compared to battery-connected case

Force using Energy Method

Force can be calculated using change in energy:

\( F = -\frac{dU}{dx} \)

Used when dielectric moves by small distance \(dx\)
Common approach in derivation-based problems

Important Observations (NEET)

Force does NOT depend on thickness of slab
Force is always attractive (slab pulled in)
Higher dielectric constant → larger force
Force is maximum when slab just starts entering

Common Mistakes to Avoid

Confusing constant \(V\) and constant \(Q\) cases
Using wrong formula for force
Assuming force depends on inserted length

29. Electric Current

Electric current is defined as the rate of flow of electric charge through any cross-section of a conductor.

\( I = \frac{dq}{dt} \)

SI unit: Ampere (A)
Direction of current is opposite to motion of electrons
Scalar quantity

Microscopic View of Current

In metallic conductors, electric current is due to the drift of free electrons under the influence of an electric field.

Electrons move randomly due to thermal motion
Applied electric field gives a small net drift velocity
This drift produces current

Drift Velocity

Drift velocity is the average velocity acquired by free electrons in the direction opposite to the electric field.

\( v_d = \frac{eE\tau}{m} \)

\(e\) = electronic charge
\(E\) = electric field
\(\tau\) = relaxation time
\(m\) = mass of electron

👉 Drift velocity is extremely small (≈ \(10^{-4}\) m/s)

Relation Between Current and Drift Velocity

Current flowing through a conductor is given by:

\( I = neAv_d \)

\(n\) = number of free electrons per unit volume
\(A\) = cross-sectional area
\(v_d\) = drift velocity

NEET Tip:
If area decreases → drift velocity increases (for same current)

Mobility of Charge Carriers

Mobility is defined as drift velocity per unit electric field.

\( \mu = \frac{v_d}{E} = \frac{e\tau}{m} \)

SI unit: m² V⁻¹ s⁻¹
Higher mobility → better conductivity

Current Density

Current density is defined as current per unit area.

\( J = \frac{I}{A} = ne v_d \)

Vector quantity
Direction same as electric field

Important Observations (NEET)

Drift velocity ≠ thermal velocity
Thermal velocity ≫ drift velocity
No current flows if electric field is zero
Even without current, electrons keep moving randomly

Common Mistakes to Avoid

Confusing drift velocity with speed of electrons
Wrong direction of current vs electron flow
Forgetting area in current formula

30. Ohm’s Law

At constant temperature, the current flowing through a conductor is directly proportional to the potential difference applied across its ends.

\( V \propto I \)

\( V = IR \)

\(V\) = Potential difference
\(I\) = Electric current
\(R\) = Resistance of conductor

Graphical Interpretation of Ohm’s Law

The graph between potential difference \(V\) and current \(I\) is a straight line passing through the origin.

Slope of V–I graph = Resistance \(R\)

NEET Tip:
Straight line graph ⇒ Ohmic conductor Curved graph ⇒ Non-ohmic conductor

Microscopic Form of Ohm’s Law

Ohm’s law can also be explained using microscopic quantities.

\( J = \sigma E \)

\(J\) = current density
\(\sigma\) = electrical conductivity
\(E\) = electric field

Since \( J = \frac{I}{A} \) and \( E = \frac{V}{l} \), macroscopic Ohm’s law can be derived.

31. Resistance

Resistance is the property of a conductor by virtue of which it opposes the flow of electric current.

\( R = \frac{V}{I} \)

SI unit: Ohm (Ω)
Scalar quantity

Factors Affecting Resistance

Length of conductor
Area of cross-section
Nature of material
Temperature

\( R = \rho \frac{l}{A} \)

\(\rho\) = resistivity of material
\(l\) = length of conductor
\(A\) = cross-sectional area

Resistivity

Resistivity is a material property that indicates how strongly a substance opposes the flow of electric current.

\( \rho = \frac{RA}{l} \)

SI unit: Ω m
Independent of length and area
Depends on nature of material and temperature

Conductivity

Conductivity is the reciprocal of resistivity.

\( \sigma = \frac{1}{\rho} \)

SI unit: S/m
Good conductors → high conductivity

Important Results (NEET)

If length doubles → resistance doubles
If area doubles → resistance becomes half
Resistivity remains unchanged for same material

Non-Ohmic Conductors

Conductors that do not obey Ohm’s law are called non-ohmic conductors.

Diodes
Thermistors
Electrolytes

32. Temperature Dependence of Resistance

The resistance of a conductor generally changes with change in temperature. For most metallic conductors, resistance increases with increase in temperature.

Metallic Conductors

For metallic conductors, resistance increases almost linearly with temperature.

\( R_T = R_0 (1 + \alpha T) \)

\(R_T\) = resistance at temperature \(T\)
\(R_0\) = resistance at 0°C
\(\alpha\) = temperature coefficient of resistance

Reason:
Increase in temperature → increase in lattice vibrations → more collisions → higher resistance

Temperature Coefficient of Resistance

Temperature coefficient of resistance is defined as the fractional change in resistance per degree change in temperature.

\( \alpha = \frac{R_T - R_0}{R_0 T} \)

Unit: per °C or per K
For metals → positive
For semiconductors → negative

Semiconductors

In semiconductors, resistance decreases with increase in temperature.

Examples: Silicon, Germanium
Temperature coefficient is negative

Reason:
Increase in temperature → more charge carriers → higher conductivity → lower resistance

Alloys

Alloys show very small change in resistance with temperature.

Examples: Manganin, Constantan
Used in standard resistors
Nearly zero temperature coefficient

Effect of Temperature on Resistivity

Resistivity also changes with temperature.

\( \rho_T = \rho_0 (1 + \alpha T) \)

For metals → resistivity increases
For semiconductors → resistivity decreases

Important NEET Points

Resistance depends on temperature, resistivity does too
Alloys preferred in resistors due to small temperature variation
Thermistors work on temperature dependence of resistance

33. Combination of Resistances

In electrical circuits, resistances are often connected together to control the flow of current. These combinations are mainly of two types:

Series combination
Parallel combination

Resistances in Series

When resistances are connected end to end, such that the same current flows through each resistance, they are said to be in series.

\( R_{eq} = R_1 + R_2 + R_3 + \dots \)

Same current flows through all resistances
Voltage divides across resistances
Equivalent resistance is always greater than the largest resistance

Voltage distribution:
\( V = V_1 + V_2 + V_3 \)

Resistances in Parallel

When resistances are connected between the same two points, so that the potential difference across each is the same, they are said to be in parallel.

\( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots \)

Same voltage across all resistances
Current divides among different branches
Equivalent resistance is always less than the smallest resistance

Current distribution:
\( I = I_1 + I_2 + I_3 \)

Special Cases

Two resistances in parallel:
\( R_{eq} = \frac{R_1 R_2}{R_1 + R_2} \)
n identical resistances in series:
\( R_{eq} = nR \)
n identical resistances in parallel:
\( R_{eq} = \frac{R}{n} \)

Power Considerations

In series: Same current → power ∝ resistance
In parallel: Same voltage → power ∝ inverse of resistance

Important NEET Points

Domestic appliances are connected in parallel
Series combination reduces current
Parallel combination allows independent operation
Short circuit → very low resistance → high current

34. Electrical Energy

When electric current flows through a conductor, electrical energy is converted into other forms of energy such as heat, light or mechanical energy.

\( W = VIt \)

\(V\) = Potential difference
\(I\) = Current
\(t\) = Time

The SI unit of electrical energy is joule (J).

Electric Power

Electric power is the rate at which electrical energy is consumed or converted.

\( P = \frac{W}{t} = VI \)

Using Ohm’s law, power can also be written as:

\( P = I^2R \)

\( P = \frac{V^2}{R} \)

SI unit of power is watt (W)
1 W = 1 J/s

Joule’s Law of Heating

When an electric current flows through a resistor, heat is produced due to collisions between electrons and atoms of the conductor.

\( H = I^2Rt \)

Heat produced ∝ square of current
Heat produced ∝ resistance
Heat produced ∝ time

Applications of Heating Effect

Electric heater
Electric iron
Electric kettle
Incandescent bulb

Electric Bulb

An electric bulb works on the principle of heating effect of current. The filament is made of tungsten because it has:

High melting point
High resistivity
Low vapor pressure

Commercial Unit of Electrical Energy

Electrical energy used in daily life is measured in kilowatt-hour (kWh).

\( 1 \text{ kWh} = 3.6 \times 10^6 \text{ J} \)

1 unit of electricity = 1 kWh

Important NEET Points

High power appliances consume more energy
Fuse wire has low melting point
Bulbs in parallel work at rated voltage
Heating ∝ \(I^2\), not I

35. Electric Cell

An electric cell is a device which converts chemical energy into electrical energy.

Positive terminal → higher potential
Negative terminal → lower potential
Current flows externally from +ve to −ve terminal

Electromotive Force (EMF)

EMF of a cell is defined as the work done by the cell in moving a unit charge through the complete circuit.

\( E = \frac{W}{q} \)

SI unit: volt (V)
EMF is not a force (name misleading)
It represents energy per unit charge

EMF vs Potential Difference

EMF	Potential Difference
Measured in open circuit	Measured in closed circuit
Independent of current	Depends on current
Cause of current	Effect of current

Internal Resistance of a Cell

The resistance offered by the electrolyte and electrodes inside the cell to the flow of current is called internal resistance.

Denoted by \( r \)
Depends on nature of electrolyte
Depends on distance between electrodes
Depends on area of electrodes immersed

Terminal Voltage of a Cell

Terminal voltage is the potential difference across the terminals of the cell when current is flowing.

\( V = E - Ir \)

\(E\) = EMF of cell
\(I\) = Current
\(r\) = Internal resistance

When no current flows (open circuit):

\( V = E \)

Current in a Closed Circuit

For a cell connected to an external resistance \(R\):

\( I = \frac{E}{R + r} \)

Short Circuit of a Cell

When external resistance \(R = 0\), the circuit is called a short circuit.

\( I_{max} = \frac{E}{r} \)

Very large current flows
Cell may get damaged

Important NEET Points

EMF is maximum voltage of a cell
Terminal voltage decreases when current increases
Internal resistance is independent of external circuit
Short circuit current is maximum

36. Combination of Cells

When more than one electric cell is connected together to obtain required voltage or current, the arrangement is called combination of cells.

Cells can be connected in two ways:

Cells in Series
Cells in Parallel

Cells Connected in Series

In series combination, the positive terminal of one cell is connected to the negative terminal of the next cell.

Total EMF = sum of individual EMFs
Total internal resistance = sum of internal resistances

\( E_{eq} = E_1 + E_2 + E_3 + \dots \)

\( r_{eq} = r_1 + r_2 + r_3 + \dots \)

If n identical cells each of emf \(E\) and internal resistance \(r\) are connected in series:

\( E_{eq} = nE \)

\( r_{eq} = nr \)

Current in Series Combination

If the external resistance is \(R\), the current flowing is:

\( I = \frac{nE}{R + nr} \)

When to use Series Combination?

When external resistance is large
When high voltage is required

Cells Connected in Parallel

In parallel combination, all positive terminals are connected together and all negative terminals are connected together.

Equivalent EMF remains same
Equivalent internal resistance decreases

For n identical cells each of emf \(E\) and internal resistance \(r\):

\( E_{eq} = E \)

\( r_{eq} = \frac{r}{n} \)

Current in Parallel Combination

If external resistance is \(R\), current is:

\( I = \frac{E}{R + \frac{r}{n}} \)

When to use Parallel Combination?

When external resistance is small
When large current is required

Series vs Parallel (NEET Comparison)

Series	Parallel
High voltage	High current
Internal resistance increases	Internal resistance decreases
Used when R is large	Used when R is small

NEET Important Tips

Maximum current → parallel combination
Maximum voltage → series combination
Battery in cars → cells in parallel
Flashlights → cells in series

37. Kirchhoff’s Laws

Kirchhoff’s laws are used to analyze complex electrical circuits where simple series or parallel rules are not sufficient.

There are two Kirchhoff’s laws:

Kirchhoff’s Junction Law (Current Law)
Kirchhoff’s Loop Law (Voltage Law)

Kirchhoff’s Junction Law (KCL)

At any junction (node) in an electric circuit, the algebraic sum of currents is zero.

\( \sum I = 0 \)

This means:

\( \text{Sum of currents entering} = \text{Sum of currents leaving} \)

Physical Reason

Junction law is based on conservation of electric charge. Charge can neither be created nor destroyed.

Example

If currents \(I_1\) and \(I_2\) enter a junction and current \(I_3\) leaves it, then:

\( I_1 + I_2 = I_3 \)

Kirchhoff’s Loop Law (KVL)

In any closed loop of a circuit, the algebraic sum of potential differences is zero.

\( \sum V = 0 \)

This means the total EMF supplied in a loop is equal to the total potential drop across resistances.

Physical Reason

Loop law is based on conservation of energy.

Sign Convention (Very Important for NEET)

When moving from negative to positive terminal of a cell → +E
When moving from positive to negative terminal of a cell → −E
In a resistor:
- Along direction of current → −IR
- Opposite to current → +IR

Loop Equation Example

Consider a loop having a cell of emf \(E\) and resistance \(R\) carrying current \(I\):

\( E - IR = 0 \)

For multiple resistors:

\( E - I(R_1 + R_2 + R_3) = 0 \)

Steps to Solve Circuits using Kirchhoff’s Laws

Assume direction of current in each branch
Apply junction law at nodes
Apply loop law for independent loops
Solve simultaneous equations

NEET Important Points

Assumed current direction can be wrong — sign will correct it
Always follow sign convention carefully
Used in multi-loop & bridge circuits
Foundation for Wheatstone bridge & Potentiometer

38. Wheatstone Bridge

Wheatstone bridge is an arrangement of four resistances used to accurately determine an unknown resistance.

Construction

It consists of four resistances arranged in a diamond shape. A galvanometer is connected between two opposite junctions and a cell is connected across the other two junctions.

Condition for Balanced Wheatstone Bridge

When no current flows through the galvanometer, the bridge is said to be balanced.

\( \frac{R_1}{R_2} = \frac{R_3}{R_4} \)

Under this condition, the galvanometer shows zero deflection.

Uses of Wheatstone Bridge

Measurement of unknown resistance
Detection of very small changes in resistance
Basis of meter bridge and potentiometer

39. Meter Bridge (Slide Wire Bridge)

Meter bridge is a practical form of Wheatstone bridge used to find an unknown resistance.

Construction

It consists of a uniform wire of length 1 meter stretched on a scale, with two gaps for resistances and a jockey for sliding contact.

Principle of Meter Bridge

Meter bridge works on the principle of Wheatstone bridge. At balance point, no current flows through the galvanometer.

\( \frac{X}{R} = \frac{l}{100 - l} \)

where:

\(X\) = unknown resistance
\(R\) = known resistance
\(l\) = balancing length in cm

How to Reduce Error in Meter Bridge

Interchange known and unknown resistances
Take mean of the two balancing lengths
Ensure uniform wire
Avoid end correction errors

End Correction

Due to non-uniformity near the ends of the wire, some error occurs in measurement.

This error is minimized by interchanging the resistances.

NEET Important Points

Galvanometer shows zero current at balance
Bridge is independent of battery emf at balance
Meter bridge is more accurate than ammeter-voltmeter method
Balance length must lie between 30 cm and 70 cm for accuracy

40. Potentiometer

Potentiometer is an electrical instrument used to measure potential difference and emf accurately without drawing any current from the source.

Key Advantage

Potentiometer is more accurate than a voltmeter because it does not draw current from the circuit under measurement.

Principle of Potentiometer

Potentiometer works on the principle that the potential difference across a uniform wire is directly proportional to its length when a steady current flows through it.

\( V \propto l \)

\( V = k l \)

where \(k\) is the potential gradient.

Potential Gradient

Potential gradient is defined as the potential difference per unit length of the potentiometer wire.

\( k = \frac{V}{L} \)

\(V\) = potential difference across the wire
\(L\) = total length of the wire

Construction of Potentiometer

Uniform wire of manganin or constantan
Length usually 10 m or more
Connected to a battery, rheostat and key
Galvanometer and jockey used for balancing

Balancing Condition

When the galvanometer shows zero deflection, the potential difference across the given cell is equal to the potential drop across the balancing length.

\( E = k l \)

Comparison of EMFs of Two Cells

If two cells have EMFs \(E_1\) and \(E_2\) and balancing lengths \(l_1\) and \(l_2\), then:

\( \frac{E_1}{E_2} = \frac{l_1}{l_2} \)

This method is independent of internal resistance of cells.

Determination of Internal Resistance of a Cell

Let \(l_1\) be the balancing length without external resistance and \(l_2\) be the balancing length with external resistance \(R\).

\( r = R\left(\frac{l_1 - l_2}{l_2}\right) \)

Advantages of Potentiometer

High accuracy
No current drawn from source
Used for calibration of voltmeter and ammeter
Measures small potential differences

NEET Important Points

Potentiometer works on null deflection method
Independent of internal resistance of cell
Potential gradient decreases when current decreases
Uniform wire is essential for accuracy

41. Heating Effect of Electric Current

When an electric current flows through a conductor, electrical energy is converted into heat energy due to collisions of electrons with atoms of the conductor. This phenomenon is called Heating Effect of Electric Current.

Joule’s Law of Heating

According to Joule’s law, the heat produced in a conductor is:

Directly proportional to the square of current flowing
Directly proportional to resistance of the conductor
Directly proportional to time for which current flows

\( H = I^2 R t \)

where,
\(I\) = current
\(R\) = resistance
\(t\) = time

Alternate Forms of Joule’s Law

\( H = VIt \)

\( H = \frac{V^2}{R}t \)

These forms are used depending on which physical quantities are given.

Units of Heat

SI unit: Joule (J)
Commercial unit: calorie

\( 1\,cal = 4.186\,J \)

Factors Affecting Heat Produced

Magnitude of current
Resistance of conductor
Time of flow of current

Applications of Heating Effect

Electric heater
Electric iron
Electric kettle
Electric fuse

Electric Fuse

A fuse is a safety device that protects electrical circuits from overloading and short-circuiting.

Made of thin wire of low melting point
Heats up and melts when excess current flows
Breaks the circuit automatically

Power Loss due to Heating

Electrical energy lost as heat in transmission wires is given by:

\( P_{loss} = I^2 R \)

To reduce power loss, current should be minimized and voltage increased.

NEET Important Points

Heating effect depends on square of current
Fuse wire has low melting point and high resistivity
Longer time → more heat produced
Power loss in transmission lines ∝ \(I^2\)

42. Electric Power

Electric power is defined as the rate at which electrical energy is consumed or converted into other forms of energy in an electric circuit.

\( P = \frac{W}{t} \)

where,
\(P\) = electric power
\(W\) = electrical energy
\(t\) = time

Formula for Electric Power

\( P = VI \)

\( P = I^2 R \)

\( P = \frac{V^2}{R} \)

These expressions are used depending upon the known quantities.

Unit of Electric Power

SI unit: watt (W)
1 watt = 1 joule/second

\( 1\,W = 1\,J\,s^{-1} \)

Commercial Unit of Electrical Energy

Electrical energy used in households is measured in kilowatt-hour (kWh).

\( 1\,kWh = 3.6 \times 10^6\,J \)

This unit is commonly called one unit of electricity.

Electrical Energy

Electrical energy consumed is given by:

\( E = Pt \)

\( E = VIt \)

Power Rating of Electrical Appliances

The power rating of an appliance indicates the rate at which it consumes electrical energy.

Higher power → more energy consumption
Lower resistance devices consume more power at same voltage

Electric Bulb Connection

Bulbs are connected in parallel in household circuits because:

Each appliance gets same voltage
Failure of one does not affect others
Brightness remains unchanged

Overloading

Overloading occurs when excessive current flows in a circuit due to connection of too many appliances.

Causes overheating
May damage appliances
Can lead to fire hazards

NEET Important Points

Power ∝ square of current for fixed resistance
kWh is commercial unit, Joule is SI unit
Parallel connection used in homes
Overloading causes excessive heating

43. Household Electrical Wiring

Electrical energy is supplied to our homes through a well-designed wiring system which ensures safety, uniform voltage supply and proper functioning of appliances.

Live Wire and Neutral Wire

Live Wire: Supplies current at high potential
Neutral Wire: Provides return path for current
Potential difference between them is usually 220 V (India)

Earth Wire

Earth wire is a safety wire connected to the metallic body of appliances.

Prevents electric shock
Has zero or very low potential
Usually color coded green

Electric Fuse

A fuse is a safety device which protects circuits and appliances from excessive current.

Made of thin wire of low melting point
Connected in series with live wire
Melts during overloading or short circuit

Working Principle of Fuse

Fuse works on the heating effect of electric current.

\( H \propto I^2 R t \)

Excess current produces more heat causing the fuse wire to melt.

Miniature Circuit Breaker (MCB)

MCB is an automatic switch that protects the circuit from overload and short circuit.

More reliable than fuse
Can be reset easily
Used in modern household wiring

Short Circuit

Short circuit occurs when live wire directly comes in contact with neutral wire.

Sudden large current flows
Produces excessive heat
May cause fire accidents

NEET Important Points

Fuse and MCB are always connected in live wire
Earth wire is a safety measure, not a current-carrying wire
Household appliances are connected in parallel
MCB works faster and is reusable

44. Electrical Safety Devices & Hazards

Electrical safety devices are essential to protect humans, appliances, and buildings from electric shocks, overloading and fire hazards.

Overloading

Overloading occurs when the current drawn from a circuit exceeds its safe carrying capacity.

Too many appliances connected to one socket
High power appliances used simultaneously
Leads to excessive heating of wires

Effects of Overloading

Damage to electrical appliances
Melting of insulation of wires
Risk of fire accidents

Electric Shock

Electric shock occurs when electric current passes through the human body.

Severity depends on magnitude of current
Also depends on duration of contact
Wet body increases risk of shock

Safe and Dangerous Currents

Current below 1 mA → generally safe
Current above 10 mA → causes muscle contraction
Current above 100 mA → can be fatal

Role of Earthing

Earthing provides a low resistance path for current to flow into the ground.

Prevents electric shock
Protects electrical appliances
Maintains zero potential on metal body

Power Rating of Appliances

Power rating indicates the rate at which an appliance consumes electrical energy.

\( P = VI \)

Higher power → more current drawn
Low resistance appliances draw more current

Electrical Safety Precautions

Do not touch switches with wet hands
Use proper earthing for appliances
Avoid loose connections
Use MCB instead of fuse where possible

NEET Exam Alert

Short circuit causes sudden rise in current
Fuse wire must have low melting point
Human body resistance decreases when wet
Electric shock severity ∝ current through body

45. Electrostatics & Current Electricity – Formula Sheet

This section contains all important formulas from Electrostatics and Current Electricity required for quick revision before NEET.

Basic Electric Quantities

Charge: \( q = ne \)

Current: \( I = \dfrac{dq}{dt} \)

Potential Difference: \( V = \dfrac{W}{q} \)

Coulomb’s Law

\( F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2} \)

Force acts along the line joining charges
Like charges repel, unlike charges attract

Electric Field

\( E = \dfrac{F}{q} \)

Point charge: \( E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2} \)

Uniform field: \( E = \dfrac{V}{d} \)

Electric Potential

Point charge: \( V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r} \)

Potential energy: \( U = qV \)

Work done: \( W = q(V_1 - V_2) \)

Capacitance

\( C = \dfrac{Q}{V} \)

Parallel plate capacitor: \( C = \dfrac{\varepsilon_0 A}{d} \)

With dielectric: \( C = \kappa \dfrac{\varepsilon_0 A}{d} \)

Energy Stored in Capacitor

\( U = \dfrac{1}{2}CV^2 \)

\( U = \dfrac{Q^2}{2C} \)

Ohm’s Law

\( V = IR \)

Resistance: \( R = \rho \dfrac{L}{A} \)

Electrical Power

\( P = VI \)

\( P = I^2R \)

\( P = \dfrac{V^2}{R} \)

Drift Velocity

\( v_d = \dfrac{I}{neA} \)

\( v_d = \dfrac{eE\tau}{m} \)

Temperature Dependence of Resistance

\( R = R_0(1 + \alpha T) \)

\(\alpha\) = temperature coefficient of resistance
For metals: resistance increases with temperature

NEET Quick Facts

Electric field inside conductor = 0
Potential is constant inside conductor
Capacitors block DC after charging
MCB works on thermal + magnetic effect

46. Common Mistakes & NEET Traps

This section highlights the most common conceptual mistakes and NEET-exam traps related to Electrostatics and Current Electricity.

Electrostatics – Common Mistakes

Confusing electric field with electric force. Field depends on source charge only, force depends on test charge also.
Assuming electric field inside a conductor is non-zero. Inside a conductor (electrostatic equilibrium), E = 0.
Taking wrong direction of electric field. Field is always from positive to negative charge.
Forgetting that potential can be zero but field non-zero (example: midpoint of equal charges).
Applying Coulomb’s law directly in dielectric without dividing by dielectric constant \(\kappa\).

Capacitor – NEET Traps

Forgetting condition: battery connected or disconnected while inserting dielectric.
Assuming capacitance depends on charge or voltage – Capacitance depends only on geometry & medium.
Wrong energy formula usage. Always check which form is suitable: \( \frac{1}{2}CV^2 \), \( \frac{Q^2}{2C} \), or \( \frac{1}{2}QV \).
Thinking capacitors allow DC continuously – capacitors block DC after charging.

Current Electricity – Common Mistakes

Assuming electrons move fast – drift velocity is very small, random velocity is high.
Mixing up EMF and terminal voltage. Terminal voltage changes with current, EMF does not.
Applying Ohm’s law to non-ohmic devices like diodes.
Ignoring internal resistance while calculating current.
Assuming current depends on area of conductor – current is same at all cross-sections.

Drift Velocity – Tricky Points

Drift velocity is directly proportional to electric field.
Drift velocity is inversely proportional to number density of electrons.
Increasing temperature decreases drift velocity in metals.

NEET PYQ Style Traps

“Potential is zero” does NOT mean “electric field is zero”.
Resistance of wire depends on temperature but resistivity is material property.
Maximum power transfer when external resistance equals internal resistance.
Voltmeter should have very high resistance.
Ammeter should have very low resistance.

47. NCERT Line-Based Key Statements

The following statements are directly inspired from NCERT text. Many NEET questions are framed by slightly twisting these exact lines.

Electrostatics – NCERT Key Lines

Electric charge is conserved in all physical processes.
Like charges repel and unlike charges attract each other.
Coulomb’s law is valid only for point charges at rest.
Electric field at a point is defined as force per unit positive test charge.
The electric field inside a conductor in electrostatic equilibrium is zero.
Excess charge on a conductor resides only on its outer surface.
Electric field is always perpendicular to the surface of a conductor.

Electric Potential – NCERT Lines

Electric potential at a point is work done per unit charge.
Potential is a scalar quantity while electric field is a vector.
Electric field is the negative gradient of electric potential.
Equipotential surfaces are always perpendicular to electric field lines.
No work is done in moving a charge along an equipotential surface.

Capacitors – NCERT Statements

Capacitance depends only on the geometry of the conductor and the medium.
Capacitance does not depend on charge or potential difference.
Dielectric increases capacitance by reducing the effective electric field.
Energy stored in a capacitor is due to the electric field between plates.
A capacitor blocks steady current but allows alternating current.

Current Electricity – NCERT Lines

Electric current is the rate of flow of electric charge.
Conventional current flows from higher to lower potential.
Drift velocity of electrons is very small compared to their random velocity.
Ohm’s law holds only for ohmic conductors under constant temperature.
Resistance of a conductor increases with increase in temperature.

EMF & Internal Resistance – NCERT Traps

EMF of a cell is the energy supplied per unit charge.
EMF is independent of the external circuit.
Terminal voltage is less than EMF when current is drawn from the cell.
Internal resistance depends on nature and concentration of electrolyte.

Measuring Instruments – NCERT Lines

An ammeter is connected in series and has very low resistance.
A voltmeter is connected in parallel and has very high resistance.
Galvanometer can be converted into an ammeter using a shunt.
Galvanometer can be converted into a voltmeter by adding series resistance.

48. PYQ Concept Mapping (2005–2024)

This section maps frequently asked NEET PYQ concepts with the exact way questions are framed and common traps.

Electrostatics – PYQ Patterns

Concept	NEET Question Type	Common Trap
Coulomb’s Law	Force ratio, medium change	Forgetting dielectric constant
Electric Field	Field due to point/sphere	Direction of field ignored
Gauss’s Law	Infinite sheet, sphere	Wrong Gaussian surface
Conductor Properties	Field inside conductor	Assuming non-zero field

Electric Potential – PYQ Mapping

Concept	Question Pattern	Trap
Potential vs Field	Relation questions	Confusing scalar & vector
Equipotential Surface	Work done = ?	Assuming non-zero work
Potential Energy	Two-charge system	Wrong sign of energy

Capacitors – Repeated PYQ Ideas

Concept	Question Type	Trap
Series / Parallel	Equivalent capacitance	Applying resistance logic
Dielectric Slab	Capacitance change	Ignoring thickness factor
Energy Stored	Energy comparison	Wrong formula selection

Current Electricity – PYQ Trends

Concept	NEET Pattern	Trap
Drift Velocity	Electron flow questions	Confusing with random speed
Ohm’s Law	V–I graph	Temperature variation ignored
Resistance Change	Stretching of wire	Not conserving volume

Cells & EMF – PYQ Traps

Concept	Question Type	Trap
Terminal Voltage	Cell under load	Assuming V = EMF always
Internal Resistance	Short circuit current	Ignoring internal drop
Maximum Power	R = r condition	Using wrong theorem

Instruments – NEET Favourite

Instrument	Question Pattern	Trap
Ammeter	Connection logic	Connecting in parallel
Voltmeter	Loading effect	Ignoring resistance value
Galvanometer	Shunt / Series conversion	Wrong formula usage

49. One-Page Formula Sheet (Last-Day Revision)

This section contains most frequently used formulas in Electrostatics & Current Electricity for quick revision.

Electrostatics – Core Formulas

Coulomb’s Law:
\( F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2} \)
Electric Field:
\( E = \dfrac{F}{q} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2} \)
Electric Flux:
\( \Phi = \vec{E}\cdot\vec{A} \)
Gauss’s Law:
\( \oint \vec{E}\cdot d\vec{A} = \dfrac{Q_{\text{enc}}}{\varepsilon_0} \)

Electric Potential

Potential:
\( V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r} \)
Relation between E & V:
\( E = -\dfrac{dV}{dr} \)
Potential Energy (two charges):
\( U = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r} \)

Capacitors

Capacitance:
\( C = \dfrac{Q}{V} \)
Parallel Plate Capacitor:
\( C = \dfrac{\varepsilon_0 A}{d} \)
Energy Stored:
\( U = \dfrac{1}{2}CV^2 = \dfrac{Q^2}{2C} \)

Current Electricity

Electric Current:
\( I = \dfrac{dq}{dt} \)
Ohm’s Law:
\( V = IR \)
Resistance:
\( R = \rho\dfrac{L}{A} \)
Drift Velocity:
\( v_d = \dfrac{I}{nqA} \)

Cells & EMF

Terminal Voltage:
\( V = E - Ir \)
Short Circuit Current:
\( I = \dfrac{E}{r} \)
Maximum Power Transfer:
\( R = r \)

Measuring Instruments

Ammeter: Low resistance, connected in series
Voltmeter: High resistance, connected in parallel
Galvanometer to Ammeter:
Shunt in parallel
Galvanometer to Voltmeter:
High resistance in series

50. Ultra-Tricky NEET MCQs (Electrostatics + Current)

These MCQs are designed to test concept clarity, not memorization. Most students lose marks here due to hidden traps.

Q1. Two point charges \(+q\) and \(-q\) are placed at a distance \(2a\). The electric field at the midpoint is:

(A) Zero
(B) \( \dfrac{kq}{a^2} \)
(C) \( \dfrac{2kq}{a^2} \)
(D) Infinite

Correct: (C)

Electric fields due to both charges act in the same direction at midpoint, hence they add.

Q2. The electric potential at a point is zero. The electric field at that point:

(A) Must be zero
(B) Must be non-zero
(C) May be zero or non-zero
(D) Is infinite

Correct: (C)

Zero potential does not imply zero field. Example: midpoint of electric dipole.

Q3. Work done in moving a charge along an equipotential surface is:

(A) Maximum
(B) Minimum
(C) Zero
(D) Depends on path

Correct: (C)

Potential difference along equipotential surface is zero, so work done is zero.

Q4. Drift velocity of electrons in a conductor increases when:

(A) Temperature increases
(B) Cross-section increases
(C) Electric field increases
(D) Number density increases

Correct: (C)

\( v_d = \dfrac{eE\tau}{m} \). Drift velocity is directly proportional to electric field.

Q5. A wire is stretched to double its length. Its resistance becomes:

(A) 2R
(B) 4R
(C) R/2
(D) R

Correct: (B)

Length doubles, area halves → \( R \propto \dfrac{L}{A} \Rightarrow 4R \)

Q6. Internal resistance of a cell is maximum when:

(A) Electrolyte level is high
(B) Plates are close
(C) Electrolyte level is low
(D) Temperature is high

Correct: (C)

Lower electrolyte level → smaller effective area → higher internal resistance.

Q7. For maximum power transfer from a cell to external circuit:

(A) External resistance = 0
(B) External resistance = internal resistance
(C) External resistance → ∞
(D) Internal resistance = 0

Correct: (B)

Maximum Power Transfer Theorem: \( R = r \)

51. Assertion–Reason & Statement Based Questions

Assertion–Reason questions check your ability to connect theory with logic. Read both statements carefully before answering.

Q1.
Assertion (A): Electric field inside a conductor is zero.
Reason (R): Free electrons inside a conductor rearrange themselves in such a way that net electric field becomes zero.

(A) A is true, R is true and R is the correct explanation of A
(B) A is true, R is true but R is not the correct explanation of A
(C) A is true, R is false
(D) A is false, R is true

Correct: (A)

Free electrons redistribute themselves until internal electric field cancels.

Q2.
Assertion (A): Electric potential at the center of a dipole is zero.
Reason (R): Electric field at the center of a dipole is also zero.

(A) Both A and R are true and R explains A
(B) Both A and R are true but R does not explain A
(C) A is true, R is false
(D) A is false, R is true

Correct: (C)

Potential cancels algebraically, but electric field vectors add.

Q3.
Assertion (A): Work done in moving a charge along an equipotential surface is zero.
Reason (R): Electric field is always perpendicular to equipotential surfaces.

(A) A and R both true, R explains A
(B) A and R both true, R does not explain A
(C) A true, R false
(D) A false, R true

Correct: (A)

No component of force acts along displacement on equipotential surface.

Q4.
Assertion (A): Drift velocity of electrons is very small.
Reason (R): Electrons collide frequently with lattice ions.

(A) Both A and R true, R explains A
(B) Both true, R not explanation
(C) A true, R false
(D) A false, R true

Correct: (A)

Frequent collisions reduce net drift motion.

Q5. Which of the following statements are correct?

Electric field lines never intersect
Electric potential is a vector quantity
Current density is a vector quantity
Drift velocity is proportional to electric field

Correct Statements: 1, 3 and 4

Potential is scalar, rest are vector/true relations.

52. NEET PYQ Based MCQs (Electrostatics)

The following questions are based on previous year NEET patterns. Focus on concept application rather than memorization.

Q1.
Two point charges +q and −q are placed at a distance 2a apart. The electric field on the perpendicular bisector at distance r from the center is:

(A) Zero
(B) \( \dfrac{1}{4\pi\varepsilon_0}\dfrac{2qa}{r^3} \)
(C) \( \dfrac{1}{4\pi\varepsilon_0}\dfrac{qa}{r^2} \)
(D) \( \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2} \)

Correct: (B)

This is the standard electric field expression of an electric dipole on its equatorial line.

Q2.
Electric potential due to a dipole at a point on the equatorial line is:

(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite

Correct: (C)

Potentials due to +q and −q cancel algebraically.

Q3.
The work done in moving a charge in a closed loop inside an electrostatic field is:

(A) Positive
(B) Negative
(C) Zero
(D) Infinite

Correct: (C)

Electrostatic field is conservative, so work over closed loop is zero.

Q4.
If the distance between two charges is doubled, the electrostatic force between them becomes:

(A) Double
(B) Half
(C) One-fourth
(D) Four times

Correct: (C)

Coulomb’s law: \(F \propto \frac{1}{r^2}\).

Q5.
The electric field inside a hollow charged conductor is:

(A) Maximum at center
(B) Zero everywhere
(C) Non-zero
(D) Depends on charge

Correct: (B)

All excess charge resides on outer surface of conductor.

Q6.
Electric potential at a point due to a point charge is proportional to:

(A) \(r\)
(B) \(r^2\)
(C) \(1/r\)
(D) \(1/r^2\)

Correct: (C)

\(V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r}\).

Q7.
Which quantity remains constant throughout a conductor carrying steady current?

(A) Drift velocity
(B) Current
(C) Electric field
(D) Potential

Correct: (B)

Current continuity principle.

53. Electrostatics – Formula Sheet (NEET Focus)

This section contains most-used NEET formulas with concept traps that students usually commit in exams.

1️⃣ Coulomb’s Law

\( F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2} \)

Force acts along the line joining charges
Like charges repel, unlike attract
Medium effect: replace \( \varepsilon_0 \) by \( \varepsilon \)

⚠️ NEET Trap: Direction of force is often ignored in vector questions.

2️⃣ Electric Field

\( \vec{E} = \dfrac{\vec{F}}{q_0} \)

For point charge: \( E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r^2} \)

Field is vector quantity
Direction is direction of force on +ve test charge

⚠️ NEET Trap: Field inside conductor = 0 (always).

3️⃣ Electric Flux

\( \Phi_E = \vec{E}\cdot\vec{A} = EA\cos\theta \)

Scalar quantity
Maximum when θ = 0°
Zero when θ = 90°

⚠️ NEET Trap: Flux depends on enclosed charge, not shape.

4️⃣ Gauss’s Law

\( \oint \vec{E}\cdot d\vec{A} = \dfrac{Q_{\text{enclosed}}}{\varepsilon_0} \)

Valid for any closed surface
Best used for symmetric charge distributions

⚠️ NEET Trap: External charges do NOT contribute to enclosed charge.

5️⃣ Electric Potential

\( V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{q}{r} \)

Scalar quantity
Algebraic sum of potentials

⚠️ NEET Trap: Potential of dipole on equatorial line = 0.

6️⃣ Relation Between Electric Field & Potential

\( \vec{E} = -\dfrac{dV}{dr} \)

Field points from high potential to low potential
Negative sign indicates direction

⚠️ NEET Trap: Zero electric field does NOT always mean zero potential.

7️⃣ Electric Dipole

Dipole moment: \( \vec{p} = q \times 2a \)

Axial field: \( E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{2p}{r^3} \)

Equatorial field: \( E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^3} \)

⚠️ NEET Trap: Direction of equatorial field is opposite to dipole moment.

54. NEET Electrostatics – MCQ Practice (Level 1 → Level 2)

These questions are strictly based on NCERT + NEET trend. Each question includes a short exam-oriented explanation.

Q1. Two point charges +Q and +4Q are separated by a distance r. The point on the line joining them where the electric field is zero lies:

(A) At midpoint
(B) Closer to +Q
(C) Closer to +4Q
(D) Outside the two charges

✅ Correct: (B)

For same sign charges, electric field cancels between the charges. The stronger charge (+4Q) produces more field, so the null point shifts towards smaller charge.

Q2. The electric field inside a hollow conducting sphere is:

(A) Zero everywhere
(B) Maximum at center
(C) Depends on radius
(D) Non-zero if charged

✅ Correct: (A)

In electrostatic equilibrium, electric field inside a conductor is zero irrespective of charge on the conductor.

Q3. Electric potential at the center of a uniformly charged spherical shell is:

(A) Zero
(B) Same as at surface
(C) Maximum
(D) Infinite

✅ Correct: (B)

Inside a spherical shell, electric field is zero but potential remains constant and equal to surface potential.

Q4. The work done in moving a charge along an equipotential surface is:

(A) Maximum
(B) Minimum
(C) Zero
(D) Depends on path

✅ Correct: (C)

On an equipotential surface, ΔV = 0. Since \( W = qΔV \), work done is zero.

Q5. If the distance between two charges is doubled, the electric force becomes:

(A) Double
(B) Half
(C) One-fourth
(D) Four times

✅ Correct: (C)

From Coulomb’s law, \( F \propto \dfrac{1}{r^2} \). Doubling r ⇒ force becomes 1/4.

Q6. Electric field lines:

(A) Can intersect
(B) Form closed loops
(C) Start from +ve and end on −ve charges
(D) Exist only in vacuum

✅ Correct: (C)

Field lines indicate direction of force on a +ve test charge. They never intersect and never form closed loops.

Q7. The electric potential due to an electric dipole at a point on its equatorial line is:

(A) Maximum
(B) Minimum
(C) Zero
(D) Infinite

✅ Correct: (C)

Potentials due to +q and −q are equal and opposite on equatorial line, hence net potential is zero.