Electrostatic Potential and Capacitance | MCQs | Set - 01

Class 12 Physics - Electrostatic Potential & Capacitance MCQs | Set - 01

Electrostatics 50 Important MCQs

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📗 Top 50 MCQs

1 Mark Each

1 mark 1

The dimensional formula of electric potential is:

1. \( [M L^2 T^{-2} A^{-1}] \)
2. \( [M L^2 T^{-3} A^{-1}] \)
3. \( [M L^{-1} T^{-3} A] \)
4. \( [M L^2 T^{-2} A] \)

Solution:

Correct Option: (B)

Electric Potential \( V = \frac{\text{Work}}{\text{Charge}} = \frac{[M L^2 T^{-2}]}{[A T]} = [M L^2 T^{-3} A^{-1}] \).

1 mark 2

The relation between electric field \( E \) and electric potential \( V \) is given by:

1. \( E = \frac{dV}{dx} \)
2. \( E = -\frac{dV}{dx} \)
3. \( V = -\frac{dE}{dx} \)
4. \( V = \frac{dE}{dx} \)

Solution:

Correct Option: (B)

Electric field is the negative gradient of electric potential. So, \( E = -\frac{dV}{dx} \).

1 mark 3

Work done in moving a charge of \( 2 \text{ C} \) across two points having a potential difference of \( 5 \text{ V} \) is:

1. \( 2.5 \text{ J} \)
2. \( 10 \text{ J} \)
3. \( 0.4 \text{ J} \)
4. \( 7 \text{ J} \)

Solution:

Correct Option: (B)

Work done \( W = q \times \Delta V = 2 \text{ C} \times 5 \text{ V} = 10 \text{ J} \).

1 mark 4

The electric potential at any point on the equatorial line of an electric dipole is:

1. Maximum
2. Zero
3. Minimum but not zero
4. Infinity

Solution:

Correct Option: (B)

Any point on the equatorial line is equidistant from both \( +q \) and \( -q \). Thus, potentials due to both charges cancel out, resulting in zero potential.

1 mark 5

The electric potential inside a conducting hollow sphere of radius \( R \) and carrying charge \( Q \) is:

1. Zero
2. Proportional to the distance from the center
3. Inversely proportional to the distance from the center
4. Uniform and equal to the potential at the surface

Solution:

Correct Option: (D)

Inside a hollow conducting sphere, the electric field is zero (\( E = 0 \)). Hence, the potential is constant and equals the potential on its surface.

1 mark 6

Two copper spheres of the same radius, one solid and the other hollow, are charged to the same potential. Which one will have more charge?

1. Solid sphere
2. Hollow sphere
3. Both will have equal charge
4. Depends on the thickness of the hollow sphere

Solution:

Correct Option: (C)

Charge resides only on the outer surface of a conductor. Since both have the same outer radius, their capacitance is same (\( C = 4 \pi \epsilon_0 R \)). Since \( Q = CV \), both will have equal charge.

1 mark 7

The work done in moving a test charge over an equipotential surface is:

1. Positive
2. Negative
3. Zero
4. Infinite

Solution:

Correct Option: (C)

Potential difference between any two points on an equipotential surface is zero (\( \Delta V = 0 \)). Therefore, work done \( W = q \Delta V = 0 \).

1 mark 8

Equipotential surfaces due to a single point charge are:

1. Concentric cylinders
2. Concentric spheres
3. Parallel planes
4. Intersecting planes

Solution:

Correct Option: (B)

For a point charge, potential \( V = \frac{kQ}{r} \). Points with equal \( r \) form concentric spheres around the charge.

1 mark 9

The electric potential \( V \) at any point \( (x, y, z) \) in space is given by \( V = 4x^2 \) volt. The electric field at the point \( (1, 0, 2) \) in \( \text{V/m} \) is:

1. \( 8 \) along negative X-axis
2. \( 8 \) along positive X-axis
3. \( 16 \) along negative X-axis
4. \( 16 \) along positive X-axis

Solution:

Correct Option: (A)

\( E_x = -\frac{\partial V}{\partial x} = -8x \). At \( x = 1 \), \( E_x = -8 \text{ V/m} \). The field is \( 8 \text{ V/m} \) along the negative x-axis.

1 mark 10

The potential energy of a dipole of dipole moment \( \vec{p} \) placed in a uniform electric field \( \vec{E} \) is given by:

1. \( \vec{p} \cdot \vec{E} \)
2. \( -\vec{p} \cdot \vec{E} \)
3. \( \vec{p} \times \vec{E} \)
4. \( -\vec{p} \times \vec{E} \)

Solution:

Correct Option: (B)

Potential energy \( U = -pE \cos\theta = -\vec{p} \cdot \vec{E} \).

1 mark 11

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles:

1. The charge on the capacitor increases
2. The voltage across the plates increases
3. The capacitance increases
4. The electrostatic energy stored in the capacitor decreases

Solution:

Correct Option: (B)

Battery is disconnected, so charge \( Q \) is constant. Distance \( d \) increases, so capacitance \( C = \frac{\epsilon_0 A}{d} \) decreases. Since \( V = \frac{Q}{C} \), voltage \( V \) increases.

1 mark 12

The capacitance of a parallel plate capacitor is \( C \). If a dielectric slab of dielectric constant \( K \) is introduced between the plates, the new capacitance will be:

1. \( \frac{C}{K} \)
2. \( K C \)
3. \( C + K \)
4. \( C - K \)

Solution:

Correct Option: (B)

Capacitance with dielectric is \( C' = \frac{K \epsilon_0 A}{d} = K C \).

1 mark 13

The energy stored in a capacitor of capacitance \( C \) charged to a potential \( V \) is:

1. \( \frac{1}{2} C V \)
2. \( \frac{1}{2} C^2 V \)
3. \( \frac{1}{2} C V^2 \)
4. \( C V^2 \)

Solution:

Correct Option: (C)

The energy stored is given by the formula \( U = \frac{1}{2} C V^2 \).

1 mark 14

When two capacitors \( C_1 \) and \( C_2 \) are connected in series, the equivalent capacitance \( C_s \) is given by:

1. \( C_1 + C_2 \)
2. \( \frac{C_1 C_2}{C_1 + C_2} \)
3. \( \frac{C_1 + C_2}{C_1 C_2} \)
4. \( | C_1 - C_2 | \)

Solution:

Correct Option: (B)

In series, \( \frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} \), which simplifies to \( C_s = \frac{C_1 C_2}{C_1 + C_2} \).

1 mark 15

Three capacitors each of capacity \( 4 \, \mu\text{F} \) are to be connected in such a way that the effective capacitance is \( 6 \, \mu\text{F} \). This can be done by:

1. Connecting all of them in series
2. Connecting all of them in parallel
3. Connecting two in series and one in parallel
4. Connecting two in parallel and one in series

Solution:

Correct Option: (C)

Two \( 4 \, \mu\text{F} \) in series give \( 2 \, \mu\text{F} \). Connecting the third \( 4 \, \mu\text{F} \) in parallel with them gives \( 2 + 4 = 6 \, \mu\text{F} \).

1 mark 16

The unit of electrical capacitance is:

1. Volt
2. Henry
3. Farad
4. Coulomb

Solution: Correct Option: (C)

Farad (F) is the SI unit of capacitance. \( 1 \text{ F} = 1 \text{ Coulomb/Volt} \).

1 mark 17

Dielectric constant for a metal is:

1. Zero
2. One
3. Greater than one
4. Infinite

Solution: Correct Option: (D)

For conductors (metals), the dielectric constant \( K \) is infinity because the induced electric field completely cancels the external electric field inside the metal.

1 mark 18

If the distance between the plates of a parallel plate capacitor is halved, its capacitance will:

1. Become half
2. Double
3. Remain the same
4. Become four times

Solution: Correct Option: (B)

\( C = \frac{\epsilon_0 A}{d} \). If \( d \) becomes \( d/2 \), \( C \) becomes \( 2C \) (Doubles).

1 mark 19

Work done to rotate an electric dipole of dipole moment \( p \) in a uniform electric field \( E \) from stable equilibrium to unstable equilibrium is:

1. \( pE \)
2. \( 2pE \)
3. \( -pE \)
4. Zero

Solution: Correct Option: (B)

Work done \( W = pE(\cos\theta_1 - \cos\theta_2) \). Stable equilibrium \( \theta_1 = 0^\circ \), unstable \( \theta_2 = 180^\circ \). \( W = pE(1 - (-1)) = 2pE \).

1 mark 20

Which of the following is an example of a capacitor in daily life?

1. Electric motor fan
2. Camera flash
3. Tuning circuits in radios
4. All of the above

Solution: Correct Option: (D)

Capacitors are used in fan motors for starting, in camera flashes for sudden energy release, and in radios for frequency tuning.

1 mark 21

An electron initially at rest is accelerated through a potential difference of \( 1 \text{ V} \). The energy acquired by the electron is:

1. \( 1 \text{ J} \)
2. \( 1.6 \times 10^{-19} \text{ J} \)
3. \( 1 \text{ erg} \)
4. \( 10^7 \text{ J} \)

Solution: Correct Option: (B)

Energy \( = qV = e \times 1 \text{ V} = 1.6 \times 10^{-19} \text{ C} \times 1 \text{ V} = 1.6 \times 10^{-19} \text{ J} \).

1 mark 22

The electric potential \( V \) at a distance \( r \) from a point charge \( Q \) is proportional to:

1. \( r \)
2. \( r^2 \)
3. \( 1/r \)
4. \( 1/r^2 \)

Solution: Correct Option: (C)

\( V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r} \). So, \( V \propto 1/r \).

1 mark 23

Energy density in an electric field \( E \) created in a space with permittivity \( \epsilon_0 \) is:

1. \( \frac{1}{2} \epsilon_0 E^2 \)
2. \( \epsilon_0 E^2 \)
3. \( \frac{1}{2} \epsilon_0 E \)
4. \( \frac{E^2}{2\epsilon_0} \)

Solution: Correct Option: (A)

Energy density (energy per unit volume) in an electric field is \( u = \frac{1}{2} \epsilon_0 E^2 \).

1 mark 24

Two capacitors of capacitances \( C_1 \) and \( C_2 \) are connected in parallel. If a charge \( Q \) is given to the combination, the charge gets shared. The ratio of the charges on the capacitors \( Q_1 / Q_2 \) is:

1. \( C_2 / C_1 \)
2. \( C_1 / C_2 \)
3. \( \sqrt{C_1 / C_2} \)
4. \( 1 \)

Solution: Correct Option: (B)

In parallel, voltage \( V \) is same for both. Since \( Q = CV \), \( \frac{Q_1}{Q_2} = \frac{C_1 V}{C_2 V} = \frac{C_1}{C_2} \).

1 mark 25

The capacitance of a spherical conductor of radius \( R \) is:

1. \( 4 \pi \epsilon_0 R \)
2. \( \frac{1}{4 \pi \epsilon_0 R} \)
3. \( 4 \pi \epsilon_0 R^2 \)
4. \( \frac{R}{4 \pi \epsilon_0} \)

Solution: Correct Option: (A)

For an isolated spherical conductor, \( C = 4 \pi \epsilon_0 R \).

1 mark 26

If \( n \) identical drops of mercury are combined to form a bigger drop, then the capacitance of the bigger drop compared to each small drop will be:

1. \( n \) times
2. \( n^{1/3} \) times
3. \( n^{2/3} \) times
4. \( n^{1/2} \) times

Solution: Correct Option: (B)

Volume of big drop = \( n \times \) Volume of small drop. So \( R = n^{1/3} r \). Since \( C \propto R \), \( C_{\text{big}} = n^{1/3} C_{\text{small}} \).

1 mark 27

Inside a dielectric, the induced electric field always:

1. Aids the external electric field
2. Opposes the external electric field
3. Acts perpendicular to the external field
4. Is zero

Solution: Correct Option: (B)

Polarization creates bound charges that produce an induced electric field which always opposes the applied external field, reducing the net field inside.

1 mark 28

A molecule with a permanent electric dipole moment is called a:

1. Polar molecule
2. Non-polar molecule
3. Conductor
4. Free charge

Solution: Correct Option: (A)

In polar molecules, the center of positive and negative charges do not coincide, leading to a permanent dipole moment (e.g., \( \text{H}_2\text{O} \)).

1 mark 29

The capacitance of a parallel plate capacitor partially filled with a dielectric slab of thickness \( t \) and dielectric constant \( K \) (where \( t < d \)) is:

1. \[\begin{array}{c} C = \frac{\epsilon_0 A}{d - t + \frac{t}{K}} \end{array}\]
2. \[\begin{array}{c} C = \frac{\epsilon_0 A}{d + t - \frac{t}{K}} \end{array}\]
3. \[\begin{array}{c} C = \frac{\epsilon_0 A}{d - t} \end{array}\]
4. \[\begin{array}{c} C = \frac{\epsilon_0 A}{t + \frac{d}{K}} \end{array}\]

Solution: Correct Option: (A)

The standard derivation yields \( C = \frac{\epsilon_0 A}{d - t + \frac{t}{K}} \).

1 mark 30

When a dielectric material is introduced between the plates of a charged and isolated capacitor, which of the following quantities remains unchanged?

1. Capacitance
2. Potential difference
3. Electric field
4. Charge

Solution: Correct Option: (D)

Since the capacitor is isolated (battery disconnected), there is no path for the charge to flow. Hence, charge \( Q \) remains conserved (unchanged).

1 mark 31

The net electric charge inside a charged hollow sphere is:

1. Maximum at the center
2. Zero
3. Uniformly distributed
4. Depends on the size of the sphere

Solution: Correct Option: (B)

All charge given to a conductor resides on its outer surface. Hence, charge inside is zero.

1 mark 32

The potential of the Earth is assumed to be:

1. Infinite
2. Positive
3. Negative
4. Zero

Solution: Correct Option: (D)

Earth is a huge conductor and taking or giving charge does not significantly affect its state, so its potential is conventionally taken as zero.

1 mark 33

If a dielectric is inserted into a capacitor connected to a battery, the energy stored in the capacitor:

1. Increases
2. Decreases
3. Remains the same
4. Becomes zero

Solution: Correct Option: (A)

Since the battery is connected, voltage \( V \) is constant. Capacitance increases (\( C' = KC \)). Energy \( U = \frac{1}{2} C V^2 \) will increase.

1 mark 34

Equipotential surfaces associated with an electric field which is increasing in magnitude along the x-direction are:

1. Planes parallel to yz-plane
2. Planes parallel to xy-plane
3. Planes parallel to xz-plane
4. Coaxial cylinders of increasing radii

Solution: Correct Option: (A)

The electric field is along the x-axis, and equipotential surfaces are always perpendicular to the electric field lines, i.e., parallel to the yz-plane.

1 mark 35

Electric potential energy of a system of two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:

1. \( \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} \)
2. \( \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r} \)
3. \( \frac{1}{4 \pi \epsilon_0} \frac{q_1 + q_2}{r} \)
4. \( \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^3} \)

Solution: Correct Option: (B)

Formula for potential energy is \( U = \frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r} \).

1 mark 36

Two point charges of \( +3 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are placed \( 2 \text{ mm} \) apart. What is the dipole moment?

1. \( 6 \times 10^{-9} \text{ C-m} \)
2. \( 6 \times 10^{-6} \text{ C-m} \)
3. \( 9 \times 10^{-9} \text{ C-m} \)
4. \( 0 \text{ C-m} \)

Solution: Correct Option: (A)

\( p = q \times 2a = 3 \times 10^{-6} \text{ C} \times 2 \times 10^{-3} \text{ m} = 6 \times 10^{-9} \text{ C-m} \).

1 mark 49

A capacitor is fundamentally used to block:

1. AC current
2. DC current
3. High frequency signals
4. Both AC and DC

Solution: Correct Option: (B)

Capacitive reactance \( X_c = \frac{1}{\omega C} = \frac{1}{2\pi f C} \). For DC, \( f = 0 \), so \( X_c = \infty \), effectively blocking DC.

1 mark 50

A metallic sphere is placed in a uniform electric field. The lines of force follow the path(s):

1. Which go straight through the sphere
2. Which curve around but do not hit the surface normally
3. Which are normal to the surface at every point and do not exist inside
4. Which enter the sphere and concentrate at the center

Solution: Correct Option: (C)

Electric field lines cannot exist inside a conductor, and they must always be perpendicular (normal) to the surface of a conductor.

Class 12 Physics

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