# Case Study Chapter 2 Electrostatic Potential and Capacitance Class 12 Physics

Please refer to below Case Study Chapter 2 Electrostatic Potential and Capacitance Class 12 Physics. These Case Study Questions Class 12 Physics will be coming in your examinations. Students should go through the Chapter 2 Electrostatic Potential and Capacitance Case Study based questions in their Class 12 Physics CBSE, NCERT, KVS book as this will help them to secure more marks in upcoming exams.

## Case Study Based Questions Physics Class 12 – Chapter 2 Electrostatic Potential and Capacitance

Potential difference (Δv) between two points A and B separated by a distance x, in a uniform electric field E is given by Δv = –Ex, where x is measured parallel to the field lines. If a charge q0 moves from A to B, the change in potential energy (Δv) is given as Δv = q0 Δv. A proton is released from rest in uniform electric field of magnitude 8.0 × 104 Vm–1 directed along the positive X–axis. The Proton undergoes a displacement of 0.50 m in the direction of E. Mass of a Proton = 1.66 × 10–27 Kg and charge on a proton = 1.6 × 10–19 C.

With the help of the passage given above, choose the most appropriate alternative for each of the following questions:

Question. As the Proton moves from A to B, then
(a) The Potential energy of Proton decreases
(b) The Potential energy of Proton Increases
(c) The Proton loses kinetic energy.
(d) Total energy of the proton Increases.

A

Question. The change in electric potential of the Proton between the points A and B is
(a) 4.0 × 104 V
(b) –4.0 × 104 V
(c) 6.4 × 10–19 V
(d) –6.4 × 10–19 V

B

Question. The change in electric potential energy of the proton for displacement from A to B is
(a) –6.4 × 1019 J
(b) 6.4 × 10–19 J
(c) –6.4 × 10–15 J
(d) 6.4 × 10–15 J

C

Question. The velocity (VB) of the proton after it has moved 0.50 m starting from rest is
(a) 1.6 × 108 ms–1
(b) 2.77 × 106 ms–1
(c) 2.77 × 104 ms–1
(d) 1.6 × 106 ms–1

B

Question. If in place of charged plates, two similar point charges of 1μC have kept in air at 1m distance from each other. Then, potential energy is
(a) 1 J
(b) 1 eV
(c) 9 × 10–3 J
(d) Zero

C

An arrangement of two conductors separated by an insulating medium can be used to store electric charge and electric energy. Such a system is called a capacitor. The more charge a capacitor can store, the greater is its capacitance. Usually, a capacitor consists of two capacitors having equal and opposite charge + Q and –Q. Hence, there is a potential difference V between them. By the capacitance of a capacitor, we mean the ratio of the charge Q to the potential difference V. By the charge on a capacitor we mean only the charge Q on the positive plate. Total charge of the capacitor is Zero. The capacitance of a capacitor is a constant and depends on geometric factors, such as the shapes, sizes and relative positions of the two conductors, and the nature of the medium between them. The unit of capacitance Farad (F), but the more convenient units are μF and PF. A commonly used capacitor consists of two long strips or metal foils, separated by two long strips of dielectrics, rolled up into a small cylinder. Common dielectric materials are plastics (such as polyestor and polycarbonates) and aluminum oxide. Capacitors are widely used in television, computer, and other electric circuits.

Question. A parallel plate capacitor C has charge Q. The actual charge on its plates are:
(a) Q, Q
(b) Q/2, Q/2
(c) Q, –Q
(d) Q/2, –Q/2

C

Question. A parallel plate capacitor is charged. If the plate are pulled apart,
(a) the capacitance increases.
(b) the potential difference increases.
(c) the total charge increases.
(d) the charge and the potential difference remains the same.

B

Question. If n capacitors, each of capacitance C, are connected in series, then the equivalent capacitance of the combination will be.
(a) n C
(b) n2 C
(c) C/n
(d) C/n2

C

Question. Three capacitors 2.0, 3.0 and 6.0 microfarad are connected in series to a 10 v source. The charge on the 3.0 microfarad capacitor is:
(a) 5 microcoulomb
(b) 10 microcoulomb
(c) 12 microcoulomb
(d) 15 microcoulomb

B

Question. What is the potential difference across 2 microfarad capacitor in the circuit shown?

(a) 12 V
(b) 4 V
(c) 6 V
(d) 18 V

C

Potential of Two Point Charges. The potential at any observation point P of a static electric field is defined as work done by the external agent (or negative of work done by electrostatic field) in slowly bringing a unit positive point charge form infinity to the observation point. The figure given below shows the potential variation along the line of charges. Two point charges Q1 and Q2 lie along a line at a distance from each other.

Question. At which the points 1, 2 and 3 is the electric field is zero?
(a) 1
(b) 2
(c) 3
(d) Both (a) and (b)

C

Question. The signs of charges Q1 and Q2 respectively are
(a) positive and negative
(b) negative and positive
(c) positive and positive
(d) negative and negative

A

Question. Which of the charges Q1 and Q2 is greater in magnitude?
(a) Q2
(b) Q1
(c) Same
(d) Cannot determined

B

Question. Which of the following statement is not true?
(a) Electrostatic force is a conservative force.
(b) Potential energy of charge q at a point is the work done per unit charge in bringing a charge form any point to infinity.
(c) When two like charges lie infinite distance apart, their potential energy is zero.
(d) Both (a) and (c).

B

Question. Positive and negative point charges of equal magnitude are kept at (0,0, a/2) and (0,0, a/2) respectively. The work done by the electric field when another positive point charge is moved from (–a, 0, 0) to (0, a, 0) is
(a) positive
(b) negative
(c) zero
(d) depends on the path connecting the initial and final positions.

C

Equipotential Surfaces. For the various charge systems, we represent equipotential surfaces by curves and line of force by full line curves. Between any two adjacent equipotential surfaces, we assume a constant potential difference the equipotential surfaces of a single point charge are concentric spherical shells with their centres at the point charge. As the lines of force point radially outwards, so they are perpendicular to the equipotential surfaces at all points.

Question. Identify the wrong statement.
(a) Equipotential surfaces due to a single point charge is spherical.
(b) Equipotential surfaces can be constructed for dipoles too.
(c) The electric field is normal to the equipotential surfaces through the point.
(d) The work done to move a test charge on the equipotential surface is positive.

D

Question. Nature of equipotential surface for a point charge is
(a) Ellipsoid with charge at foci.
(b) Sphere with charge at the centre of the sphere.
(c) Sphere with charge on the surface of the sphere.
(d) Plane with charge on the surface.

B

Question. A spherical equipotential surface is not possible
(a) inside a uniformly charged sphere.
(b) for a dipole.
(c) inside a spherical condenser.
(d) for a point charge.

B

Question. The work done in carrying a charge q once round a circle of radius a with a charge Q at its centre is

D

Question. The work done to move a unit charge along an equipotential surface from P to Q
(a) must be defined as

(b) is zero
(c) can have a non-zero value
(d) Both (a) and (b) are correct

D

Spherical Capacitor. The electrical capacitance of a conductor is the measure of its ability to hold electric charge. An isolated spherical conductor of radius R. The charge Q is uniformly distributed over its entire surface. It can be assumed to be concentrated at the sphere. The potential at any point on the surface of the surface of the spherical conductor will be V = 1/4π∈0, Q/R

Capacitance of the spherical conductor situated in vacuum is

Clearly, the capacitance of a spherical conductor is proportional to its radius. The radius of the spherical conductor of 1F capacitance is R = 1/ 4π∈ 0 . C and this radius is about 1500 times the radius of the earth (∼ 6 × 103 km).

Question. If an isolated sphere has a capacitance 50pF. Then radius is
(a) 90 cm
(b) 45 cm
(c) 45 m
(d) 90 m

B

Question. How much charge should be placed on a capacitance of 25 pF to raise its potential 105 V?
(a) 1 μC
(b) 1.5 μC
(c) 2 μC
(d) 2.5 μC

D

Question. Dimensions of capacitance is
(a) [M–1 L–2 T4 A2]
(b) [M–1 L–1 T3 A1]
(c) [M L–2 T4 A2]
(d) [M0 L–2 T4 A1]

A

Question. Metallic sphere of radius R is charged to potential V. Then charge q is proportional to
(a) V
(b) R
(c) Both V and R
(d) none of these