Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 2

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Capacitance formula

Capacitance Formula

Q: 3. Two charges are placed at points A and B apart.

(A) Identify an equipotential surface of the system.

(B) What is the direction of the electric field at every point on this surface?

Answer:

(A) The situation is represented in the given figure.

Q 3 1 Image of the Equipotential Surface of the System

Q 3 1 Image of the Equipotential Surface of the System

An equipotential surface is the plane on which total potential is zero everywhere. This plane is normal to line AB. The plane is located at the mid-point of line AB because the magnitude of charges is the same.

(B) The direction of the electric field at every point on this surface is normal to the plane in the direction of AB.

Q: 4. A spherical conductor of radius has a charge of distributed uniformly on its surface. What is the electric field:

(A) Inside the sphere

(B) Just outside the sphere

(C) At a point from the centre of the sphere?

Answer:

(A) Radius of the spherical conductor,

Charge is uniformly distributed over the conductor,

Electric field inside a spherical conductor is zero. This is because if there is field inside the conductor, then charges will move to neutralize it.

(B) Electric field E just outside the conductor is given by the relation,

Where,

Permittivity of free space

Therefore, the electric field just outside the sphere is.

(C) Electric field at a point from the centre of the sphere

Distance of the point from the centre,

Therefore, the electric field at a point from the centre of the sphere is

Q: 5. A parallel plate capacitor with air between the plates has a capacitance of What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant?

Answer:

Capacitance between the parallel plates of the capacitor,

Initially, distance between the parallel plates was d and it was filled with air. Dielectric constant of air,

Capacitance, C, is given by the formula,

Where,

Permittivity of free space

If distance between the plates is reduced to half, then new distance,

Dielectric constant of the substance filled in between the plates,

Hence, capacitance of the capacitor becomes

Taking ratios of equations (i) and (ii), we obtain

Therefore, the capacitance between the plates is.

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