# Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 15

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Q: 32. A cylindrical capacitor has two co-axial cylinders of length and radii and. The outer cylinder is earthed and the inner cylinder is given a charge of. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).

Answer:

Length of a co-axial cylinder,

Radius of outer cylinder,

Radius of inner cylinder,

Charge on the inner cylinder,

Capacitance of a co-axil cylinder of radii and is given by the relation,

Where,

Permittivity of free space

Potential difference of the inner cylinder is given by,

Q: 34. A parallel plate capacitor is to be designed with a voltage rating, using a material of dielectric constant and dielectric strength about. (Dielectric strength is the maximum electric field a material can tolerate without breakdown, i.e., without starting to conduct electricity through partial ionization.) For safety, we should like the field never to exceed, say of the dielectric strength. What minimum area of the plates is required to have a capacitance of?

Answer:

Potential rating of a parallel plate capacitor,

Dielectric constant of a material,

Dielectric strength

For safety, the field intensity never exceeds of the dielectric strength.

Hence, electric field intensity,

Capacitance of the parallel plate capacitor,

Distance between the plates is given by,

Capacitance is given by the relation,

Where,

Area of each plate

Permittivity of free space

Hence, the area of each plate is about.

Q: 34. Describe schematically the equipotential surfaces corresponding to

(A) A constant electric field in the z-direction,

(B) A field that uniformly increases in magnitude but remains in a constant (say, z) direction,

(C) A single positive charge at the origin, and

(D) A uniform grid consisting of long equally spaced parallel charged wires in a plane.

Answer:

(A) Equidistant planes parallel to the x-y plane are the equipotential surfaces.

(B) Planes parallel to the x-y plane are the equipotential surfaces with the exception that when the planes get closer, the field increases.

(C) Concentric spheres centered at the origin are equipotential surfaces.

(D) A periodically varying shape near the given grid is the equipotential surface. This shape gradually reaches the shape of planes parallel to the grid at a larger distance.

Q: 35. In a Van de Graff type generator a spherical metal shell is to be an electrode. The dielectric strength of the gas surrounding the electrode is. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)

Answer:

Potential difference,

Dielectric strength of the surrounding gas

Electric field intensity, Dielectric strength

Minimum radius of the spherical shell required for the purpose is given by,

Hence, the minimum radius of the spherical shell required is.