A spherical capacitor consists of two concentric spherical conductors- held in position by suitable insulating supports Fig- 2-36- Showgiven by C-4 -0 r1 r2-r1-r2where r1 and r2 are the radii of outer and inner spheres- respectively-

Radius of the outer shell = r1 Radius of the inner shell = r2 The inner surface of the outer shell has charge +Q. The outer surface of the inner shell has induc ...

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Standard XII

Physics

Increasing Capacitance Even More

A spherical c...

Question

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show

that the capacitance of a spherical capacitor is given by

where r₁ and r₂ are the radii of outer and inner spheres, respectively.

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Solution

Radius of the outer shell = r₁

Radius of the inner shell = r₂

The inner surface of the outer shell has charge +Q.

The outer surface of the inner shell has induced charge −Q.

Potential difference between the two shells is given by,

Where,

= Permittivity of free space

Hence, proved.

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A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show that the capacitance of a spherical capacitor is given by where r1 and r2 are the radii of outer and inner spheres, respectively.

Radius of the outer shell = r1 Radius of the inner shell = r2 The inner surface of the outer shell has charge +Q. The outer surface of the inner shell has induced charge −Q. Potential difference between the two shells is given by, Where, = Permittivity of free space Hence, proved.

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Fig. 2.36). Show

that the capacitance of a spherical capacitor is given by

where r₁ and r₂ are the radii of outer and inner spheres, respectively.

Radius of the outer shell = r₁

Radius of the inner shell = r₂

The inner surface of the outer shell has charge +Q.

The outer surface of the inner shell has induced charge −Q.

Potential difference between the two shells is given by,

Where,

= Permittivity of free space

Hence, proved.