Ncert Exercises & Solutions

Question 2.29:

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 C = $\frac{4 {πε}_{0} r_{1} r_{2}}{r_{1} - r_{2}}$ Where r₁ and r₂ are the radii of outer and inner spheres, respectively.

Radius Of the outer shell =

r_{1}

, 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.

The potential difference between the two shells is given by,

V = \frac{Q}{4 {πϵ}_{0} r_{2}} - \frac{Q}{4 {πϵ}_{0} r_{1}}

Where,

ε_{0}

= Permittivity of free space

\begin{aligned} V & = \frac{Q}{4 {πϵ}_{0}} [\frac{1}{r_{2}} - \frac{1}{r_{1}}] \\ = \frac{Q (r_{1} - r_{2})}{4 {πϵ}_{0} r_{1} r_{2}} \end{aligned}

Capacitance Of the given system is given by,

\begin{aligned} C & = \frac{Charge (Q)}{Potential difference (V)} \\ = \frac{4 {πϵ}_{0} r_{1} r_{2}}{r_{1} - r_{2}} \end{aligned}

Hence, proved.

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions