Question

Find the capacity of a spherical shell of diameter 15 cm inside which is another sphere of diameter 10 cm. The outer is earthed

Answer 1

Explanation:

Given,

Diameter of parallel plate r=20mm=0.02m

Area of plate, A=πr

2

=π×0.02

2

Capacitance $${{C}_{1}}=\dfrac{{{\varepsilon }_{0}}A}{d}=\dfrac{{{\varepsilon }_{0}}\pi \times {{0.02}^{2}}}{d}$$ (where, d= separation)

Radius of spherical capacitor R=1m

$${C_2} = 4\pi {\varepsilon _0}R = 4\pi {\varepsilon _0}$$

If both have equal capacitance

$${C_1} = {C_2}$$

$$\dfrac{{{\varepsilon }_{0}}\pi \times {{0.02}^{2}}}{d}=4\pi {{\varepsilon }_{0}}$$

$$d=\dfrac{{{0.02}^{2}}}{4}=0.1\ mm$$

Hence, Separation between plate is 0.1mm