Question

A spherical capacitor contains a charge of 3.30 nC when connected to a potential difference of 220 V. If its plates are separated by vacuum and the inner radius of the outer shell is 4.00 cm, calculate:

(a) the capacitance

(b) the radius of the inner sphere;

(c) the electric field just outside the surface of the inner sphere.

Short answer

The capacitance is 15.0 pF

The radius of the inner sphere is 3.0cm.

The electric field according to gauss law is$3.3\times {10}^{4}N/C$

Step-by-step solution

Step 1:

Given $r_b=4.0cm,V=220V,Q=3.3nC$.

The capacitance is given by

Hence the capacitance is 15.0pF

Step 2:

Hence the capacitance is given by

Simplify equation(1)

Simplify above equation

Hence the radius of the inner sphere is 3.0cm.

Step 3:

The electric field according to gauss law

Substitute in equation(3)

Therefore the electric field according to gauss law is$3.3\times {10}^{4}N/C$