A spherical capacitor contains a charge of 3.30 nC when connected to a potential difference of 250.0 V. Its plates are separated by vacuum and the inner radius of the outer shell is 4.70 cm. calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.

(a)

(b)

(c)

Explanation:

Given data

Charge q=3.3 nC

Voltage V=250.0 V

Radius r=4.70 cm=0.047 m

Required

(a) Capacitance C

(b) The Radius of inner sphere

(c) Electric field

Solution

For Part (a) Capacitance

The Capacitance is given by:

For Part (b) The radius of inner sphere

The Capacitance of spherical co-ordinates is given by:

For Part (c) The electric field

The electric field according to Gauss Law is given by:

(75°f − 32) × 5/9 = 23.889°c

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