First slide

Capacitors and capacitance

Question

A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is earthed, and the inner sphere is given a charge of 2.5 $μ$ C. The space between the concentric spheres is filled with a liquid of dielectric constant 32. Determine the potential of the inner sphere

Moderate

A

400 V
B

450 V
C

500 V
D

300 V

Solution

$V - 0 = \frac{Q}{C} = \frac{Q (b - a)}{K 4 {πε}_{0} ab}$
or $V = \frac{9 \times 10^{9} \times 2 .5 \times 10^{- 6} (0 .13 - 0 .12)}{32 \times 0 .13 \times 0 .12} = 450 V$

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