1. Tardigrade
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  4. 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 . The capacitance of the capacitor is

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Q. 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 $2.5 \,\mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant $32 .$ The capacitance of the capacitor is

Electrostatic Potential and Capacitance

Solution:

Here, $r_{a}=12\, cm =12 \times 10^{-2} m$
$r_{b}=13 \,cm =13 \times 10^{-2} m$
$q=2.5 \,\mu C =2.5 \times 10^{-6} C , K=32$
As $C=4 \pi \varepsilon_{0} \frac{K r_{a} r_{b}}{r_{b}-r_{a}}$
$=\frac{1}{9 \times 10^{9}} \frac{32 \times 12 \times 10^{-2} \times 13 \times 10^{-2}}{(13-12) \times 10^{-2}}$
$=5.5 \times 10^{-9} F$