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Q.
The capacitance of two concentric spherical shells of radii $R_{1}$ and $R_{2}\left(R_{2}>R_{1}\right)$ when inner sphere is earthed will be:
Electrostatic Potential and Capacitance
Solution:
We know that concentric spheres shell
$\left( R _{2}> R _{1}\right)$
$V _{ R _{1}}=\frac{1}{4 \pi \varepsilon_{ 0 }} \frac{ Q }{ R _{1}}$
$V _{ R _{2}}=\frac{1}{4 \pi \varepsilon_{ 0 }} \frac{ Q }{ R _{2}}$
$V = V _{ R _{1}}- V _{ R _{2}}=\frac{1}{4 \pi \varepsilon_{ 0 }} Q \left(\frac{1}{ R _{1}}-\frac{1}{ R _{2}}\right)$
If the capacitance of two concentric spherical shells be C then
$C=\frac{Q}{V}=\frac{Q}{\frac{Q}{4 \pi \varepsilon_{0}}\left(\frac{R_{2}-R_{1}}{R_{1} R_{2}}\right)}$
$=4 \pi \varepsilon_{0} \frac{\left(R_{1} R_{2}\right)}{\left(R_{2}-R_{1}\right)}$
