Question

A sphercial capacitor is made of two conducting spherical shells of radii a and b. The space between the shells is filled with a dielectric of dielectric constant K up to a radius c as shown in figure (31-E27). Calculate the capacitance.
Figure

Answer 1

Answer:

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Explanation:

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Answer 2

The capacitance   $C=\frac{4 \pi \varepsilon_{0} \mathrm{kabc}}{\mathrm{ka}(\mathrm{b}-\mathrm{c})+\mathrm{b}(\mathrm{c}-\mathrm{a})}$

Explanation:

From the above figure consider a capacitor as $C_ac$ and $C_bc$ connected in series.

$\mathrm{Cac}=\frac{4 \pi \varepsilon_{0} \mathrm{ack}}{\mathrm{k}(\mathrm{c}-\mathrm{a})}$

$C b c=\frac{4 \pi \varepsilon_{0} b c}{(b-c)}$

   $\frac{1}{c}=\frac{1}{c a c}+\frac{1}{c b c}$

      $=\frac{(c-a)}{4 \pi \varepsilon_{0} a c k}+\frac{(b-c)}{4 \pi \varepsilon_{0} b c}$

     $=\frac{b(c-a)+k a(b-c)}{k 4 \pi \varepsilon_{0} a b c}$

 $C=\frac{4 \pi \varepsilon_{0} \mathrm{kabc}}{\mathrm{ka}(\mathrm{b}-\mathrm{c})+\mathrm{b}(\mathrm{c}-\mathrm{a})}$

Where C = Capacitance

            K= dielectric constant.