A Cylindrical capacitor of length 8 cm is made of two concentric rings having an inner radius as 3 cm and outer radius as 6 cm, C is the capacitance of the capacitor. Calculate the value of C $\times 10^{- 12}$ .

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Solution

Given:
Length L = 8 cm,
inner radius a = 3 cm,
outer radius b = 6 cm.
The cylindrical capacitor formula is given by,
$\frac{C}{L} = \frac{2 π k ϵ_{o}}{l n (b / a)}$
Capacitance, $C = L \frac{2 π k ϵ_{o}}{l n (b / a)}$ $, C = 8 \times 10^{- 2} m \frac{2 π \times 1 \times 8.854 \times 10^{- 12} F / m}{l n (6 / 3)}$ $, C = 6.42 \times 10^{- 10} F .$
Therefore, the capacitance of the capacitor is $6.42 \times 10^{- 10} F .$

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