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Question: The figure shows a spherical capacitor with inner sphere earthed. The capacitance of the system is ...

The figure shows a spherical capacitor with inner sphere earthed. The capacitance of the system is

A

4πε0abb−a\frac{4\pi\varepsilon_{0}ab}{b - a}

B

4πε0b2b−a\frac{4\pi\varepsilon_{0}b^{2}}{b - a}

C

4πε0(b+a)4\pi\varepsilon_{0}(b + a)

D

None

Answer

4πε0b2b−a\frac{4\pi\varepsilon_{0}b^{2}}{b - a}

Explanation

Solution

Let V be potential on the outer sphere. Thus we can consider two capacitors between the outer sphere and inner sphere (1) and outer sphere and infinity.

Thus, C1=4πε0abb−aC_{1} = 4\pi\varepsilon_{0}\frac{ab}{b - a}

C2=4πε0bC_{2} = 4\pi\varepsilon_{0}\mathbf{b}

C=4πε0abb−a+4πε0bC = 4\pi\varepsilon_{0}\frac{ab}{b - a} + 4\pi\varepsilon_{0}b

Ž C=4πε0b2b−aC = \frac{4\pi\varepsilon_{0}b^{2}}{b - a}