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Question

The capacitance of a spherical conductor is 1μF. What is its diameter?

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Solution

Given that,

Capacitance of a spherical conductor = 1µF

We know that,

V=q4πε0r

Now,

C=qV....(I)

Now, put the value of V in equation (I)

C=q(4πε0r)q

C=4πε0r

r=C4πε0

r=1×106×9×109

r=9×103m

Now the diameter is

D=2r

D=2×9×103

D=18×103m

Hence, the diameter is 18×103m


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