Question

The capacitance of a spherical conductor is $1\mu F$. What is its diameter?

Answer 1

Given that,

Capacitance of a spherical conductor = 1µF

We know that,

$V=\frac{q}{4\pi {\epsilon }_{0}r}$

Now,

$C=\frac{q}{V}....\left(I\right)$

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

$C=\frac{q\left(4\pi {\epsilon }_{0}r\right)}{q}$

$C=4\pi {\epsilon }_{0}r$

$r=\frac{C}{4\pi {\epsilon }_0}$

$r=1\times {10}^{-6}\times 9\times {10}^9$

$r=9\times {10}^{3}m$

Now the diameter is

$D=2r$

$D=2\times 9\times {10}^3$

$D=18\times {10}^{3}m$

Hence, the diameter is $18\times {10}^{3}m$