Answer
Please see the work below.
Work Step by Step
(a) We know that
$C=\frac{\epsilon_{\circ}A}{d}$
$C=\frac{\epsilon_{\circ}(\pi R^2)}{d}$
This can be rearranged as:
$R=\sqrt{\frac{Cd}{\pi \epsilon_{\circ}}}$
We plug in the known values to obtain:
$R=\sqrt{\frac{(1.0\times 10^{-6})(1.5\times 10^{-3})}{\pi(8.85\times 10^{-12})}}=7.3 m$
(b) If the separation is increased then the radius of the plates should be increased to maintain the capacitance because area and hence radius is directly proportional to capacitance.
(c) We know that
$C=\frac{\epsilon_{\circ}A}{d}$
$C=\frac{\epsilon_{\circ}(\pi R^2)}{d}$
This can be rearranged as:
$R=\sqrt{\frac{Cd}{\pi \epsilon_{\circ}}}$
We plug in the known values to obtain:
$R=\sqrt{\frac{(1.0\times 10^{-6})(3.0\times 10^{-3})}{\pi(8.85\times 10^{-12})}}=10m$
