Aparallel-plate capacitor has plates of area a. the plates are initially separated by a distance d, but this distance can be varied. the capacitor is connected to a battery. what should the plate separation be if you want to halve the energy density?

d' = d /2

Explanation:

Given that

Distance = d

Voltage =V

We know that energy in capacitor given as

If energy become double U' = 2 U then d'

2 d ' = d

d' = d /2

So the distance between plates will be half on initial distance.

if you already have the answer to (a), then just work out how many periods there are in 1 minute, and that's the answer to (c).