If a 500µF can store 0.02J of energy, what must the voltage supplied to the capacitor be

The energy stored on a capacitor can be expressed in terms of the work done by the battery. Voltage represents energy per unit charge, so the work to move a charge element dq from the negative plate to the positive plate is equal to V dq, where V is the voltage on the capacitor.

U = 0.5CV^2

0.02 = 0.5 (500x10^-6) V^2

Solve for V

V = 8.94 volts