Question

At a certain point in space, there is a potential of 800 V relative to zero. What is the potential energy of the system when a +1.0 μC charge is placed at that point in space?

Answer 1

To solve this problem we will apply the concepts related to electric potential and electric potential energy. By definition we know that the electric potential is determined under the function:

$V = \frac{k_e q}{r}$

$k_e$ = Coulomb's constant

q = Charge

r = Radius

At the same time

$U = \frac{k_e q_1q_2}{r}$

The values of variables are the same, then if we replace in a single equation we have this expression,

$U = Vq$

If we replace the values, we have finally that the charge is,

$V = 800V$

$q = 1\mu C$

$U = (800V)(1*10^{-6}C)$

$U = 8*10^{-4}J$

Therefore the potential energy of the system is $8*10^{-4} J$