# Question 618a2

Jul 6, 2015

Their electrical potential energy is 22,500 J.

#### Explanation:

The electric potential energy associated with two charges, ${q}_{1}$ and ${q}_{2}$, separated by a distance $r$ can be written like this

$U = {k}_{e} \cdot \frac{{q}_{1} \cdot {q}_{2}}{r}$, where

${k}_{e}$ - Coulomb's constant, equal to $9.0 \cdot {10}^{9} {\text{N m"^2"C}}^{- 2}$.

As you can see, this is simply a plug-and-play problem in which you use the given values to determine $U$.

SInce one spere is 75 mm from point P and the other is 25 mm from the same point P, in opposite directions, it follows that the distance between them is equal to

$r = 75 + 25 = \text{100 mm}$

This means that their electric potential energy is

$U = {k}_{e} \cdot \frac{q \cdot q}{r}$

U = 9.0 * 10^(9)"N" * "m"^(cancel(2))/cancel("C"^2) * ((500 * 10^(-6))^2cancel("C"^2))/(100 * 10^(-3)cancel("m")

U = 9.0 * cancel(10^9) * 250000/100 * cancel(10^(-9))underbrace("N" * "m")_(color(blue)("=Joule"))#

$U = \textcolor{g r e e n}{\text{+22,500 J}}$