Question

Question #618a2

Answer 1

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 * (q_1 * q_2)/r`, where

`k_e` - Coulomb's constant, equal to `9.0 * 10^(9)"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 = "100 mm"`

This means that their electric potential energy is

`U = k_e * (q * 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 = color(green)("+22,500 J")`