Question

Two charges of `-1 C` and `-3 C` are positioned on a line at points `-5` and `2`, respectively. What is the net force on a charge of `4 C` at `1`?

Answer 1

The net force is `1.07xx10^11N`, acting to the right.

Explanation:

We solve this problem by separately calculating the force acting on the `4C` charge due to each of the other two charges, then add them together. In this, I will assume the line referred to is measured in metres.

First, the force due to the `-1C` charge. I will call this `F_1`

`F_1=(1/(4pi epsilon_o)) ((q_1q_2)/r^2) = ((9xx10^9)(1)(4))/6^2=1xx10^9 N`

(Notice I have deliberately left out the signs on the charges. This is because I prefer to let the formulas determine the magnitude of the force. I already know the direction. Since these are unlike charges, they attract. So, `F_1` points toward the `-1C` charge - the to left.)

Next `F_3`, the force due to the `3C` charge

`F_1=(1/(4pi epsilon_o)) ((q_1q_2)/r^2) = ((9xx10^9)(3)(4))/1^2=1.08xx10^11 N`

This force acts toward the `-3C` charge, meaning to the right.

Since the two forces act in opposite directions, we subtract the two values to get the net force

`1.08xx10^11 N-1xx10^9N = 1.07xx10^11N`, acting to the right.