Question

Consider a system composed of charges placed on the corners and on the center of a square of side 2d. What is the magnitude of the net electric force on the charge at the center of the square? (top left and bottom right charge: -q; top right and bottom left charge: q; center charge: -q)

Answer 1

I'm going to say draw a picture, and start guessing but you're long gone and it looks like someone's probably typing out the whole method and answer mabob. So good luck! However in general if you don't know:

1. Draw a picture and label it.

2. Write out equations that involve those values.

3. Take guesses, and if you're wrong, keep guessing or take a short break like eat a snack, go for a jog, and see if you can come at it fresh.

Answer 2

There'll be 4 vector forces acting on the center charge which is equidistant away from all 4 charges on the square - add em up, and make sure to keep track of the vector components!!! Each will have an x and a y component.

For the positive charges:
\[ \textbf F_e = \frac{1}{4\pi \epsilon_0} \frac{(q)(-q)}{r^2} \hat{\textbf r} \]

For the negative charges
\[ \textbf F_e = \frac{1}{4\pi \epsilon_0} \frac{(-q)(-q)}{r^2} \hat{\textbf r} \]