How Does Charge Distribution Affect Electric Field in a Square Configuration?

[bpichich]

1. The problem
There are four charges at the corners of a square of side L. Three of the charges are -q and one is
-Q(upper left corner).
A) Find the force on -Q, assuming -Q< 0.

B) If -Q=-q, find the electric field at the center of the square.

Homework Equations

Coulomb's Law
E = k (Q1)(Q2)/r²
E = E₁ + E₂ + ...

3. The attempt

A) I basically did E = k [(2q)(-Q)/ (L)² + (q)(-Q)/(2L²)^1/4] or something like that on the test. In my textbook it says to use the superposition principle, when there's multiple charges.

 

[Simon Bridge]

A) I basically did E = k [(2q)(-Q)/ (L)² + (q)(-Q)/(2L²)^1/4] or something like that on the test. In my textbook it says to use the superposition principle, when there's multiple charges.

hint: electric field is a vector

 

[kosovo dave]

Here's how I'd do it (not the quickest way, but by doing it this way you can make your own shortcuts later on).

a) using F=kq1q2/r^2, find the force btwn -Q and -q1, -Q and -q2, -Q and -q3. Add these up. This will be the net force at the point you interested in.

b) pretend that you put a positive point charge +q at the center of the square. Ignoring the influence of any of the three corners, which way will the test charge move? This will be the direction of the electric field due to your given source charge. do this for each corner. do any of the vectors look like they cancel? if you can't tell right away, try breaking each vector up into x and y components and seeing if they add/subtract/cancel.

 

[Simon Bridge]

a) using F=kq1q2/r^2, find the force btwn -Q and -q1, -Q and -q2, -Q and -q3. Add these up. This will be the net force at the point you interested in.

This is what OP did. However, you left out that it has to be a vector sum.