# Electric Field at Center of Square.

1. Feb 4, 2012

1. The problem statement, all variables and given/known data

Calculate the electric field at the center of a square with side length .360 m. The charges, clockwise from top left on the corners, are Q1 = 4 x 10^-6, Q2 = 3 x 10^-6, Q3 = 1 X 10^-6 and Q4 = 5 x 10^-6 Coulombs.

2. Relevant equations

E = kq/r^2 where k = Coloumb's constant, q = charge and r = distance between two points

3. The attempt at a solution

I'm really stuck on this problem. I've tried multiple guesses, all wrong, and I'm at what I assume is essentially the penultimate step, but must be missing an understanding.

Using Pythagorean Theorem to get the diagonal of the square, and dividing that by 2, I calculated the distance from each charge to the center to be .2545. I worked out the effect each charge has on the center as follows:

EQ1 = 5.55 x 10^5 N/C
EQ2 = 4.16 x 10^5 N/C
EQ3 = 1.39 x 10^5 N/C
EQ4 = 6.94 x 10^5 N/C

Here is where I'm having trouble. I know electric field is a vector, and as such, I must sum the above vectors to get the net field at the center. But no matter what way I add them, it turns out to be wrong. I've tried considering opposite corners to have opposite directions and subtracting them, simply adding them all up, and various other methods. Nothing works.

Can anyone offer advice as to how I can finish this problem?

2. Feb 4, 2012

### Staff: Mentor

You will get the right answer if you add the vectors correctly. You're on the right track when you consider that the opposite corners have opposite directions, but you also have to consider that the two diagonals of the square are crosswise (neither same direction nor opposite) to each other, so their sizes can't be added directly.

The general technique for adding four vectors pointing in various directions (this is the general technique; there are shortcuts that you could use in this problem to simplify the calculation, but you have to understand the general technique before you can see the shortcuts) is:

1) Write each of your four vectors as the sum of a vector in the horizontal direction and a vector in the vertical direction. Be careful to get the signs right; for example a vector pointing up and to the left is negative in the horizontal direction and positive in the vertical direction.
2) The horizontal component of the sum is the sum of the horizontal components of the four vectors you're adding. Likewise, the vertical component of the sum is the sum of the vertical components of the vectors you're adding.