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.

 

[Nickie]

So I tried to break it down into two separate components and then add them together.

B) For this part, I'm not too sure how to approach it. I'm thinking of using the electric field formula, E = k (Q1)/r2, and plugging in the values of the three -q charges at the corners and the distance to the center of the square. However, since the charges are all the same magnitude and the distance to the center is not specified, I'm not sure if this approach would work. Another approach could be to use the superposition principle again and break down the electric field into its components from each individual charge and then add them together. This would give us an overall electric field at the center of the square.

I would like to commend your efforts in attempting to solve this problem and using the appropriate equations. However, I would like to clarify a few points and provide some guidance in your approach.

Firstly, in Coulomb's Law, the distance between the charges is squared, not the side length of the square. So the correct equation to use would be E = k (Q1)(Q2)/r^2, where r is the distance between the charges.

For part A, you are correct in using the superposition principle to break down the electric field into its components and then adding them together. However, I would recommend using the vector form of Coulomb's Law, which takes into account the direction of the electric field. This would give you the correct magnitude and direction of the electric field at the location of -Q.

For part B, you are on the right track in using the electric field formula, E = k (Q1)/r^2. However, since the charges are all the same magnitude, you can simply use the principle of superposition again and add the electric fields from each individual charge at the center of the square. This would give you an overall electric field at the center of the square.

In conclusion, to solve this problem accurately, it is important to use the correct equations and consider the direction of the electric field. I would also recommend drawing a diagram to better visualize the problem and guide your calculations. Keep up the good work in applying scientific principles to solve problems.