# Electric field of a point charge

• Snowman2526
In summary, the question asked for the magnitude of the net electric field at the center of a square with four point charges fixed to its corners. The equation used was E=kq/r^2, with the sides of the square converted to meters using the Pythagorean theorem. The final answer is 19.82 N/C, but it must be multiplied by 2 due to the symmetry of the charges, giving a net electric field of 39.64 N/C.

## Homework Statement

Four point charges have the same magnitude of 3.1 x 10-12 C and are fixed to the corners of a square that is 5.3 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square.

E=k*abs(q)/r^2

## The Attempt at a Solution

I set up the equation E=(8.99*10^9)(3.1*10^-12)/(3.75^2).

1.98*10^-3 is not correct

A post I was reading mentioned using the formula E=kq/r...which can be found here: https://www.physicsforums.com/showthread.php?t=151884

Now, my book has a similar picture which mentions an E24 vector pointing at the negative point charge, I'm not sure what I'm doing wrong...any help is welcome.

Welcome to PF.

The charges that are the same will off set each other. But the pair that are the opposite charge will have the effect of adding at the center. Sounds like the |ΣE| will be 2*|E|. Because the other 2 net to 0.

Convert the cm to meters.
You have four E vectors - all the same magnitude but different directions - to add.
Begin with a diagram! Symmetry may help!

you are correct delphi, its kind of embarassing, but i forgot to convert cm to m. but I am still getting the wrong answer.

After plugging the sides of my square into the Pythagorean theorem i get .075...but i want to divide that number by 2, giving me the .0375.

my equation now reads:

E=(8.99*10^9)(3.1*10^-12)/.0375^2

I got 19.82 N/C but the stupid wiley site tells me that I am wrong.

Is there something wrong with the way I am setting up my equation?

Snowman2526 said:
you are correct delphi, its kind of embarassing, but i forgot to convert cm to m. but I am still getting the wrong answer.

After plugging the sides of my square into the Pythagorean theorem i get .075...but i want to divide that number by 2, giving me the .0375.

my equation now reads:

E=(8.99*10^9)(3.1*10^-12)/.0375^2

I got 19.82 N/C but the stupid wiley site tells me that I am wrong.

Is there something wrong with the way I am setting up my equation?

You are apparently only calculating the |E| from one of the point charges.

They asked for the Σ of the E.

I got 19.82 N/C but the stupid wiley site tells me that I am wrong.
Looks okay (I disagree only in the 4th digit) but you aren't finished yet!
LowlyPion gave you a huge hint on how to combine the FOUR vectors, each of which have this magnitude. Diagram. FOUR arrows beginning on the center point, pointing away from the positive charges and toward the negative charge.

Aha! Thank you very much! Problem solved

## 1. What is the formula for the electric field of a point charge?

The formula for the electric field of a point charge is E = kq/r^2, where E is the electric field, k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge.

## 2. How does the electric field of a point charge vary with distance?

The electric field of a point charge decreases with distance according to the inverse square law. This means that as the distance from the point charge increases, the electric field strength decreases proportionally.

## 3. Can the electric field of a point charge be negative?

Yes, the electric field of a point charge can be negative. This indicates that the direction of the electric field is opposite to the direction of the force that would be experienced by a positive test charge placed at that point.

## 4. How does the electric field of a point charge compare to the electric field of multiple point charges?

The electric field of multiple point charges can be calculated by summing the individual electric fields of each point charge at a given point. This means that the overall electric field may be stronger or weaker depending on the relative positions and charges of the individual point charges.

## 5. What is the relationship between the electric field and the potential of a point charge?

The electric field and potential of a point charge are closely related. The potential is a measure of the electric potential energy per unit charge at a given point, while the electric field is a measure of the force per unit charge at that point. The electric field can be calculated from the potential using the formula E = -∇V, where ∇ is the gradient operator.