Electric field of a point charge

[Snowman2526]

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.

Homework Equations

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.

 

[LowlyPion]

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.

 

[Delphi51]

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!

 

[Snowman2526]

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?

 

[LowlyPion]

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.

 

[Delphi51]

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.

 

[Snowman2526]

Aha! Thank you very much! Problem solved