Easy homework problem I know, how original.

[WardenOfTheMint]

Homework Statement

Four point charges are situated at the corners of a square with sides of length a.
Find the resultant force on the positive charge q. HINT: write an expression for the resultant force, use Ke for Ke, q for q, and a for a! That makes sense, because not much information is given.


HERE is a picture.

Homework Equations

F=Ke ( q1q2 / m^2 )

Ke is the constant 8.99e9 Nm^2/C^2.

Q1 and Q2 are any two charges of interest. That m^2 basically means the distance between two should be charges squared. So if distance between two charges is 5 cm, then it should be (0.05m)^2.

The Attempt at a Solution

F of top left negative charge on positive charge = Ke ( q^2 / a^2 ) ?

F of top right negative charge on positive charge =Ke ( q^2 / ( (2sqrt(a))^2 ) ?

F of bottom right negative charge on positive charge = Ke ( q^2 / a^2 ) ?

I don't know what I'm doing.
I figured that if you make a 45 45 90 triangle out of that square, the length between the positive charge and the top right charge should be 2sqrt(a). Other than that I do not know.

 

[learningphysics]

That distance should be $$\sqrt{a^2+a^2} = a\sqrt{2}$$ So the distance square is just 2a^2.

Draw a picture of the 3 force vectors... You need to add the 3 vectors... but the problem can be simplified when you see the symmetry...