Force on 1 point charge in a 4 point charge system

[Josh930]

Homework Statement

Four identical charges are placed at the corners of a square of side side L.
Find the magnitude total force exerted on one charge by the other three charges.
Express your answer in terms of the variables Q, L and appropriate constants.

where did the L root2 in the solution come from?

Homework Equations

F=k(q1q2/r^2)

The Attempt at a Solution

let the charge Q at bottom left corner be considered, it is ready to move under repulsion

f1 = F(top, bottom) = kQ^2/L^2 [south] = x
f2=F(right, bottom) = kQ^2/L^2 [west] = x
f3 = F(diagonal, bottom) = kQ^2/[L root2]^2 [south-west]
f3 = x/2
--------------------------------------…
resolve f3 along south & west

F(net south) = x + [x/2] cos 45 = x[1+ 1/2root2]
F(net south) = x[1+2root2] /2root2 = F
F(net west) = x[1+2root2] /2root2 =F

F(resultant) = sqrt[F^2 + F^2] = F root2
F(resultant) = [ x[1+2root2] /2root2 ][root2]
F(resultant) = x[1+2root2] /2
F(resultant) = kQ^2[1+2root2] /2L^2

 

[rl.bhat]

Use Pythagoras theorem to find the diagonal of the cube.