Point Charges in a Square: Could the Force on Each Be Zero?
1. The problem statement, all variables and given/known data
A charge Q is fixed at each of two opposite corners of a square, while a charge q is fixed at the other two corners. (a) if the resultant electrical force on Q is zero, how are Q and q related? (b) could q be choosen to make the resultant electrical force on every charge zero? explain. F1 = force between Q's F2 = force between one Q and q's a = side of the square 2. Relevant equations F = (1/(4*pi*E))(q1*q2/r^2) 3. The attempt at a solution (a) F1 = (1/(4*pi*E))(Q^2/2a^2) F2 = (1/(4*pi*E))((Qq*sqrt(2))/(a^2)) I set them equal to each other and got: Q = 2q*sqrt(2) The answers weren't in the back of the book, so I'm not sure if that's correct or not The part I'm having trouble with is part (b). I don't think there can be a value for q that would make the forces on all the charges zero, but I don't know how to explain that. Thanks! 
Re: Point Charges in a Square: Could the Force on Each Be Zero?
whats the distance between the Q's?
and where did the sqr(2) come from in your F2 equation? 
Re: Point Charges in a Square: Could the Force on Each Be Zero?
the distance of the side of the square is a, so the diagonal is a*sqrt(2)

Re: Point Charges in a Square: Could the Force on Each Be Zero?
I misread it as (2a)^2.
still dont understand the F2 equation. you cant just set them equal to each other. they are vectors. 
Re: Point Charges in a Square: Could the Force on Each Be Zero?
i saw the equation: (1/(4*pi*E))((Qq)/(a^2)) as the force on one of the sides of the square between Q and q. and i know there's another force pointing perpendicular on the adjacent side of the square. the addition of those two vectors would give me the hypotenuse of a 454590 triangle. therefore, i saw that the magnitude of the hypotenuse is that force times sqrt(2).
would that be right? 
Re: Point Charges in a Square: Could the Force on Each Be Zero?
sounds good.

Re: Point Charges in a Square: Could the Force on Each Be Zero?
that's good.
do you know about part (b) ? 
Re: Point Charges in a Square: Could the Force on Each Be Zero?
you know what q must be for the force on Q to be zero. what must the charge on Q be to make the force on q be zero?

Re: Point Charges in a Square: Could the Force on Each Be Zero?
Since it's a square, the charge for q would be the same formula as it was for Q, just the Q and q are switched:
q = 2Qsqrt(2) 
Re: Point Charges in a Square: Could the Force on Each Be Zero?
yes. and so? what is your conclusion?

Re: Point Charges in a Square: Could the Force on Each Be Zero?
so would that mean that the value of q would be Q ?
i know q =/= Q because then the charges would all repel each other. if i plug one equation into the other, like: q = 2(2q*sqrt(2))sqrt(2), i just get that q=8q. which is why i think there can't be a value for q. though, i don't know the explanation. 
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