Physics- Total Force, Coulomb's Law

Question

This is the question:

A square with sides of length L has a point charge at each of its four corners. Two corners that are diagonally opposite have charges equal to +2.15 μC ; the other two corners have charges equal to Q.

Find the magnitude and sign of the charges Q such that each of the +2.15-μC charges experiences zero total force from the other three charges.

Answer 1

since each 2.15 charge is the same, and symmetry exists, you just need to solve for one of the 2.15 chages.

since the 2.15 charges are like, they repel, so Q must be negative.

calculate the repelling force between the 2.15 charges, separation = Lsqrt(2) and (cos45,sin45) for the components. Then each q pulls in the X and Y direction only so set that attraction force equal to one of the components from the other 2.15 charge. easy.

Answer 2

since each 2.15 charge is the same, and symmetry exists, you just need to solve for one of the 2.15 chages.

since the 2.15 charges are like, they repel, so Q must be negative.

calculate the repelling force between the 2.15 charges, separation = Lsqrt(2) and (cos45,sin45) for the components. Then each q pulls in the X and Y direction only so set that attraction force equal to one of the components from the other 2.15 charge. easy.