Identical +4.78 µC charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total electric potential at the remaining empty corner is 0 V?
a = length of the side of square
r = length of the diagonal = sqrt(2) a
VA = electric potential at D due to charge at A = k Q/a
VB = electric potential at D due to charge at B = k Q/r
VC = electric potential at D due to charge at C = k q/a
Given that:
VA + VB + VC = 0
k Q/a + k Q/r + k q/a = 0
k Q/a + k Q/(sqrt(2) a) + k q/a = 0
Q + Q/(sqrt(2)) + q = 0
4.78 + 4.78/(sqrt(2)) + q = 0
q = - 8.16 C
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