Identical 846 C charges are fixed to adjacent corners of a s

Identical +8.46 C 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 potential at the remaining empty corner is 0 V?

Solution

Given,

Q = +8.46 uC

Let the unknown charge be Q.

We know that potential of a single point charge is given by:

V = k q/r

as per the given condition:

V1 + V2 + V3 = 0

kq/r + kq/sqrt(2)r + kQ/r = 0

8.46/1 + 8.46/1.41 + Q = 0 => Q = 8.46(1 + 1/1.414) = 14.44 uC

Hence, Q= -14.44 uC.