A cube has point charges at all corners. No two charges have the same value; all are unique. Is it possible for the electric (not the electric field!) at the center of the cube to be zero? (Assume the point charge definition of potential in which V = 0 at infinity.)
Because potentials are scalars they can be added. The potential at the centre of the cube can be zero because positive potentials from the positive charges can be balanced by negative potentials from the negative charges.
Call the 8 different charges q1, q2, ... q8. Suppose the distance from any corner to the centre is d.
Potential from a point charge, V = kq/r
With zero potential at the centre of the cube:
kq1/d + kq2/d + ...... + kq8/d = 0
Cancelling out k/d gives
q1 + q2 + ... + q8 = 0
This means the total amount of positive charge must equal the total amount of negative charge
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