(a) Two equal positive charges are to be placed on two corners of a square so th

Question

(a) Two equal positive charges are to be placed on two corners of a square so that the electric potential at the other two corners is equal. Check all the configurations of the charges that will have this result. (b) A positive charge and a negative charge of equal magnitude are to be placed on two corners of a square so that the electric potential at the other two corners is equal. Check all the configurations of the charges that will have this result.


(a)
Opposite corners
Adjacent corners

(b)
Opposite corners
Adjacent corners

Explanation / Answer

U = kQ/r

assume the side of the square is d

(a) when two charges are +q and +q.

if they are placed at opposite corners, then the U at each of the other two corners is

U = kq/d + kq/d

if they are placed at at adjacent corners, then the U at each of the other two corners is

U = kq/d + kq/2d

so both configurations satisfy the requirement.

(b) one charge is +q, other charge is -q

if they are placed at opposite corners, then the U at each of the other two corners is

U = kq/d -kq/d = 0

if they are placed at at adjacent corners, then the U at one of corner is

U1 = kq/d - kq/2d

the U at the other corner is

U2 = -kq/d + kq/2d

U1 and U2 are not equal.

Only opposite corners satisfy the requirement.

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