A point charge +q is placed at the origin and a second charge +9q is placed at (d,0,0). The point between them where the electric field vanishes is:
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Question

A point charge +q is placed at the origin and a second charge +9q is placed at (d,0,0). The point between them where the electric field vanishes is:

G1 Physics · Accepted Answer

Let the zero-field point be at x from the charge +q, so its distance from +9q is d-x. Between two like charges the electric fields are opposite, so for cancellation: kq/x² = k(9q)/(d-x)². Cancel kq: 1/x² = 9/(d-x)². Taking the positive square root: 1/x = 3/(d-x) ⇒ d-x = 3x ⇒ d = 4x ⇒ x = d/4. Therefore the point is (d/4, 0, 0). Correct option: D.