A point charge Q = -500 nC and two unknown point charges,q₁ and q₂,are placed as shown in the figure.The electric field at the origin O,due to charges Q,q₁ and q₂,is equal to zero.The charge q₁ is closest to A)130 nC. B)76 nC. C)150 nC. D)-76 nC. E)-130 nC.

Question

Quizplus · Accepted Answer

Since the electric field at the origin is zero, the sum of the electric field vectors due to each of the three charges must be zero. Let q1 be the charge at point S1, and q2 be the charge at point S2. Then we have:

E1 + E2 + E3 = 0

where

E1 = kQ/r^2, where r is the distance from Q to the origin
E2 = kq1/d^2, where d is the distance from S1 to the origin
E3 = kq2/D^2, where D is the distance from S2 to the origin

Since the magnitudes of E1 and E3 are fixed, the magnitude of E2 must be equal but opposite in direction in order to make the sum of the three electric field vectors zero. Therefore, q1 must be negative, and its magnitude must be greater than Q, since it is closer to the origin. The only choice that satisfies these conditions is A) 130 nC.

A Point Charge Q = -500 NC and Two Unknown