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Two point charges q1 and q2 lie on a circle of unit radius. The net electric field at the centre of the circle due to both charges is vector E. If the position vector of the centre measured from q1 is vector r1, find the position vector of the centre measured from q2.

1. (E + k*q1*r1)/(k*q2)
2. -(E + k*q1*r1)/(k*q2)
3. (k*q1*r1 - E)/(k*q2)
4. (E - k*q1*r1)/(k*q2)

Correct answer: (E - k*q1*r1)/(k*q2)

Solution

With unit radius, the field at the centre from q1 is k*q1*r1 (r1 points from q1 to centre). Let r2 be the position of centre from q2; field from q2 is k*q2*r2. Sum equals E, so r2 = (E - k*q1*r1)/(k*q2).

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