Two charges Q₁ = q and Q₂ = mq are placed at the points P₁(a,b) and P₂(ma,mb), respectively, in the XY plane, where a,b ≠ 0 and m ≠ 0,1. If V₁ is the potential at a point in the XY plane due to charge Q₁ and V₂ is the potential at that point due to charge Q₂. Correct statement(s) for the points at which |V₁| = |V₂| is/are:
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Question

Two charges Q₁ = q and Q₂ = mq are placed at the points P₁(a,b) and P₂(ma,mb), respectively, in the XY plane, where a,b ≠ 0 and m ≠ 0,1. If V₁ is the potential at a point in the XY plane due to charge Q₁ and V₂ is the potential at that point due to charge Q₂. Correct statement(s) for the points at which |V₁| = |V₂| is/are:

Select all that apply

G1 Physics · Accepted Answer

The condition |V₁| = |V₂| gives r₂ = |m|r₁, an Apollonius-circle condition. For m = −1 it reduces to equal distances from P₁ and P₂, whose perpendicular bisector is ax + by = 0. Substitution for m = 2 and m = −2 gives the circle parameters in B and C. The locus in D is not obtained. Therefore A, B and C are correct.