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:

Step-by-step solution

The potential at a point (x, y) due to charge Q₁ is V₁ = 1 4 ₀ q (x-a)^2 + (y-b)^2 . The potential at (x, y) due to charge Q₂ is V₂ = 1 4 ₀ mq (x-ma)^2 + (y-mb)^2 . Given |V₁| = |V₂| , we have: 1 (x-a)^2 + (y-b)^2 = m^2 (x-ma)^2 + (y-mb)^2 Cross-multiplying and expanding both sides: (x-ma)^2 + (y-mb)^2 = m^2[(x-a)^2 + (y-b)^2] x^2 + m^2a^2 - 2max + y^2 + m^2b^2 - 2mby = m^2(x^2 + a^2 - 2ax + y^2 + b^2 - 2by) x^2 + y^2 - 2m(ax+by) + m^2(a^2+b^2) = m^2(x^2+y^2) - 2m^2(ax+by) + m^2(a^2+b^2) Canceling m^2(a^2+b^2) from