Two charges +Q and -2Q are placed at ( -a,0) & (+a,0). The locus of points in the plane of the charges where the potential is zero will be :

straight line

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circle

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parabola

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ellipse

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Solution

The correct option is B circle
Let (x,y) be the point where potential due to the two charges is zero.
Therefore,
$k Q / \sqrt{(x + a)^{2} + y^{2}} - 2 k Q / \sqrt{(x - a)^{2} + y^{2}} = 0$
$(x - a)^{2} + y^{2} = 4 ((x + a)^{2} + y^{2}) \Rightarrow 3 x^{2} + 3 y^{2} + 10 x a + 3 a^{2} = 0$
The locus is thus a circle.

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Two charges +Q and -2Q are placed at ( -a,0) & (+a,0). The locus of points in the plane of the charges where the potential is zero will be :

The correct option is B circleLet (x,y) be the point where potential due to the two charges is zero.Therefore,kQ/√(x+a)2+y2−2kQ/√(x−a)2+y2=0(x−a)2+y2=4((x+a)2+y2)⇒3x2+3y2+10xa+3a2=0The locus is thus a circle.