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Question

Two electric charges q and -2q are placed at a distance 3a apart. The locus of points in the plane of the charges where the field potential is zero is:


A
straight line
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B
circle
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C
ellipse
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D
hyperbola
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Solution

The correct option is D circle
Let at point (x, y) potential be zero.
then we have.
kqx2+y2+k(2q)(3ax)2+y2=0
1x2+y2=2(3ax)2+y2
(3ax)2+y2=4x2+4y2
9a2+x26ax+y2=4x2+4y2
3x2+3y2+6ax9a2=0
y2+(x+a)2=4a2
circle at center (-a, 0) with radius 2a.

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