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प्रश्न
Two point charges of magnitude +q and –q are placed at (–d/2, 0, 0) and (d/2, 0, 0), respectively. Find the equation of the equipotential surface where the potential is zero.
उत्तर
Let the plane be at a distance x from the origin. The potential at the point P is
`1/(4piε_0) q/([(x + d/2)^2 + h^2]^(1/2)) - 1/(4piε_0) q/([(x - d/2)^2 + h^2]^(1/2))`
If this is to be zero.
`1/([(x + d/2)^2 + h^2]^(1/2)) = 1/([(x - d/2)^2 + h^2]^(1/2))`
Or, (x - d/2)2 + h2 = (x + d/2)2 + h2
⇒ x2 – dx + d2 /4 = x2 + dx + d2 /4
Or, 2dx = 0
⇒ x = 0
The equation is that of a plane x = 0.
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