Q32 of 33 Page 14

Two charges q1 and q2 are placed at (0, 0, d) and (0, 0, –d) respectively. Find locus of points where the potential a zero.

Given


Positon of charge with magnitude q1 = (0, 0, d)


Positon of charge with magnitude q2 = (0, 0, -d)


The potential due to a point charge q at a distance r is given by




Let the potential of due to the two charges at any point having coordinates (x, y, z) be V, then



Where


and



Therefore, the equation for potential becomes:



If the potential is zero then, V=0




Squaring both sides, we have



Using the property




We have,




Comparing the equation with the general equation of a sphere, we have



The center of the sphere to be a=0, b=0 and c=, therefore the equipotential surface is a sphere with center [0, 0,


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