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Force between a point charge and conducting sphere

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Using method of images, find the force of attraction between an external point charge +Q and a conducting sphere of potential V_0. Take the charge to be a distance D from the center of the sphere. What value of V_0 makes the force equal 0?

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Solution Summary

This is a good application of method of images of electrostatics. The force between a point charge and conducting sphere is determined.

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SOLUTION
Y r2

P(x,y)
R D
R1

+Q X
q

d
Method of image

Let us consider a point charge +Q placed at a distance D from the centre of a conducting sphere (radius R) at a potential V as shown in the fig..
Let us first consider the case V = 0. Let us consider an imaginary charge q placed at some point on the line joining the location of charge +Q (on the X axis) and the centre of the sphere. Let this imaginary charge be at a distance d from the sphere centre. Net potential at any point (x.y) on the surface of the sphere will be obtained by addition of the individual potentials at the point due to charges +Q and imaginary charge q. If by appropriate selection of the magnitude and location of the imaginary charge q we can have the net potential due to the two charges at any point on the sphere equal to zero, then the presence or absence of the sphere would not make any difference and the sphere could as well be removed without making any difference to the ...

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