Question
Asked Oct 25, 2019
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Consider the configuration shown in the figure: An in- finite plane conductor has a small hemispherical knob of radius a as indicated. A point charge q is placed directly to the right hand side of the hemispherical knob at a distanceb from its center. Assume that the boundary, i.e. the in- finite plane with the knob, is kept at zero potential. Find the potential V at a generic point P on the right hand side.

P(r)
a
b
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P(r) a b

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Expert Answer

Step 1

In the diagram given below, q’ is the image charge at distance x from the origin. Consider three points P, Q and R on the conductor as shown in the diagram.

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b

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Step 2

Find the potential at these three points P,Q and R and set that equal to zero(boundary condition must satisfy) and solve for distance x.

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(1) = k} b-а VP а — х q --2) V=k Va2b2 /x? +а V, = k Va2b --(3) уx? + а?

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Step 3

Note that equation (2) and (3) are same, So, plug 0 for Vp and VQ­ in both the equat...

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