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Question

An infinite number of charges, each equal to q, are placed along the x-axis at x =1, x=2, x=8, ... and so on. The potential at the point x =0 due to this set of charges is

A
qπϵ0
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B
q2πϵ0
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C
q3πϵ0
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D
q4πϵ0
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Solution

The correct option is B q2πϵ0
The potential at x = 0 due to a set of the infinite number of charges placed on the x-axis as shown in Fig. 20.40, is

Electric potential is given as 14πε0qr

In this case the electric potential will be given as

V=14πε0q[1+12+14.....]

This can be written as

V=14πε0q[1112] ( sum of infinite GP)

After solving this equation we get

V=q2πε0

Hence, the potential at the origin is q2πε0



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