There is an infinite straight chain of alternating charges `q` and `-q` . The distance between teh neighbouring charges is equal to `a`. Find the interaction energy of each charge with all the others.
Instruction . Make use of the expansion of In `(1 + alpha)` in a power series in `alpha`.

Options

A. `- (2 q)/(4 pi epsilon_0 a)`
B. ` (2 q^2 log_e 2)/(4 pi epsilon_0 a)`
C. ` -(2 q^2 log_e 2)/(4 pi epsilon_0 a)`
D. none of these.

Answer

c

Explanation

`U = 2 kq^2 [-(1)/A + (1)/(2 a) - (1)/(3a) + (1)/(4 a) +...]`
=`-(2 q^2)/(4 pi epsilon_0 a)[1 - (1)/(2) + (1)/(3) - (1)/(4) + ...] = -(2q^2 log_e 2)/(4 pi epsilon_0 a)`
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