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Question

Two like charged infinitely long parallel wires with the same linear charge density of 3×108 C/cm are 2 cm apart. The work done against electrostatic force per unit length to be done in bringing them closer by 1 cm is x100 J/m. Find the value of x.

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Solution

The electric field at distance x from an infinite line of charge (linear charge density, λ) is
E=14πϵ02λx
So, force per unit length is,
F=qE

F=λ1λ2l2πϵor

F=Fl

usingλ1=λ2

F=8 N

Therefore, the work done is,

W=Fs
W=8×1cm
W=8100 J/C
x=8


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