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Question

The linear charge densities on two straight parallel long linear charges are λ1 and λ2. Obtain the formula for force acting per unit length between them.

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Solution

Electric field intensity at distance from a wire of linear charge density λ1
E1=14πε02λ1d=12πε0λ1d
As second conductor is also in this field. Therefore force acting on its unit length (Charge q=λ2)
F=E1λ2=12πε0λ1d×λ2
or F=λ1λ22πε0d

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