Question

Two mutually perpendicular infinite wires carry positive charge densities λ1 and λ2. The electric lines of force makes angle α with second wire then λ1λ2 is

A
tan2α
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B
cot2α
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C
sin2α
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D
cos2α
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Solution

The correct option is B cot2αThe direction of net electric field due to both infinite charged wires will be along the electric lines of force. The directions of electric fields due to both wires at any point P at distance from the point of intersection of both wires is shown in the given figure. Here, E1= electric field due to infinite charged wire of charge density λ1; E2= electric field due to infinite charged wire of charge density λ2; So, from the figure, tanα=E2E1 ⇒tanα=2kλ2/r22kλ1/r1 [∵E=2kλr] ⇒tanα=λ2×r1λ1×r2 ⇒tanα=λ2λ1×rcosαrsinα=λ2λ1×cotα ⇒λ1λ2=cot2α Hence, option (b) is the correct answer.

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