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Question

Two mutually perpendicular wire carry charge densities λ1 and λ2. The electric line of force makes angle α with second wire, then the ratio λ1λ2 is equal to (in terms of angle α)


A
cot2α
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B
tan2α
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C
sin2α
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D
cos2α
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Solution

The correct option is A cot2α

E1=λ12πε0x

E2=λ22πε0y

tanα=E2E1=λ2λ1(xy)(1)

From the figure,

From eq. (1) tanα=yx

λ1λ2=1tanα1(yx)=1tan2α

λ1λ2=cot2α

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