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Question

For a finite line charge, the net electric field at the non-axial point P is directed toward the line PQ where PQ makes an angle θ with the axis of line charge. Find the value of θ.

A
tan1(10)
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B
tan1(2)
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C
tan1(14)
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D
tan1(26)
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Solution

The correct option is C tan1(14)

From Pythagoras theorem, in ΔAPC and ΔBPC,

AP=5 m and BP=32 m

So, sinα=45, cosα=35, sinβ=12 and cosβ=12

We know that, the electric field at the non-axial point P,

E=kQLr [sinα+sinβ] ......(1)

E||=kQLr [cosβcosα] .......(2)

Now, tanθ=EE||

So, from eqs. (1) and (2)

tanθ=sinα+sinβcosβcosα

tanθ=45+121235

tanθ=14

θ=tan1(14)

Hence, (c) is the correct option.

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