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Question

For a finite line charge, find the electric field in a direction parallel to the axis of the line charge at point P.

A
3.4 N/C
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B
4.4 N/C
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C
5.4 N/C
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D
6.4 N/C
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Solution

The correct option is D 6.4 N/C
Given:
r=3 m; λ=20 nC/m=20×109 C/m


From Pythagoras theorem, in ΔPAC and ΔPBC,

AP=5 m and BP=32 m

So, cosα=35 and cosβ=12

We know that, the electric field at non-axial point P parallel to line charge axis

E||=kQLr[cosβcosα]

E||=kλr[cosβcosα] (λ=Q/L)

E||=9×109×20×1093[1235]

E||=6.4 N/C

Hence, option (d) is correct.

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