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Question

For the given charge distribution, the net electric field at the centre of the non-conducting ring is


A
180 N/C
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B
220 N/C
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C
320 N/C
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D
360 N/C
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Solution

The correct option is D 360 N/C
Given:
λ1=10 nC/m=10×109 C;R=1 m
λ2=10 nC/m=10×109 C.



Electric field due to upper half will be directed toward OB and also, electric field due to lower half will be directed toward OB.
Electric field due to arc of a circle,
E=2kλRsinα2

Electric field due to semicircle at the centre,
α=180
E=2kλR

Therefore, net electric field at centre

Enet=2kλ1R+2kλ2R [Along OB]

Enet=4kλR (λ1=λ2=λ)

Enet=4×9×109×10×1091

Enet=360 N/C

Hence, (d) is correct answer.

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