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Four point charges – q, + q, + q and – q...

Four point charges – q, + q, + q and – q are placed on y-axis at y = – 2d, y = – d, y = + d and y = + 2d, respectively. The magnitude of the electric field E at a point on the x-axis at x = D, with D >> d, will behave as:

A

`Eprop(1)/(D)`

B

`Eprop(1)/(D^(2))`

C

`Eprop(1)/(D^(4))`

D

`Eprop(1)/(D^(3))`

Text Solution

Verified by Experts

The correct Answer is:
C

`E=(K2qD)/((D^(2)+d^(2))^(3//2))-(K2qD)/((D^(2)+4d^(2))^(3//2))`
`=(2KqD)/(D^(3))[(1+(d^(2))/(D^(2)))^(-3//2)-(1+(4d^(2))/(D^(2)))^(-3//2)]`
`=(2KqD)/(D^(2))[1-(3d^(2))/(2D^(2))-(1-(6d^(2))/(D^(2)))]=(2Kq)/(D^(2))[(9d^(2))/(2D^(2))]`
`E=(9Kqd^(2))/(D^(4))impliesEprop(1)/(D^(4))`.
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