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Two point charges q and –q are at positi...

Two point charges q and –q are at positions (0,0,d) and (0,0, –d) respectively . What is the electric field at (a,0,0 ) ?

A

`(2qd)/(4pi epsilon_(0) (d^(2)+a^(2))^(3//2)) hatk`

B

`(qd)/( 4pi epsilon_(0)(d^(2)+a^(2))^(3//2))hatk`

C

`(-2qd)/(4pi epsilon_(0)(d^(2)+a^(2))^(3//2)) hatk`

D

`(-qd)/( 4pi epsilon_(0) (d^(2) +a^(2))^(3//2)) hatk`

Text Solution

Verified by Experts

The correct Answer is:
C

At P there are two fields
(1) Due to `A =E_(A) =(kq)/(r^(2))`
(2) Due to `B=E_(B)=(kq)/(r^(2))`
`r=(a^(2)+d^(2))^(1//2)" at angle" 180-2theta`
`E_("net")=2E_(A)"cos"(1)/(2)(180-2theta) =2E_(A) cos (90-theta)`
`=2E_(A) sin theta =(2kq)/(r^(2)) (d)/((r ))`
`=(2kqd)/((a^(2)+d^(2))^(3//2) )` in -z direction.
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