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The dipole moment of a system of charge ...

The dipole moment of a system of charge ` +q` distribyted uniformly on an arc of radius `R` subtending an angle ` pi //2` at its centre where another charge ` -q` is placed is :

A

`(2sqrt2qr)/(pi)`

B

`(sqrt2qr)/(pi)`

C

`(qr)/(pi)`

D

`(2qr)/(pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
Linear charge density
`lamda =(2q)/(pi R)`
Charge on element ` d_q= lamda Rd theta`
`P_x= int dp costheta= int_0 ^(pi//2) lamda R^2 cos theta d theta`
`P_x= lamda R^2 |sin theta|_0^(pi//2) =lamda R^2`
Similarly `P_y= int_0^(pi//2) lamda R^2 sin theta d theta =lamda R^2|- cos theta|_0^(pi//2) =lamda R^2`
`P=sqrt(P_X^2+ P_Y^2)= lamda R^2 sqrt2 =(2q)/(pi R). R^2 sqrt2`
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