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 :

Options

A. `(2sqrt(2)qR)/(pi)`
B. `(sqrt(2)qR)/(pi)`
C. `(qR)/(pi)`
D. `(2qR)/(pi)`

Answer

A

Explanation

`dP=Rdq=Rlambdadx=RlambdaRd thetaP_(y)=intdP sintheta`
`=lambdaR^(2)int_(0)^(pi//2)sinthetad theta=lambdaR^(2) =(2qR^(2))/(piR)=(2piR)/(pi)`
`P_(x)=(2qR)/(pi)vec(P)=P_(x)hat(i)+P_(y)hat(j)`