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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

`(2 sqrt 2 qR)/(pi)`

B

` (sqrtqR)/(pi)`

C

` (qR)/(pi)`

D

`( 2 qR)/(pi)`

Text Solution

Verified by Experts

The correct Answer is:
A
` (##NG_PHY_C01_E01_045_S01.png" width="80%">
` dP = dq. R = (2q)/(piR) Rd theta . R = (2q) /(pi) d theta`
` P_x = int _0 ^(90^@) dP cos theta = (2q)/(pi) int_0^(90^@) dP cos theta`
` P_x = (2 qR)/(pi) [sin theta]_0^(90^@) = (2qR)/(pi)`
` P_y int_0^(90^@) dP sin theta = (2 qR)/(pi)`
` P= (sqrt 2 qR)/(pi)`
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