Question

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)`

Answer 1

Correct Answer - A
` 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)`