A thin non-conducting ring of radius `R` has a linear charge density `lambda=lambda_(0) cos theta`, where `theta` is measured as shown. The total electric dipole moment of the charge distribution is

Options

A. `R^(2)lambda_(0)`
B. `2 pi R^(2)lambda_(0)`
C. `(pi R^(2)lambda_(0))/(2)`
D. `piR^(2)lambda_(0)`

Answer

d

Explanation

Dipole moment of the charge pair at `P` and `Q`

`dp=[(lambda_(0)cos theta)Rd theta](2R cos theta)`
Total dipole moment
`=2 lambda_(0)R^(2) underset(-pi//2)overset(pi//2)int cos^(2) theta d theta= pi R^(2)lambda_(0)`