The given two fixed rings of radius `R` lie in `XY` plane as shown in the figure. Linear charge density of the rings `A` and `B` varies as per the relation`lambda=lambda_(0)sintheta` and `lambda=lambda_(0)costheta` respectively where theta is measured from `+x` axis. Distance between the centre of the two rings is `r gt gt R`

Options

A. Force of interaction between the two ring is` (3)/(4)xx(lambda_(0)^(2)pi)/(in_(0))((R )/(r ))^(4)`
B. Force of interection between the two rings is` (3)/(2)xx(lambda_(0)^(2)pi)/(in_(0))((R )/(r ))^(4)`
C. Potential energy of interaction between the two ring of `(pilambda_(0)^(2)R^(4))/(4epsilon_(0)r^(3))`
D. Potential energy of interaction between the two ring is zero.

Answer

A, D

Explanation

`intdp=intdq(2Rsintheta)`

`p=underset(0)overset(pi)(int)(lambda_(0)sinthetaxxRd theta)(2Rsintheta)`
`p=pilambda_(0)R^(2)" ".....(i)`
`F=(3kp^(2))/(r^(4))`
`=(3lambda_(0)^(2)piR^(4))/(4epsilon_(0)r^(4))" ".....(ii)`

`U=-P_(2)E_(1)cos90^(@)=0" "......(iii)`