Two point electric dipoles with dipole moment `P_(1)` and `P_(2)` are separated by a distance `r` with their dipole axes mutually perpendicular as shown. The force of interaction between the dipoles is (where `k=(1)/(4piepsilon_(0))`)

Options

A. `(2kP_(1)P_(2))/(r^(4))`
B. `(3kP_(1)P_(2))/(r^(3))`
C. `(4kP_(1)P_(2))/(r^(4))`
D. `(6kP_(1)P_(2))/(r^(4))`

Answer

B

Explanation

The electric field due to `vecP_(1)` at the position of `vecP_(2)` is
`E_(1)=(KP_(1))/(r^(3))`
`therefore` force of interaction between the dipoles is
`F=P_(2)|(dE_(1))/(dr)|`
`F=(3kP_(1)P_(2))/(r^(4))`