Two identical magnetic dipoles of magnetic moments `2Am^2` are placed at a separation of `2m` with their axes perpendicular to each other in air. The resultant magnetic field at a mid point between the dipole is

Options

A. `4sqrt5xx10^-5T`
B. `2sqrt5xx10^-5T`
C. `4sqrt5xx10^-7T`
D. `2sqrt5xx10^-7T`

Answer

D

Explanation

The point P lies on the axial line of magnet `N_1S_1` at distance `r_1(=1m)` and on equatorial line of magnet `N_2S_2` at distance `r_2(=1m)`, figure.

`:. B_1=(mu_0)/(4pi)(2M_1)/(r_1^3)=10^-7xx(2xx2)/(1^3)=4xx10^-7T`
`B_2=(mu_0)/(4pi)(M_2)/(r_2^3)=10^-7xx(2)/(1^3)=2xx10^-7T`
Resultant magnetic field at P,
`B=sqrt(B_1^2+B_2^2)=sqrt((4xx10^-7)^2+(2xx10^-7)^2)`
`=2sqrt5xx10^-7T`