Two identical magnetic dipoles of magnetic moments `1*0Am^2` each are placed at a separation of `2m` with their axes perpendicular to each other. What is the resultant magnetic field at a point midway between the dipoles?

Explanation

In figure point P is midway between the two dipoles. For dipole `N_1S_1`, P lies on axial line and for dipole `N_2S_2`, P lies on equatorial line.
`:. B_1=(mu_0)/(4pi)(2M)/(r_1^3)=(10^-7xx2xx1)/((1)^3)`
`=2xx10^-7T`, along `S_1N_1`
and `B_2=(mu_0)/(4pi)(M/r_2^3)=10^-7xx1/1^3`
`=10^-7T`, along `N_2S_2`
As `B_1` and `B_2` are perpendicular to each other, the resultant magnetic field,
`B=sqrt(B_1^2+B_2^2)`
`=sqrt((2xx10^-7)^2+(10^-7)^2)=10^-7sqrt(2^2+1^2)`
`B=sqrt5xx10^-7T`, and
`tan theta=B_2/B_1=(10^-7)/(2xx10^-7)=1/2`
`theta=tan^-1(0*5)=26*6^@`