Two identical dipoles each of magnetic moment 1.0 A-`m^(2)` are placed at a separation of 2 m with their axes perpendicular to each other. What is the magnetic field at a point midway between the dipoles?

Explanation

The point P will be in end-on position with respect to one dipole and in broad-side on position with respect to the other.

So, `B_(1)=(mu_(0))/(4pi) (2M_(1))/(r_(1)^(3))=10^(-7) xx (2xx1)/((1)^(3)) = 2 xx 10^(-7)T`
and , `(mu_(0))/(4pi) (M)/(r_(2)^(3)) = 10^(-7) (1)/(13) =10^(-7)T`
However, as `B_(1) and B_(2)` are perpendicular to each other, `B=sqrt(B_(1)^(2)+B_(2)^(2)) = 10^(-7) xx sqrt(2^(2) +1^(2)) =sqrt( 5) xx 10^(-7)T`
And `tan phi = (B_(2))/(B_(1)) =(1)/(2) , i.e., phi = tan^(-1) (0.5) = 26.6^(@)`