Figure shows two identical magnetic dipoles `a and b` of magnetic moments `M` each, placed at a separation `d`, with their axes perpendicular to each other. Find the magnetic field at the point `P` midway between the dipoles.

Explanation

The point P is in end on position for the dipole `(a)` and in broadside on position for the dipole `(b)`.The magnetic field at `P` due to `a` is `B_(a)=(mu_(0))/(4pi)(2M)/(d//2)^(3)` along the axis of `a`, and that due to `b` is `B_(b)=(mu_(0))/(4pi)(2M)/(d//2)^(3)` parallel to the axis of `b` as shown in figure.The resultant field at `P` is therefore.
The direction of this field makes an angle `alpha` with `B_(a)` such that `tan alpha=B_(b)//B_(a)=1//2`.