When a bar magnet is placed at 90° to a uniform magnetic field, it is acted upon by a couple which is maximum…

Q: When a bar magnet is placed at 90° to a uniform magnetic field, it is acted upon by a couple which is maximum. For the couple to be half of the maximum value, at what angle should the magnet be inclined to the magnetic field B ?

Sol: We know that,  τ = MB sin θ

If θ = 90° then  τmax = MB     ….(i)

τmax/2 = M B sin θ      …..(ii)

From equations (i) and (ii)

2 = 1/sin⁡θ

or sin θ = 1/2

or θ = 30°