Two short magnets of equal dipole moments `M` are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance `d` from the centre on the bisector of the right angle is

Options

A. `mu_(0)/(4pi)M/d^(3)`
B. `mu_(0)/(4pi)(Msqrt(2))/d^(3)`
C. `mu_(0)/(4pi)(2sqrt(2)M)/d^(3)`
D. `mu_(0)/(4pi)(2M)/d^(3)`

Answer

C

Explanation

Resultant magnetic moment of the two magnets is
`M_("net")=sqrt(M^(2)+M^(2))=sqrt(2)M`

Imagine a short magnet lying along `OP` with magnetic moment equal to `Msqrt(2)`. Thus point `P` lies on the axial line of the magnet.
:. Magnitude of magnetic field at `P` is given by
`B=mu_(0)/(4pi).(2sqrt(2)M)/d^(3)`