A magnetic dipole is acted upon by two magnetic fields with inclined to each other at an angle of `75^(@)`. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of `30^(@)` with this field. The magnitude of the other field (in mT) is close to

Options

A. 1
B. 11
C. 36
D. 1060

Answer

B

Explanation

The magnetic dipole attains stable equilibrium under the influence of these two fields making an angle `theta_(1)=30^(@)` with
`B_(1)` and `theta_(2)=75^(@)-30^(@)=45^(@)` with `B_(2)`
for stable equilibrium net torque
acting on dipole must be zero.
i.e. `vec(tau_(1))+vec(tau_(2))=0` or `tau_(1)+tau_(2)` or `mB_(1)sin theta_(1)=mB_(2)sin theta_(2)`
`implies B_(2)=B_(1)(sin theta_(1))/(sin theta_(2))=15 mT xx(sin 30^(@))/(sin 45^(@))=15 mTxx1/2xxsqrt(2)=10.6mT=11mT`