Physics - Magnetism Question with Solution | TestHub

Let one of the magnetic fields is B₁and other is B₂. Angle between B₁and B₂is 60^o.

Given,                B₁= 1.2 x 10^-2T

Dipole is in equilibrium at an angle 15^ofrom B₁or 60^o- 15^o= 45^ofrom B₂

Torque on dipole due to magnetic field B₁

${\tau }_1=\text{M}\times {\text{B}}_1\text{ sin}\mathrm{ 1}{5}^{\text{o}}$......(i)

                

where, M is the magnetic moment. Torque on dipole due to magnetic field B₂

${\tau }_2=\text{M}\times {\text{B}}_2\text{ sin}\mathrm{ 4}{5}^{\text{o}}$.....(ii)

As dipole is in the equilibrium, then

${\tau }_1={\tau }_2$

M X B₁sin 15^o= M x B₂sin 45^o[From Eqs. (i) and (ii)]

$\frac{1\text{.}2\times 10^{-2}\times \text{sin }15^{\text{o}}}{\text{sin }45^{\text{o}}}={\text{B}}_2$

${\text{B}}_2=\frac{1\text{.}2\times 10^{-2}\times 0\text{.}2588}{0\text{.}7071}=4\text{.}4\times 10^{-3}\text{ T}$

Thus, the magnitude of the other field is 4.4. x 10^-3T.