A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 750.  One of the fields has a magnitude of 15 mT.  The dipole attains stable equilibrium at an angle of 300 with this field.  The magnitude of the other field (in mT ) is close to :

  • Option 1)

    11

  • Option 2)

    36

  • Option 3)

    1

  • Option 4)

    1060

 

Answers (1)

As we learnt in 

Torque -

\overrightarrow{\tau}=\overrightarrow{M}\times \overrightarrow {B}(where\ M=NiA)

\tau=MB\sin \theta =NBiA\sin \theta

 

- wherein

M - magnetic moment 

 

 For stable equilibrium, net torque acting on dipole must be zero

\vec{}\tau_1+ \vec{}\tau_{2}= 0

or,
\vec{}\tau_1 = \vec{}\tau_{2}

MB_1\sin \theta_1= MB_2\sin\theta_2

B_2=B_1\frac{\sin \theta_1}{\sin \theta_2}= 15mT\frac{\sin 30^0}{\sin 45^0}

B_2=15 mT\times \frac{1}{2} \times \sqrt{2}= 10.6 \:mT= 11\: mT


Option 1)

11

This is correct option.

Option 2)

36

This is incorrect option.

Option 3)

1

This is incorrect option.

Option 4)

1060

This is incorrect option.

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