A magnetic dipole is under the influence of two magnetic fields the angle between the two field directions is $60^{0}$ and one of the fields has a magnitude of $1.2 X 10^{- 2} T$ . If the dipole comes to stable equilibrium at an angle of $15 °$ with this field, what is the magnitude of the other field?

Question

Infinity Learn · Accepted Answer

Given  $$B1=1.2$$×$$10$$−$$2TInclination$$ of dipole with  $$B1$$ is θ$$1=15$$°Therefore Inclination of dipole with   $$B2$$ is θ$$2=60$$°$$-15$$°$$=45$$°  As the dipole is in equilibrium the torque on the dipole due to the two fields are equal and opposite. If  M is the magnetic dipole moment of the dipole, then ∴$$MB1sin$$θ$$1=MB2sin$$θ$$2$$⇒$$B2=B1sin$$θ$$1sin$$θ$$2$$⇒$$B2=1.2$$×$$10-2$$×$$sin15$$°$$sin45o=1.2$$×$$10-2$$×$$0.25880.707$$⇒$$B2=4.39$$×$$10-3T$$

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A magnetic dipole is under the influence of two magnetic fields the angle between the two field directions is 600 and one of the fields has a magnitude of 1.2X10-2T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?

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