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Q.

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60⁰, and one of the fields has a magnitude of 1.2×10^-2T. If the dipole comes to stable equilibrium at an angle of 15⁰ with this field, N×10^-2T is the magnitude of the other field then N=____. (Take sin15⁰=0.26)

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answer is 0.44.

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Detailed Solution

$Here, θ = 60^{\circ}, b 1 = 1.2 \times 10^{- 2} tesla, θ_{1} = 15^{\circ}, θ_{2} = 60^{\circ} - 15^{0} = 45^{\circ} .$

IN EQUILIBRIUM, TORQUE DUE TO TWO FIELDS MUST BALANCE I.e. $τ_{1} = τ_{2}$

$M B_{1} \sin θ_{1} = M B_{2} \sin θ_{2}$

$\Rightarrow 1.2 \times 10^{- 2} \times \sin 15^{0} = B_{2} \sin (45)^{0}$

$\Rightarrow B_{2} = 4.4 \times 10^{- 3} T$

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A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 600, and one of the fields has a magnitude of 1.2×10-2T. If the dipole comes to stable equilibrium at an angle of 150 with this field, N×10-2T is the magnitude of the other field then N=____. (Take sin150=0.26)