A magnetic dipole is under the influence of two magnetic fields B₁ and B₂. The angle between the fields direction is 60° and one of the fields has a magnitude of 1.2×10^–2T. If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field (sin15° = 0.2588)

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2.6×10^–2T

1.5×10^–3T

4.39×10^–3T

3.49×10^–3 T

answer is C.

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Detailed Solution

$τ_{1} = τ_{2} \Rightarrow {MB}_{1} Sin θ_{1} = {MB}_{2} Sin θ_{2} \Rightarrow M \times 1.2 \times 10^{- 2} \times Sin 15 ° = {MB}_{2} Sin 45 ° \Rightarrow B_{2} = \frac{1.2 \times 10^{- 2} \times 0.2588}{Sin 45 °} \Rightarrow B_{2} = 4.39 \times 10^{- 3} T$

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