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A magnetic dipole is placed in two magnetic fields whose directions differ by 60°. If one field has magnitude 1.2 × 10⁻² T and the dipole settles in stable equilibrium making an angle of 15° with that field, what is the magnitude of the second field?

1. 4.4 × 10⁻³ tesla
2. 5.2 × 10⁻³ tesla
3. 3.4 × 10⁻³ tesla
4. 7.8 × 10⁻³ tesla

Correct answer: 4.4 × 10⁻³ tesla

Solution

In stable equilibrium the torques balance: B1*sin(theta1) = B2*sin(theta2) with theta1 = 15 deg and theta2 = 60 - 15 = 45 deg. So B2 = 1.2e-2 * sin15/sin45 = 4.4e-3 T.

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