What is the torque on a magnetic dipole μ in a uniform magnetic field B?

What is the torque on a magnetic dipole μ in a uniform magnetic field B?

• A. τ = μ × B
• B. τ = μ × E
• C. τ = μ B
• D. τ = B × μ

Answer: (A)

Torque on a magnetic dipole in a magnetic field comes from the tendency to rotate the dipole so that its moment μ aligns with the field B. This interaction is described by the cross product τ = μ × B. The magnitude is τ = μ B sinθ, with θ the angle between μ and B, and the direction is perpendicular to both μ and B, given by the right-hand rule. In a uniform field, the torque depends only on orientation, not position, and it vanishes when μ is aligned with B. Why the others don’t fit: a torque involving electric field, μ × E, would pertain to electric rather than magnetic interactions. Using μ B gives a magnitude without direction and ignores the dependence on the angle. Reversing the order to B × μ would give the opposite torque direction.

Torque on a magnetic dipole in a magnetic field comes from the tendency to rotate the dipole so that its moment μ aligns with the field B. This interaction is described by the cross product τ = μ × B. The magnitude is τ = μ B sinθ, with θ the angle between μ and B, and the direction is perpendicular to both μ and B, given by the right-hand rule. In a uniform field, the torque depends only on orientation, not position, and it vanishes when μ is aligned with B.

Why the others don’t fit: a torque involving electric field, μ × E, would pertain to electric rather than magnetic interactions. Using μ B gives a magnitude without direction and ignores the dependence on the angle. Reversing the order to B × μ would give the opposite torque direction.