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Regarding the three orientations of a magnetic dipole moment in a constant magnetic field, which statements apply to the magnetic dipole-field system?

(A) The potential energy is at its maxiμm in configuration C.
(B) Configuration A experiences a stable equilibrium.
(C) Configuration B represents a state of unstable equilibrium.
(D) Configuration C is in a state of miniμm potential energy.

User Ken
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1 Answer

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Final answer:

In a magnetic field, a dipole has the lowest potential energy in configuration A (stable equilibrium) and the highest in configuration C. Configuration B represents an unstable equilibrium with the dipole perpendicular to the field. For maximum torque, the dipole moment needs to be perpendicular to the field.

Step-by-step explanation:

In a constant magnetic field, the orientations of a magnetic dipole moment can have different energies and stability. The potential energy of a magnetic dipole in a magnetic field is given by U = −μ · B. Based on this equation, when the magnetic dipole moment is aligned with the magnetic field (configuration A), it has the lowest potential energy, and when it is anti-aligned (pointing in the opposite direction, configuration C), it has the highest potential energy. Therefore:

  • (A) The potential energy is at its maximum in configuration C.
  • (B) Configuration A experiences a stable equilibrium because any small perturbations will result in forces that tend to return the dipole to alignment with the magnetic field.
  • (C) Configuration B, where the magnetic dipole moment is perpendicular to the magnetic field, represents a state of unstable equilibrium since a small perturbation could lead it to align with or anti-align with the field, thus moving into a more stable state.
  • (D) Configuration C is indeed in a state of maximum potential energy, not minimum.

Additionally, for a magnetic dipole in a magnetic field, the torque is maximum when the dipole is perpendicular to the field. This would correspond to an intermediate situation between configurations A and C, somewhat like configuration B but not precisely the same, depending on the specific setup.

User Justiceorjustus
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