Question

For a loop of current-carrying wire in a uniform magnetic field the potential energy is a minimum if the magnetic dipole moment of the loop is:

a) in the same direction as the field
b) in the direction opposite to that of the field
c) perpendicular to the field
d) at an angle of 45° to the field
e) none of the above

Answer 1

The potential energy of a current-carrying loop is at a minimum when its magnetic dipole moment is aligned in the same direction as the magnetic field.

Step-by-step explanation:

The potential energy of a current-carrying loop in a uniform magnetic field is at a minimum when the loop's magnetic dipole moment is aligned with the magnetic field direction. The potential energy (U) of a magnetic dipole in a magnetic field is given by U = -μ ⋅ B, where μ is the magnetic dipole moment and B is the external magnetic field. This equation shows that potential energy is lowest (most negative) when μ and B are in the same direction because the dot product of two vectors in the same direction is maximum. Therefore, for a loop of current-carrying wire in a uniform magnetic field, the potential energy is a minimum if the magnetic dipole moment of the loop is:

a) in the same direction as the field