Question

The diagrams show five possible orientations of a magnetic dipole μ in a uniform magnetic field B. For which of these is the potential energy the greatest?

a.A
b.B
c.C
d.D
e.E

Answer 1

The potential energy is the greatest for orientation B.

Step-by-step explanation:

The potential energy (U) of a magnetic dipole in a uniform magnetic field is given by the formula U = -μ ⋅ B ⋅ cos(θ), where μ is the magnetic dipole moment, B is the magnetic field strength, and θ is the angle between the dipole moment and the magnetic field. In orientation B, the angle θ is 180 degrees, resulting in cos(180) = -1. Since potential energy is proportional to the negative of cos(θ), the potential energy is at its maximum in orientation B.

In orientations A, C, D, and E, the angles between the dipole moment and the magnetic field are less than 180 degrees, causing cos(θ) to be greater than -1. Consequently, the potential energy is lower in these orientations compared to orientation B.

In summary, orientation B corresponds to the dipole moment being aligned opposite to the magnetic field, resulting in the maximum potential energy. This explanation relies on the fundamental relationship between magnetic dipole orientation and potential energy as defined by the given formula.