Question

The magnetic moment (5 J/T) of a bar magnet points along a uniform magnetic field 0.4 T.

Answer 1

Magnetic Moment and Potential Energy

Given:

• Magnetic moment, \( M = 5 \, \text{J/T} \)
• Magnetic field, \( B = 0.4 \, \text{T} \)

The potential energy \( U \) of a magnetic dipole in a uniform magnetic field is calculated using:

\[ U = -MB \cos \theta \]

(i) Potential Energy of the Bar Magnet:

With the magnetic moment initially aligned with the magnetic field, \( \theta = 0^\circ \), the potential energy is:

\[ U = -MB \cos(0^\circ) = -MB \]

Substituting the given values:

\[ U = -5 \times 0.4 = -2 \, \text{J} \]

The potential energy of the bar magnet is -2 J.

(ii) Work Done in Turning the Magnet by 180°:

When the magnet is rotated by 180°, the angle between the magnetic moment and the magnetic field becomes \( \theta = 180^\circ \). The new potential energy \( U' \) is:

\[ U' = -MB \cos(180^\circ) = +MB \]

Substituting the values:

\[ U' = +5 \times 0.4 = +2 \, \text{J} \]

The work done \( W \) is the difference in potential energy:

\[ W = U' - U = 2 - (-2) = 4 \, \text{J} \]

The work done in turning the magnet by 180° is 4 J.