2. Construct an ensemble to represent a closed system of 10 elementary magnets (that can point...

2. Construct an ensemble to represent a closed system of 10 elementary magnets (that can point only up and down, corresponding to magnetic moments ±m) in an external magnetic field B, each system with energy -8mB. Show all systems in the ensemble.

Expert Solution

Given the magnetic moment of the magnet is m and the magnetic field is B.

The energy due to a magnetic dipole in a field is , when the angle between the magnetic field and magnetic dipole moment is zero then . The direction of the magnetic moment is South to North.

We have to arrange 10 magnetic dipoles in such a way that the energy is -8mB.

This implies that we should have a net magnetic dipole moment 8m.

We have to arrange 9 magnets in up direction and 1 magnet in the downward direction so that the net magnetic moment is . Clearly, we have to align 9 magnets along the magnetic field and 1 magnetic against the magnetic field. Now the net magnetic moment of this ensemble is 8m which leads to the energy .

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