(a) Magnetic field lines show the direction (at every point) along which a small magnetised needle aligns (at the point). Do the magnetic field lines also represent the lines of force on a moving charged particle at every point? (b) If magnetic monopoles existed, how would the Gauss’s law of magnetism be modified? (c) Does a bar magnet exert a torque on itself due to its own field? Does one element of a current-carrying wire exert a force on another element of the same wire? (d) Magnetic field arises due to charges in motion. Can a system have magnetic moments even though its net charge is zero?
No. The magnetic force is always normal to B (magnetic force = qv × B). It is misleading to call magnetic field lines as lines of force because the force on a moving charged particle is perpendicular to the field lines, not along them.
Gauss's law of magnetism states that the flux of B through any closed surface is always zero. If monopoles existed, the right hand side would be equal to the monopole (magnetic charge) qm enclosed by S, analogous to Gauss's law of electrostatics.
No, a bar magnet does not exert a torque on itself due to its own field. There is no force or torque on an element due to the field produced by that element itself. However, one element of a current-carrying wire does exert a force on another element of the same wire. For the special case of a straight wire, this force is zero.
Yes. The average charge in the system may be zero, yet the system can have magnetic moments. This is because magnetic moments arise from the motion of charges, and even if the net charge is zero, the distribution and motion of charges can create a net magnetic moment.
Explanation
This example tests conceptual understanding of magnetic field lines, Gauss's law, and magnetic moments. Part (a) clarifies that magnetic field lines are NOT lines of force for moving charges since magnetic force is perpendicular to B. Part (b) explains how Gauss's law would change if monopoles existed - the flux would equal μ₀qₘ instead of zero. Part (c) distinguishes between self-interaction (no effect) and interaction between different elements of the same wire (force exists). Part (d) confirms that magnetic moments can exist in neutral systems like atoms where charges are in motion but net charge is zero.