(a) Magnetic field lines show the directions (at every point) which a small magnetised needle takes up (at that point). Do the magnetic field lines also represent the lines of force of a moving charged particle at every point?
(b) Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?
(c) If magnetic monopoles existed, how would Gauss's law of magnetism be modified?
(d) 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?
(e) Magnetic field arises due to charges in motion. Can a system have magnetic moment even though its net charge is zero?
(f) Magnetic force is always normal to the velocity of a charge and therefore does no work. An iron nail held near a magnet, when released, increases its kinetic energy as it moves to cling to the magnet. What agency is responsible for this increase in kinetic energy if not the magnetic field?

Explanation

(a) No. the mangetic force is always normal to B (remember magnetic force =(nxxB). It is misleading to call mangetic field lines as lines of force.
(b) If field lines were entirely confined between two ends of a straight solenoid, the flux through the cross-section at each end would be non-zero. But the flux of field B through any closed surface must always be zero. For a toroid, this difficulty is absent because it has no ‘ends’. (c) Gauss’s law of magnetism states that the flux of B through any
closed surface is always zero `int_(s)B,DeltaS=0`
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, `int_(s)B,DeltaS=mu_(0)q_(m)` where `q_(m)` is the (monopole) magnetic charge enclosed by S.]
(d) No. There is no force or torque on an element due to the field produced by that element itself. But there is a force (or torque) on an element of the same wire. (For the special case of a straight wire, this force is zero.) (e) Yes. The average of the charge in the system may be zero. Yet, the mean of the magnetic moments due to various current loops may not be zero. We will come across such examples in connection with paramagnetic material where atoms have net dipole moment through their net charge is zero.