(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) 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 the Gauss's law of magnetism be modified?
(d) Does a bar magnet exert a torque on itsell due to its own field? Does one element of a current-carrying wire exert a force on another element of the same wtre?
(e) Magnetic field arises due to charges in motion. Can a system have magnetic moments even though its net charge is zero?

Explanation

(a) No. The magnetic force is always normal to B (remember magnette force `=qv xx B).` It is misleading to call magiette fteld ithes 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. triangleS=0`
If monopoles existed, the right hand side would be equal to the monopole (magnetic charge) `q_(m)` enclosed by S. (Analogous to Gauss.s law of electrostaties, `int_(S) B. triangleS=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 zer. 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 thorugh their net charge is zero.