NCERT Solutions for Chapter: Magnetism and Matter, Exercise 3: SA

Verify the Gauss’s law for magnetic field of a point dipole of dipole moment $m$ at the origin for the surface which is a sphere of radius $R$.

Three identical bar magnets are rivetted together at centre in the same plane as shown in figure. This system is placed at rest in a slowly varying magnetic field. It is found that the system of magnets does not show any motion. The north-south poles of one magnet is shown in the figure. Determine the poles of the remaining two.

Suppose we want to verity the analogy between electrostatic and magneto static by an explicit experiment. Consider the motion of $\left(i\right)$ electric dipole $p$ in an electrostatic field $E$ and $\left(ii\right)$ magnetic dipole m in a magnetic field $B$. Write down a set of conditions on $E, B, p, m$ so that the two motions are verified to be identical. (Assume identical initial conditions.)

A bar magnet of magnetic moment m and moment of inertia $I$ (about centre, perpendicular to length) is cut into two equal pieces, perpendicular to length. Let $T$ be the period of oscillations of the original magnet about an axis through the mid point, perpendicular to length, in a magnetic field $B$. What would be the similar period $T\text{'}$ for each piece?

Use $\left(i\right)$ the Ampere’s law for $H$ and $\left(ii\right)$ continuity of lines of $B$, to conclude that inside a bar magnet, $\left(a\right)$ lines of $H$ run from the $N$ pole to $S$ pole, while $\left(b\right)$ lines of $B$ must run from the $S$ pole to $N$ pole.