# (a) Magnetic field lines can be entirely confined within the core of a     toroid, but not within a straight solenoid. Why? (b) Does a bar magnet exert a torque on itself due to its own field?      Justify your answer. (c) When an electron revolves around a nucleus, obtain the expression for the magnetic moment associated with it.

(a) If the magnetic field lines were extremely confined between the two ends of a straight solenoid then the flux through the cross-section at each end would be
non zero, but the flux of field B through any closed the surface must always be Zero. Hence, the lines can be easily or entirely confined within the core of a toroid
not within the straight solenoid.
(b) No, because there is no force on torque on an element
due to the field produced by that element itself.

(c)The magnetic moment of an electron when revolving around a nucleus is given as:-

we have $I= \frac{e}{T} \left ( \because T= \frac{2\pi r}{V} \right )$
So,         $I= \frac{e}{2\pi \frac{r}{V}}$
$I= \frac{ev}{2\pi r}$
Hence, magnetic moment $\left ( \mu \right )= I\pi r^{2}$,on putting the value of I,
we have,
$\mu = \frac{ev}{2\not{\pi }\not{r}}\times \not{\pi }r^{\not{2}}= \frac{evr}{2}$

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