NCERT Exemplar Q & A

Hint

(c) Toroid: A toroid can be considered as a ring shaped closed solenoid. Hence it is like an endless cylindrical solenoid.

The magnetic field is only confined inside the body of a toroid in the form of concentric magnetic lines of force. For any point inside the empty space surrounded by toroid and outside the toroid, the magnetic field \(\mathbf{B}\) is zero because the net current enclosed in these spaces is zero. Thus, the magnetic moment of toroid is zero.

Hint

(b) The electrostatic field lines, do not form a continuous closed path (this follows from the conservative nature of electric field) while the magnetic field lines form the closed paths.
According to Gauss’s law of electrostatic field \(\oint_s E . d s=\frac{q}{\varepsilon_0}\). so it does not contradict for electrostatic field as the electric field lines do not form continuous path. According to Gauss’s law of magnetic field \(\oint_s B . d s=0\). It contradicts for magnetic field, because there is magnetic field inside the solenoid and no field outside the solenoid marrying current, but the magnetic field lines from the closed paths. This implies that number of magnetic field lines entering the Gaussian surface is equal to the number of magnetic field lines leaving it.

Hint

(b) \(I(\text { magnetization }) \propto \frac{B(\text { magnetic field induction })}{t(\text { temperature in kelvin })} \Rightarrow \frac{I_2}{I_1}=\frac{B_2}{B_1} \times \frac{t_1}{t_2}\)
Let us suppose, here \(I_1=8 \mathrm{Am}^{-1}\)
\(
B_1=0.6 \mathrm{~T}, \quad t_1=4 \mathrm{~K}
\)
\(
\begin{aligned}
B_2 & =0.2 \mathrm{~T}, \quad t_2=16 \mathrm{~K} \\
I_2 & =?
\end{aligned}
\)
\(
\begin{aligned}
& \Rightarrow \quad \frac{0.2}{0.6} \times \frac{4}{16}=\frac{I_2}{8} \\
& \Rightarrow \quad I_2=8 \times \frac{1}{12}=\frac{2}{3} \mathrm{Am}^{-1}
\end{aligned}
\)

Hint

(a, d) The primary origin of magnetism lies in the fact that the electrons are revolving and spinning about the nucleus of an atom, and we know that an moving charge carries current along with it. We meant this current here as atomic current and which is responsible to produce an orbital magnetic moment. This atomic current gives rise to magnetism. The revolving and spinning about nucleus of an atom is called intrinsic spin of electron, which gives rise to spin magnetic moment. So, total magnetic moment is the sum of orbital magnetic moment and spin magnetic moment.

Hint

(a, d) The magnetic field intensity \(\mathrm{H}=\mathrm{nI}\), where \(\mathrm{n}=\) number of turns per metre of a solenoid and \(\mathrm{I}=\) current and \(\mathrm{B}=\mu_0 \mu_{\mathrm{r}} \mathrm{I}\).
Also, at normal temperature, a solenoid behaves as a ferromagnetic substance and at the temperature beyond the Curie temperature, it behaves as a paramagnetic substance.
\(\mathrm{n}=1000\) turns per metre, \(\mu_{\mathrm{r}}=1000\)
\(\mathrm{H}=\mathrm{nI}=1000 \times 1=1000 \mathrm{Amp}\). So \(\mathrm{H}\) is constant verifies the answer a
\(
\mathrm{B}=\mu_0 \mu_{\mathrm{r}} \mathrm{nl}=\left(\mu_0 \mathrm{nl}\right) \mu_{\mathrm{r}}=\mathrm{K} \mu_{\mathrm{r}}(\mathrm{~K}=\text { constant })
\)
\(
\text { So, } \mathrm{B} \propto \mu_r
\)
but there is a large decrease in the susceptibility of the core on heating it beyond critical temperature, hence magnetic field will decrease drastically. Now, for magnetisation in the core, when temperature of the iron core of a solenoid is raised beyond Curie temperature, then it behaves as a paramagnetic material, where
\(
\begin{aligned}
& \left(\chi_m\right)_{\text {Fero }} \approx 10^3 \\
\text { and } & \left(\chi_m\right)_{\text {Para }} \approx 10^{-5} \\
\Rightarrow & \frac{\left(\chi_m\right)_{\text {Fero }}}{\left(\chi_m\right)_{\text {Para }}}=\frac{10^3}{10^{-5}}=10^8
\end{aligned}
\)

Hint

(a, c, d) Electrostatic shielding is the phenomenon to block the effects of an electric field. The conducting shell can block the effects of an external field on its internal content or the effect of an internal field on the outside environment. For protecting a sensitive equipment from the external magnetic field it should be placed inside an iron cane (magnetic shielding). Magnetostatic shielding is done by using an enclosure made of a high permeability magnetic material to prevent a static magnetic field outside the enclosure from reaching objects inside it or to confine a magnetic field within the enclosure.