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4
MCQ (Single Correct Answer)

Consider the two idealised systems (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length $L \gg R$, radius of cross-section. In (i) $\mathbf{E}$ is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below

A
case (i) contradicts Gauss' law for electrostatic fields
B
case (ii) contradicts Gauss' law for magnetic fields
C
case (i) agrees with $\oint \mathrm{E} . \mathrm{dl}=0$.
D
case (ii) contradicts $\oint \mathrm{H} \cdot \mathrm{dl}=I_{\mathrm{en}}$
5
MCQ (Single Correct Answer)

A paramagnetic sample shows a net magnetisation of $8 \mathrm{Am}^{-1}$ when placed in an external magnetic field of 0.6 T at a temperature of 4 K . When the same sample is placed in an external magnetic field of 0.2 T at a temperature of 16 K , the magnetisation will be

A
$\frac{32}{3} \mathrm{Am}^{-1}$
B
$\frac{2}{3} \mathrm{Am}^{-1}$
C
$6 \mathrm{Am}^{-1}$
D
$2.4 \mathrm{Am}^{-1}$
6
MCQ (Multiple Correct Answer)

$S$ is the surface of a lump of magnetic material.

A
Lines of $\mathbf{B}$ are necessarily continuous across $S$
B
Some lines of $\mathbf{B}$ must be discontinuous across $S$
C
Lines of $\mathbf{H}$ are necessarily continuous across $S$
D
Lines of $\mathbf{H}$ cannot all be continuous across $S$
7
MCQ (Multiple Correct Answer)

The primary origin (s) of magnetism lies in

A
atomic currents
B
Pauli exclusion principle
C
polar nature of molecules
D
intrinsic spin of electron
8
MCQ (Multiple Correct Answer)

A long solenoid has 1000 turns per metre and carries a current of 1 A . It has a soft iron core of $\alpha_r=1000$. The core is heated beyond the Curie temperature, $T_c$.

A
The $\mathbf{H}$ field in the solenoid is (nearly) unchanged but the $\mathbf{B}$ field decreases drastically
B
The $\mathbf{H}$ and $\mathbf{B}$ fields in the solenoid are nearly unchanged
C
The magnetisation in the core reverses direction
D
The magnetisation in the core diminishes by a factor of about $10^8$