The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:
\( \frac{\mu_0 I}{2 \pi a} \)
\( \frac{\mu_0 I}{\pi a} \)
\( \frac{\mu_0 I}{4 \pi a} \)
- Magnetic field contributions due to segments \( BC \) and \( ET \) are outward at point \( O \).
Total magnetic field:
\[ B = \frac{\mu_0 I}{4 \pi r} + \frac{\mu_0 I}{4 \pi r} = \frac{\mu_0 I}{\pi a}. \]

A substance 'X' (1.5 g) dissolved in 150 g of a solvent 'Y' (molar mass = 300 g mol$^{-1}$) led to an elevation of the boiling point by 0.5 K. The relative lowering in the vapour pressure of the solvent 'Y' is $____________ \(\times 10^{-2}\). (nearest integer)
[Given : $K_{b}$ of the solvent = 5.0 K kg mol$^{-1}$]
Assume the solution to be dilute and no association or dissociation of X takes place in solution.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]