Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
Reason (R): The magnetic field in that region is along the direction of velocity of the electron.
In the light of the above statements, choose the correct answer from the options given below:
- Assertion (A) is true because an electron moving in a straight line with constant velocity in the presence of a magnetic field must not experience any force in the direction of motion. This implies the velocity of the electron is perpendicular to the magnetic field, so there is no magnetic force component along the velocity.
- Reason (R) is also true since the magnetic field must be perpendicular to the velocity for the force to not affect the motion of the electron. However, the statement that the magnetic field is "along the direction of velocity" contradicts the nature of the magnetic force, which acts perpendicular to both the magnetic field and the velocity. Thus, Reason (R) does not correctly explain Assertion (A).
Final Answer: Both (A) and (R) are true, but (R) is not the correct explanation of (A).
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 _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]
\(XPQY\) is a vertical smooth long loop having a total resistance \(R\), where \(PX\) is parallel to \(QY\) and the separation between them is \(l\). A constant magnetic field \(B\) perpendicular to the plane of the loop exists in the entire space. A rod \(CD\) of length \(L\,(L>l)\) and mass \(m\) is made to slide down from rest under gravity as shown. The terminal speed acquired by the rod is _______ m/s. 
Two p-n junction diodes \(D_1\) and \(D_2\) are connected as shown in the figure. \(A\) and \(B\) are input signals and \(C\) is the output. The given circuit will function as 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.