A series combination of inductance \((L)\) and resistance \((R)\) is connected to a battery of emf \(E\). The final value of current depends on:

1.	\(L\) and \(R\)	2.	\(E\) and \(R\)
3.	\(E\) and \(L\)	4.	\(E\), \(L\), and \(R\)

The back emf induced in a coil, when current changes from \(1\) ampere to zero in one milli-second, is \(4\) volts. The self-inductance of the coil is:
1. \(1~\text{H}\)
2. \(4~\text{H}\)
3. \(10^{-3}~\text{H}\)
4. \(4\times10^{-3}~\text{H}\)

A uniform magnetic field of induction \(B\) is confined to a cylindrical region of radius \(R.\) The magnetic field is increasing at a constant rate of \(\frac{dB}{dt}\) (tesla/second). An electron of charge \(q,\) placed at the point \(P\) $\mathrm{}$on the periphery of the field experiences an acceleration of:

A conducting circular loop is placed in a uniform magnetic field of \(0.04\) T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of \(2\) mm/s. The induced emf in the loop when the radius is \(2\) cm is:
1. \(3.2\pi ~\mu \text{V}\)

2. \(4.8\pi ~\mu\text{V}\)

3. \(0.8\pi ~\mu \text{V}\)

4. \(1.6\pi ~\mu \text{V}\)

Choose the correct option for the above statements:

A coil is wound of a frame of rectangular cross-section. If the linear dimensions of the frame are doubled and the number of turns per unit length of the coil remains the same, then the self inductance increases by a factor of:

A circular disc of the radius \(0.2~\text m\) is placed in a uniform magnetic field of induction \(\dfrac{1}{\pi} \left(\dfrac{\text{Wb}}{\text{m}^{2}}\right)\) in such a way that its axis makes an angle of \(60^{\circ}\) with \(\vec {B}.\) The magnetic flux linked to the disc will be:
1. \(0.02~\text{Wb}\)
2. \(0.06~\text{Wb}\)
3. \(0.08~\text{Wb}\)
4. \(0.01~\text{Wb}\)

An electron moves on a straight-line path \(XY\) as shown. The \(abcd\) is a coil adjacent to the path of the electron. What will be the direction of the current, if any induced in the coil?