Two conducting circular loops of radii \(R_1\)$\mathrm{and}$\(R_2\) are placed in the same plane with their centres coinciding. If \(R_1>>R_2\) the mutual inductance \(M\) between them will be directly proportional to:

1.	\(\dfrac{R^2_1}{R_2}\)	2.	\(\dfrac{R^2_2}{R_1}\)
3.	\(\dfrac{R_1}{R_2}\)	4.	\(\dfrac{R_2}{R_1}\)

For a coil having \(L=2~\text{mH},\) the current flow through it is \(I=t^2e^{-t}.\) The time at which emf becomes zero is:
1. \(2\) s
2. \(1\) s
3. \(4\) s
4. \(3\) s

The magnetic flux through a circuit of resistance \(R\) changes by an amount \(\Delta \phi\) in a time \(\Delta t\). Then the total quantity of electric charge \(Q\) that passes any point in the circuit during the time \(\Delta t\) is represented by:
1. \(Q= \frac{\Delta \phi}{R}\)
2. \(Q= \frac{\Delta \phi}{\Delta t}\)
3. \(Q=R\cdot \frac{\Delta \phi}{\Delta t}\)
4. \(Q=\frac{1}{R}\cdot \frac{\Delta \phi}{\Delta t}\)

For an inductor coil, \(L = 0.04 ~\text{H}\), the work done by a source to establish a current of \(5~\text{A}\) in it is:
1.  \(0.5~\text{J}\)
2.  \(1.00~\text{J}\)
3.  \(100~\text{J}\)
4.  \(20~\text{J}\)

As a result of a change in the magnetic flux linked to the closed-loop shown in the figure, an emf, \(V\) volt is induced in the loop. The work done (joules) in taking a charge \(Q\) coulomb once along the loop is:

Two coils have a mutual inductance \(0.005\) H. The current changes in the first coil according to equation \(I=I_{0}\sin\omega t\) where \(I_{0}=2\) A and \(\omega=100\pi \) rad/s. The maximum value of emf in the second coil is:
1. \(4\pi\) V
2. \(3\pi\) V
3. \(2\pi\) V
4. \(\pi\) V

In a coil of resistance \(10\) \(\Omega\), the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:

1. \(2\)
2. \(6\)
3. \(4\)
4. \(8\)

A wheel with \(20\) metallic spokes, each \(1\) m long, is rotated with a speed of \(120\) rpm in a plane perpendicular to a magnetic field of \(0.4~\text{G}\). The induced emf between the axle and rim of the wheel will be:
\((1~\text{G}=10^{-4}~\text{T})\)
1. \(2.51 \times10^{-4}\) V
2. \(2.51 \times10^{-5}\) V
3. \(4.0 \times10^{-5}\) V
4. \(2.51\) V

The magnetic flux linked with a coil (in Wb) is given by the equation \(\phi=5 t^2+3 t+60\). The magnitude of induced emf in the coil at \(t=4\) s will be:
1. \(33\) V
2. \(43\) V
3. \(108\) V
4. \(10\) V