Self-inductance of a solenoid is 5 mH. If the current is decreasing through it at the rate 10⁺³ A/s, then emf induced in the solenoid is

1. -5V

2. 5V

3. 2.5V

4. -2.5V

Keeping number of turns constant self inductance L of a solenoid varies with its length l as

1. L$\propto$l

2. L$\propto \frac{1}{\mathrm{l}}$

3. L$\propto {\mathrm{l}}^2$

4. L$\propto \frac{1}{{\mathrm{l}}^2}$

A conducting rod AC of length 4l is rotated with angular velocity $\omega$ about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the plane of the paper. If AO = l and OC = 3l, then the potential difference between A and C, V_A - V_C is

1. $2{\mathrm{B\omega l}}^2$

2. ${\mathrm{B\omega l}}^2$

3. $3{\mathrm{B\omega l}}^2$

4. $4{\mathrm{B\omega l}}^2$

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the circle. The radius \(r\) of the circle changes with time \(t\) as shown in the figure. The graph of the magnitude of induced emf \(|\varepsilon|\) versus time \(t\) in the circle is represented by:

1.		2.
3.		4.

A cylindrical space of radius \(R\) is filled with a uniform magnetic induction \(B\) parallel to the axis of the cylinder. If \(B\) changes at a constant rate, the graph showing the variation of the induced electric field with distance \(r\) from the axis of the cylinder is:

1.		2.
3.		4.

A long conducting wire AH is moved over a conducting triangular wire CDE with a constant v in a uniform magnetic field $\overrightarrow{B}$ directed into the plane of the paper. Resistance per unit length of each wire is r. Then

1. A clockwise induced current will flow in the closed-loop.

2. No induced current will flow in the closed-loop.

3. Induced current in the closed-loop alternately changes its direction.

4. An anticlockwise induced, the current will flow in the closed-loop.

The figure below shows a square loop of side 0.5 m and resistance 10 $\Omega$. The magnetic field has a magnitude B = 1.0 T. The work done in pulling the loop out of the field slowly and uniformly in 2 seconds is

1. 3.125$\times {10}^{-3}J$

2. 6.25$\times {10}^{-4}J$

3. 1.25$\times {10}^{-2}J$

4. 5.0 $\times {10}^{-4}J$

The wires \(\mathrm{P}_1\mathrm{Q}_1\) and \(\mathrm{P}_2\mathrm{Q}_2\) are made to slide on the rails with the same speed \(10~\text{m/s}\). If \(\mathrm{P}_1\mathrm{Q}_1\) moves towards the left and \(\mathrm{P}_2\mathrm{Q}_2\) moves towards the right, then the electric current in the \(19~\Omega\) resistor is:

1. zero
2. \(10~\text{mA}\)
3. \(0.1~\text{mA}\)
4. \(1~\text{mA}\)

The triangular circuit ABC shown in the figure is in a very long solenoid of radius R such that the plane of the triangular circuit is normal to the length of the solenoid. If the magnetic field changes at the rate dB/dt, then the induced emf in the triangular circuit is

1. $R^3\frac{dB}{dt}$

2. $R^2\frac{dB}{dt}$

3. $R\frac{dB}{dt}$

4. $\sqrt{R}\frac{dB}{dt}$

If conducting triangle is pulled out with a uniform velocity from the uniform magnetic field, as shown in the figure, then which graph of induced current versus time is possible?
       

1.             2. 
3.             4.