A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of:

1.	\({mgR \over Bl}\)	2.	\({mgR \over B^2l^2}\)
3.	\({mgR \over B^3l^3}\)	4.	\({mgR \over B^2l}\)

A conducting rod AC of length 4l is rotated about point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. If AO = l and OC = 3l, then:

1. $V_A-V_O=\frac{B\omega l^2}{2}$
2. $V_O-V_C=\frac{7}{2}B\omega l^2$
3. $V_A-V_C=4B\omega l^2$
4. $V_C-V_O=\frac{9}{2}B\omega l^2$

The graph gives the magnitude \(B(t)\) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first:

A square loop of side 5 cm enters a magnetic field with 1 cms^-1. If the front edge enters the magnetic field at t = 0, then which graph best depicts emf?

1.		2.
3.		4.

A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity $\mathrm{\omega }$. The maximum value of the emf induced in it is:

1. $\frac{\mathrm{NBA}}{\mathrm{\omega }}$                             

2. $\mathrm{NBA\omega }$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega }}^2}$                             

4. ${\mathrm{NBA\omega }}^2$

A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4 x 10^-3 Wb. The self-inductance of the solenoid is:

1. 3 H

2. 2 H

3. 1 H

4. 4 H

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is:

A coil has 500 turns and the flux through the coil is \(\phi=3t^{2} +4t+9\) milliweber. The magnitude of induced emf between the ends of the coil at t = 5 s is:

1. 34 millivolt

2. 17 volt

3. 17 millivolt

4. 34 volt

The current I in an inductance coil varies with time t according to the graph shown in the figure. Which one of the following plots shows the variation of voltage in the coil with time?

1.		2.
3.		4.

A bar magnet is released along the vertical axis of the conducting coil. The acceleration of the bar magnet is: