A rectangular loop with a sliding connector of length \(l= 1.0\) m is situated in a uniform magnetic field \(B = 2T\) perpendicular to the plane of the loop. Resistance of connector is \(r=2~\Omega\). Two resistances of \(6~\Omega\) and \(3~\Omega\) are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity \(v = 2\) m/s is:

          
1. \(6~\text{N}\)
2. \(4~\text{N}\)
3. \(2~\text{N}\)
4. \(1~\text{N}\)

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. $\frac{mgR}{Bl}$

2. $\frac{mgR}{B^2{l}^2}$

3. $\frac{mgR}{B^3{l}^3}$

4. $\frac{mgR}{B^{2}l}$

A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. 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 figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current, in descending order, through the battery \((i)\) just after the switch is closed and \((ii)\) a long time later:

The network shown in the figure is a part of a complete circuit. If at a certain instant the current i is 5 A and is decreasing at the rate of 10³ A/s then V_B – V_A is

1. 5 V

2. 10 V

3. 15 V

4. 20 V

A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2θ. The earth’s magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is 

1. $2BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{1/2}$

2. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

3. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{3/2}$

4. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^2$

The variation of induced emf (E) with time (t) in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as:
    

1.		2.
3.		4.

A loop \(abcd\) is moved across the pole pieces of a magnet as shown in the figure with a constant speed \(v.\) When the edge \(ab\) of the loop enters the pole pieces at time \(t = 0~\text{sec}. \) Which one of the following graphs represents correctly the induced EMF in the coil?

1.		2.
3.		4.

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

1. 2

2. 4

3. 6

4. None of these

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

1. b > (d = e) < (a = c)

2.  b > (d = e) > (a = c)

3. b < d < e < c < a

4. b > (a = c) > (d = e)