A uniform but time-varying magnetic field \(B(t)\) exists in a circular region of radius \(a\) and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point \(P\) at a distance \(r\) from the centre of the circular region:

1. is zero
2. decreases as \(\frac{1}{r}\)
3. increases as \(r\)
4. decreases as \(\frac{1}{r^2}\)

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be:

A conducting rod of length \(2l\) is rotating with constant angular speed \(\omega\) about its perpendicular bisector. A uniform magnetic field \(\vec {B}\) exists parallel to the axis of rotation. The emf induced between the two ends of the rod is:

1. \(B\omega l^2\)
2. \(\frac{1}{2} B \omega l^{2}\)
3. \(\frac{1}{8} B \omega l^{2}\)
4. zero

A conductor ABOCD moves along its bisector with a velocity of \(1\) m/s through a perpendicular magnetic field of \(1~\text{wb/m}^2\), as shown in fig. If all the four sides are of \(1\) m length each, then the induced emf between points A and D is:
        
1. \(0\)

2. \(1.41\) volt

3. \(0.71\) volt

4. None of the above

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:

A conducting rod \(AC\) of length \(4l\) is rotated about point \(O\) in a uniform magnetic field \(\vec {B}\) 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. \(V_{A} - V_{C} = 4 B \omega l^{2}\)
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 \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)

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 \(4\times 10^{-3}\) Wb. The self-inductance of the solenoid is:
1. \(3\) H
2. \(2\) H
3. \(1\) H
4. \(4\) H