A thin semicircular conducting the ring \((PQR)\) of radius \(r\) is falling with its plane vertical in a horizontal magnetic field \(B,\) as shown in the figure. The potential difference developed across the ring when it moves with speed \(v\) is: 

     

1.	zero
2.	\(Bv\pi r^{2}/2\) and \(P\) is at a higher potential
3.	\(\pi rvB\) and \(R\) is at a higher potential
4.	\(2BvR\) and \(R\) is at higher potential

A coil of self-inductance \(L\) is connected in series with a bulb \(\mathrm{B}\) and an AC source. The brightness of the bulb decreases when:

A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:$$
1. \(0.5~\text{A}\)
2. \(0.1~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)

The current (\(I\)) in the inductance is varying with time (\(t\)) according to the plot shown in the figure. 

          
Which one of the following is the correct variation of voltage with time in the coil?

1.		2.
3.		4.

The current \(i\) in a coil varies with time as shown in the figure. The variation of induced emf with time would be:
     

1.		2.
3.		4.

A conducting circular loop is placed in a uniform magnetic field, \(B=0.025~\text{T}\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1~\text{mm s}^{-1}\).  The induced emf, when the radius is \(2~\text{cm}\), is:
1. \(2\pi ~\mu\text{V}\)
2. \(\pi ~\mu\text{V}\)
3. \(\frac{\pi}{2}~\mu\text{V}\)
4. \(2 ~\mu \text{V}\)

A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of 2 mm/s. The induced e.m.f. in the loop when the radius is 2 cm is:

1. \(3.2\pi ~\mu V\)

2. \(4.8\pi ~\mu V\)

3. \(0.8\pi ~\mu V\)

4. \(1.6\pi ~\mu V\)

A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, $\overrightarrow{\mathrm{v}}=\mathrm{v}\hat{\mathrm{i}}$. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops out of the field region, will not remain constant for: