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 a higher potential

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.

In which of the following devices, the eddy current effect is not used?
1. Electric heater
2. Induction furnace
3. Magnetic braking in train
4. Electromagnet

A \(800\) turn coil of effective area \(0.05~\text{m}^2\) is kept perpendicular to a magnetic field \(5\times 10^{-5}~\text{T}\). When the plane of the coil is rotated by \(90^{\circ}\)$$around any of its coplanar axis in \(0.1~\text{s}\), the emf induced in the coil will be:

A conducting square frame of side \(a\) and a long straight wire carrying current \(I\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v.\) The emf induced in the frame will be proportional to:
     
1. \( \dfrac{1}{x^2} \)
2. \( \dfrac{1}{(2 x-a)^2} \)
3. \( \dfrac{1}{(2 x+a)^2} \)
4. \(\dfrac{1}{(2 x-a)(2 x+a)}\)

An electron moves on a straight-line path \(XY\) as shown. The \({abcd}\) is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil?