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. \(\dfrac{1}{(2 x-a)(2 x+a)}\)

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 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 emf in the loop when the radius is \(2\) cm is:
1. \(3.2\pi ~\mu \text{V}\)

2. \(4.8\pi ~\mu\text{V}\)

3. \(0.8\pi ~\mu \text{V}\)

4. \(1.6\pi ~\mu \text{V}\)

The primary and secondary coils of a transformer have \(50\) and \(1500\) turns respectively. If the magnetic flux \(\phi\) linked with the primary coil is given by; \(\phi=\phi_0+4t,\) where \(\phi\) is in Weber, \(t\) is time in seconds, and \(\phi_0\)  is a constant, the output voltage across the secondary coil is:
1. \(90~\mathrm{V}\)
2. \(120~\mathrm{V}\)
3. \(220~\mathrm{V}\)
4. \(30~\mathrm{V}\)

Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:

1. 10 mH

2. 6 mH

3. 4 mH

4. 16 mH

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