What is the dimensional formula of magnetic flux?

1. $[\mathrm{M}$ ${\mathrm{L}}^2$ ${\mathrm{T}}^{-2}$ ${\mathrm{A}}^{-1}]$

2. $[\mathrm{M}$ ${\mathrm{L}}^1$ ${\mathrm{T}}^{-1}$ ${\mathrm{A}}^{-2}]$

3. $[\mathrm{M}$ ${\mathrm{L}}^2$ ${\mathrm{T}}^{-3}$ ${\mathrm{A}}^{-1}]$

4. $[\mathrm{M}$ ${\mathrm{L}}^{-2}$ ${\mathrm{T}}^{-2}$ ${\mathrm{A}}^{-2}]$

When a conducting wire XY is moved towards the right, a current flows in the anti-clockwise direction. Direction of magnetic field at point O is:

Two coaxial coils are very close to each other and their mutual inductance is 5 mH. If a current 50 sin 500t is passed in one of the coils, then the peak value of induced e.m.f. in the secondary coil will be:

The adjoining figure shows two different arrangements in which two square wireframes are placed in a uniform magnetic field B decreasing with time.
         

The direction of the induced current I in the figure is:

A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

1. 35 Wb

2. 25 Wb

3. 30 Wb

4. 20 Wb

Current in a circuit falls from \(5.0\) A to \(0\) A in \(0.1\) s. If an average emf of \(200\) V is induced, the self-inductance of the circuit is:
1. \(4\) H
2. \(2\) H
3. \(1\) H
4. \(3\) H

A \(1~\text{m}\) long metallic rod is rotating with an angular frequency of \(400~\text{rad/s}\)$$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of \(0.5~\text{T}\) parallel to the axis exists everywhere. The emf induced between the center and the ring is:
1. \(200~\text{V}\)
2. \(100~\text{V}\)
3. \(50~\text{V}\)
4. \(150~\text{V}\)

A copper rod of mass m slides under gravity on two smooth parallel rails l distance apart and set at an angle $\theta$ to the horizontal as shown in fig. At the bottom, the rails are joined by a resistance R. There is a uniform magnetic field perpendicular to the plane of the rails. The terminal velocity of the rod is:

1. $\frac{mgR\cos \theta }{B^2{l}^2}$

2. $\frac{mgR\sin \theta }{B^2{l}^2}$

3. $\frac{mgR\tan \theta }{B^2{l}^2}$

4. $\frac{mgR\mathrm{co}t\theta }{B^2{l}^2}$ 

A 10 H inductor carries a current of 20 A. How much ice at 0°C could be melted by the energy stored in the magnetic field of the inductor?
Latent heat of ice is  2.26 × ${10}^3$ J/kg .

Some magnetic flux is changed from a coil of resistance 10 $\mathrm{\Omega }$. As a result, an induced current is developed in it, which varies with time as shown in the figure. The magnitude of change in flux through the coil in Wb is: