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 centre and the ring is:
1. \(200~\text{V}\)
2. \(100~\text{V}\)
3. \(50~\text{V}\)
4. \(150~\text{V}\)
1. | \(2.5 \times 10^{-3} ~\text V\) | 2. | \(1.5 \times 10^{-4} ~\text V\) |
3. | \(2.5 \times 10^{-4}~\text V\) | 4. | \(1.5 \times 10^{-3} ~\text V\) |
Current in a circuit falls from \(5.0\) A to \(0\) A in \(0.1~\text{s}\). 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 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 |
What is the dimensional formula of magnetic flux?
1. \(\left[ M L^2 T^{-2}A^{-1}\right]\)
2. \(\left[ M L^1 T^{-1}A^{-2}\right]\)
3. \(\left[ M L^2 T^{-3}A^{-1}\right]\)
4. \(\left[ M L^{-2} T^{-2}A^{-2}\right]\)
A cylindrical magnet is kept along the axis of a circular coil. On rotating the magnet about its axis, the coil will have induced in it:
1. | No current |
2. | A current |
3. | Only an emf |
4. | Both an emf and a current |
The magnetic flux through a coil varies with time \(t\) as shown in the diagram. Which graph best represents the variation of the emf \(E\) induced in the coil with time \(t\)?
1. | ![]() |
2. | ![]() |
3. | ![]() |
4. | ![]() |
A bar magnet is made to fall through a long surface copper tube. The speed \((v)\) of the magnet as a function of time \((t)\) is best represented by:
1. | \(a\) | 2. | \(b\) |
3. | \(c\) | 4. | \(d\) |
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:
1. | parallel to the motion of wire. |
2. | along with \(XY\). |
3. | perpendicular outside the paper. |
4. | perpendicular inside the paper. |
1. | \(\dfrac{B^{2} AL}{2\mu_{0}^{2}}\) | 2. | \(\dfrac{AL}{2 \mu_{0}}\) |
3. | \(\dfrac{1}{2} \mu_{0} B^{2} AL\) | 4. | \(\dfrac{B^{2} AL}{2 \mu_{0}}\) |