A horizontal ring of radius r spins about its vertical axis with an angular velocity $\omega$ in a uniform vertical magnetic field of magnitude B. The emf induced in the ring is

1. Zero

2. $\pi r^{2}B\omega$

3. $\frac{1}{2}B\omega r^2$

4. $B\omega r^2$

If N is the total number of turns in a coil, then the value of self-inductance varies as

1. N$°$

2. N

3. N²

4. $\sqrt{N}$

Eddy currents are produced in a material when it is:
 

Lenz's law associated with Faraday's laws of electromagnetic induction are consequence of the conservation of

1. Charge

2. Energy

3. Magnetic field

4. Mass

Self inductances of two uncoupled coils are 40 mH and 90mH. Their mutual inductance is

1. 60 mH

2. 130 mH

3. 50 mH

4. Zero

Magnetic flux through a circuit of resistance \(20~\Omega\) is changed from \(20\) Wb to \(40\) Wb in \(5\) ms. The charge passed through the circuit during this time is:
1. \(1\) C
2. \(2\) C
3. zero
4. \(0.5\) C

A long straight conductor, carrying current I, is fixed on a smooth plane. A circular loop is placed on the same plane as shown in the figure. If the current I through the wire is increasing, then the loop will move towards:

1. Right

2. Left

3. Up 

4. Down

Two coils have a mutual inductance of 5 mH. The current changes in the first coil according to the equation \(I=I_{0}cos\omega t,\) where \(I_{0}=10~A\) and $\omega$ = 100$\pi$ rad/s. The maximum value of e.m.f. induced in the second coil is:

1. 5$\pi$ Volt

2. 2$\pi$ Volt

3. 4$\pi$ Volt

4. $\pi$ Volt

A circular loop is placed near a current-carrying conductor as shown. If the current in the straight conductor is decreasing, then the direction of the induced current in the loop is

1. Clockwise

2. Anticlockwise

3. Into the page 

4. Out of the page

Two rails of a railway track insulated from each other on the ground are connected to a millivoltmeter. The reading of millivoltmeter when the train travels at a speed of 20m/s along the track is (Given: B_v = 0.2$\times$10^-4 Wb/m² and distance between the rails is 1m)

1. 10 mV

2. 0.4 mV

3. 40 mV

4. 4 mV