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 \(I_{0}=10~\text{A}\) and \(\omega = 100\pi ~\text{rad/s}\). The maximum value of emf induced in the second coil is:
1. \(5\pi~\text{V}\)
2. \(2\pi~\text{V}\)
3. \(4\pi~\text{V}\)
4. \(\pi~\text{V}\)

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

Self-inductance of primary and secondary of a perfectly coupled coil is 40 mH and 90mH respectively. Coefficient of mutual induction between them is

1. 65 mH

2. 50 mH

3. 130 mH

4. 60 mH

A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A constant magnetic field B exists as shown in the figure. Mechanical power required to maintain its uniform velocity is

1. $\frac{B^2{L}^2{v}^2}{R}$

2. $\frac{B^2{L}^2{v}^2}{2R}$

3. $\frac{B^2{L}^2{v}^2}{4R}$

4. Zero

A conducting disc of radius r rotates about its axis with an angular speed $\omega$ in a uniform magnetic field B perpendicular to the plane of the disc as shown. A resistance R is connected between centre and rim of the disc, then-

1. No e.m.f. will induce across the resistance

2. E.m.f. will induce and A is at high potential

3. Current in resistance will flow from A to B

4. Resistance becomes hot due to Joule's heating

A train is moving on a straight horizontal track. Induced emf across the axle is maximum when it moves

1. At poles

2. At equator

3. Along the direction where the angle of dip is 45$°$

4. Emf is not induced

A square loop enters a magnetic field with velocity v as shown in the figure. The front edge enters the magnetic field at time t = 0. Which of the following graphs gives the correct variation of emf$\epsilon$ induced in the loop with time t for its constant velocity in the magnetic field? [Take anticlockwise current as negative and vice versa]

A rectangular metal loop ABCD of is passed through the magnetic field with a constant velocity v. Which of the following represents power (P) dissipated vs time (t) graph?

1.                2. 
3.                4.