A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\frac{dB}{dt}$. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of the magnetic field as shown in the figure. Then, the emf generated is:

       

1.  Zero in loop 1 and zero loop 2

2.  $-\frac{dB}{dt}\pi r^2$ in loop 1 and zero in loop 2

3.  $-\frac{dB}{dt}\pi R^2$ in loop 1 and zero in loop 2

4.  Zero in loop 1 and not defined in loop 2

The key K is inserted at time t= 0. The initial (t=0) and final $\left(t\to \infty \right)$ currents through battery are :

1. $\frac{1}{15}Amp, \frac{1}{10}Amp$

2. $\frac{1}{10}Amp, \frac{1}{15}Amp$

3. $\frac{2}{15}Amp, \frac{1}{10}Amp$

4. $\frac{1}{15}Amp, \frac{2}{25}Amp$

A current-carrying wire is placed below a coil in its plane, with current flowing as shown.

If the current increases –

1. no current will be induced in the coil 

2. an anticlockwise current will be induced in the coil 

3. a clockwise current will be induced in the coil 

4. the current induced in the coil will be first anticlockwise and then clockwise

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

(1) 2

(2) 4

(3) 6

(4) None of these

When the current in a certain inductor coil is 5.0 A and is increasing at the rate of 10.0 A/s, the potential difference across the coil is 140V. When the current is 5.0 A and decreasing at the rate of 10.0 A/s, the potential difference is 60V. The self-inductance of the coil is –

1.  2H                 

2.  4H

3.  8H                 

4.  12H

An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction of:

1. \(P\)
2. \(Q\)
3. \(L\)
4. \(M\)

A conducting rod PQ of length L = 1.0 m is moving with a uniform speed v = 2 m/s in a uniform magnetic field B = 4.0 T directed into the paper. A capacitor of capacity C = 10 μF is connected as shown in figure. Then

(1) q_A = + 80 μC and q_B = – 80 μC

(2) q_A = – 80 μC and q_B = + 80 μC

(3) q_A = 0 = q_B

(4) Charge stored in the capacitor increases exponentially with time

The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

(1) b > (d = e) < (a = c)

(2) b > (d = e) > (a = c)

(3) b < d < e < c < a

(4) b > (a = c) > (d = e)