A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0 so that a time-dependent current I₁(t) starts flowing through the coil. If I₂(t) is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to I₁(t), then as a function of time (t > 0), the product I₂ (t) B(t) 

1. Increases with time

2. Decreases with time

3. Does not vary with time

4. Passes through a maximum

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be 

1. Maximum in situation (A)

2. Maximum in situation (B)

3. Maximum in situation (C)

4. The same in all situations

As shown in the figure, P and Q are two coaxial conducting loops separated by some distance. When the switch S is closed, a clockwise current I_P flows in P (as seen by E) and an induced current $I_{Q_1}$ flows in Q. The switch remains closed for a long time. When S is opened, a current $I_{Q_2}$ flows in Q. Then the directions of $I_{Q_1}$ and $I_{Q_2}$ (as seen by E) are 

1. Respectively clockwise and anticlockwise

2. Both clockwise

3. Both anticlockwise

4. Respectively anticlockwise and clockwise

A conducting wireframe is placed in a magnetic field that is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires \(AB\) and \(CD\) are:

A square metallic wire loop of side \(0.1~\text m\) and resistance of \(1~\Omega\) is moved with a constant velocity in a magnetic field of \(2~\text{wb/m}^2\) as shown in the figure. The magnetic field is perpendicular to the plane of the loop and the loop is connected to a network of resistances. What should be the velocity of the loop so as to have a steady current of \(1~\text{mA}\) in the loop?

          
1. \(1~\text{cm/s}\)
2. \(2~\text{cm/s}\)
3. \(3~\text{cm/s}\)
4. \(4~\text{cm/s}\)

A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of 1 wb/m², as shown in fig. If all the four sides are of 1m length each, then the induced emf between points A and D is

1. 0

2. 1.41 volt

3. 0.71 volt

4. None of the above

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 resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is \(10~\Omega.\) The current in the circuit will be:

Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction B = B₀e^–t is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch, at t=0, is equal to

1. $\frac{B_0^2\pi r^2}{R}$

2. $\frac{B_{0}10r^3}{R}$

3. $\frac{B_0^2{\pi }^2{r}^{4}R}{5}$

4. $\frac{B_0^2{\pi }^2{r}^4}{R}$

A highly conducting ring of radius R is perpendicular to and concentric with the axis of a long solenoid as shown in fig. The ring has a narrow gap of width d in its circumference. The solenoid has a cross-sectional area A and a uniform internal field of magnitude B₀. Now beginning at t = 0, the solenoid current is steadily increased so that the field magnitude at any time t is given by B(t) = B₀ + αt where α > 0. Assuming that no charge can flow across the gap, the end of the ring which has an excess of positive charge and the magnitude of induced e.m.f. in the ring are respectively

1. X, Aα

2. X πR²α

3. Y, πA²α

4. Y, πR²α