In an LR-circuit, the time constant is that time in which current grows from zero to the value (where I₀ is the steady-state current) 

1. 0.63 I₀

2. 0.50 I₀

3. 0.37 I₀

4. I₀

A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity ω. The induced e.m.f. between the two ends is 

1. $\frac{1}{2}B\omega l^2$

2. $\frac{3}{4}B\omega l^2$

3. $B\omega l^2$

4. $2B\omega l^2$

A circular loop of radius R carrying current I lies in the x-y plane with its centre at the origin. The total magnetic flux through the x-y plane is 

1. Directly proportional to I

2. Directly proportional to R

3. Directly proportional to R²

4. Zero

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

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 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 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

A rectangular loop with a sliding connector of length \(l= 1.0\) m is situated in a uniform magnetic field \(B = 2T\) perpendicular to the plane of the loop. Resistance of connector is \(r=2~\Omega\). Two resistances of \(6~\Omega\) and \(3~\Omega\) are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity \(v = 2\) m/s is:

          
1. \(6~\text{N}\)
2. \(4~\text{N}\)
3. \(2~\text{N}\)
4. \(1~\text{N}\)

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

1. $\frac{mgR}{Bl}$

2. $\frac{mgR}{B^2{l}^2}$

3. $\frac{mgR}{B^3{l}^3}$

4. $\frac{mgR}{B^{2}l}$

A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. AO = l and OC = 3l. Then

1. $V_A-V_O=\frac{B\omega l^2}{2}$

2. $V_O-V_C=\frac{7}{2}B\omega l^2$

3. $V_A-V_C=4B\omega l^2$

4. $V_C-V_O=\frac{9}{2}B\omega l^2$