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 small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to 

1. l / L

2. l² / L

3. L/l

4. L²/l

A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region 

1. Is zero

2. Decreases as $\frac{1}{r}$

3. Increases as r

4. Decreases as $\frac{1}{r^2}$

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

A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is 

1. BΩl²

2. $\frac{1}{2}B\omega l^2$

3. $\frac{1}{8}B\omega l^2$

4. Zero

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