The e.m.f. induced in a coil of wire, which is rotating in a magnetic field, does not depend on:

A bar magnet is moved along the axis of copper ring placed far away from the magnet. Looking from the side of the magnet, an anticlockwise current is found to be induced in the ring. Which of the following may be true?

For L-R circuit, the time constant is equal to:

Coefficient of mutual inductance for the given coils does not depend on :

An L-R circuit is connected to a battery  at t=0. Which of the following quantities is not zero just after the circuit is formed?

The adjoining figure shows two different arrangements in which two square wireframes are placed in a uniform magnetic field B  decreasing with time.
         

The direction of the induced current I in the figure is:

A square of side L meters lies in the XY-plane in a region, where the magnetic field is given by $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+4\hat{\mathrm{k}}\right) \mathrm{T}$ where ${\mathrm{B}}_0$ is a constant. The magnitude of flux passing through the square is:

A loop, made of straight edges has six corners at A(0, 0, 0), B(L, 0, 0), C(L, L, 0), D(0, L, 0), E(0, L, L) and F(0, 0, L). A magnetic field B=${\mathrm{B}}_0\left(\hat{\mathrm{i}}+\hat{\mathrm{k}}\right)$ T is present in the region. The flux passing through the loop ABCDEFA (in that order) is:

The magnetic flux linked with a coil (in Wb) is given by the equation $\mathrm{\varphi }=5{\mathrm{t}}^2+3\mathrm{t}+60$. 
The magnitude of induced emf in the coil at t=4 s  will be:

A wheel with 20 metallic spokes, each 1 m long, is rotated with a speed of 120 rpm in a plane perpendicular to a magnetic field of 0.4 G. The induced emf between the axle and rim of the wheel will be, $( 1 \mathrm{G} ={10}^{-4} \mathrm{T} )$ 

Q. 3. A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then,

Q. 4. There are two coils A and B as shown in the figure. A current starts flowing in B as shown when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that:

Q. 5. Same as problem 4 except coil A is made to rotate about a vertical axis (figure). No current flows in B if A is at rest. The current in coil A, when the current in B (at t-0) is counter-clockwise and the coil A is as shown at this instant, t=0, is:

Q. 6. The self-inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as:

Q. 7 A metal plate is getting heated. It can be because

(a) a direct current is passing through the plate

(b) it is placed in a time-varying magnetic field

(c) it is placed in space varying magnetic field but does not vary with the time

(d) a current (either direct or alternating) is passing through the plate

Q. 8. An emf is produced in a coil, which is not connected to an external voltage source. This can be due to:

(a) the coil being in a time-varying magnetic field

(b) the coil moving in a time-varying magnetic field

(c) the coil moving in a constant magnetic field

(d) the coil is stationary in an external spatially varying magnetic field, which does not change with time

Q. 9. The mutual inductance M₁₂ of coil 1 with respect to coil 2

(a) increases when they are brought nearer

(b) depends on the current passing through the coils

(c) increases when one of them is rotated about an axis

(d) is the same as M₂₁ of coil 2 with respect to coil 1

A square loop of side 10 cm and resistance 0.5 $\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 0.70 s at a steady rate. The magnitude of induced current during this time interval is:

A circular coil of radius 10 cm, 500 turns, and resistance 2 $\Omega$ is placed with its plane perpendicular to the horizontal component of the earth’s magnetic field. It is rotated about its vertical diameter through 180° in 0.25 s. The magnitude of the current induced in the coil is:

(The horizontal component of the earth’s magnetic field at the place is 3.0 × 10^–5 T)

Consider the figure. What would you do to obtain a large deflection of the galvanometer?    

The figure shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normally to the plane of the loop away from the reader. The direction of the induced current in each loop  is:

Mark the correct statement:

A rectangular loop and a circular loop are moving out of a uniform magnetic field region (as shown in the figure) to a field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops.

The polarity of the capacitor in the given figure is:

A metallic rod of 1 m length is rotated with a frequency of 50 rev/s, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 m, about an axis passing through the centre and perpendicular to the plane of the ring (as shown in the figure). A constant and uniform magnetic field of 1 T parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?

A wheel with 10 metallic spokes each 0.5 m long is rotated with a speed of 120 rev/min in a plane normal to the horizontal component of earth’s magnetic field H_E at a place. If H_E  = 0.4 G at the place, what is the induced emf between the axle and the rim of the wheel? $\left(1 G={10}^{-4} T\right)$

$$\begin{gathered} 1. 5.12\times {10}^{-5} V \\ 2. 0 \\ 3. 3.33\times {10}^{-5} V \\ 4. 6.28\times {10}^{-5} V \end{gathered}$$

Refer to figure. The arm PQ of the rectangular conductor is moved from x = 0, outwards. The uniform magnetic field is perpendicular to the plane and extends from x = 0 to x = b and is zero for x > b. Only the arm PQ possesses substantial resistance r. Consider the situation when the arm PQ is pulled outwards from x = 0 to x = 2b with a constant speed v. The induced emf is:

$$\begin{gathered} 1. -\mathrm{Blv} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 2. +\mathrm{Blv} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 3. -\mathrm{Blv} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b} \\ 4. +\mathrm{Blv} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b} \end{gathered}$$

Refer to the figure. The arm PQ of the rectangular conductor is moved from x = 0, outwards. The uniform magnetic field is perpendicular to the plane and extends from x = 0 to x = b and is zero for x > b. Only the arm PQ possesses substantial resistance r. Consider the situation when the arm PQ is pulled outwards from x = 0 to x = 2b with constant speed v. The force necessary to pull the arm is:

$$\begin{gathered} 1. \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 2. \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{2\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 3. 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{\mathrm{r}} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 4. 0 \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{2\mathrm{r}} \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \end{gathered}$$

Refer to figure. The arm PQ of the rectangular conductor is moved from x = 0, outwards. The uniform magnetic field is perpendicular to the plane and extends from x = 0 to x = b and is zero for x > b. Only the arm PQ possesses substantial resistance r. Consider the situation when the arm PQ is pulled outwards from x = 0 to x = 2b and is then moved back to x = 0 with constant speed v. The power dissipated as Joule heat is: 

$$\begin{gathered} 1. \frac{{\mathrm{B}}^2{\mathrm{l}}^2\mathrm{v}}{2\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 2. \frac{{\mathrm{B}}^2{\mathrm{l}}^2{\mathrm{v}}^2}{\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b}, 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b} \\ 3. 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2{\mathrm{v}}^2}{\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b} \\ 4. 0 \mathrm{for} \mathrm{b}\le \mathrm{x}<2\mathrm{b}, \frac{{\mathrm{B}}^2{\mathrm{l}}^2{\mathrm{v}}^2}{2\mathrm{r}} \mathrm{for} 0\le \mathrm{x}<\mathrm{b} \end{gathered}$$

Two concentric circular coils, one of small radius r₁ and the other of large radius r₂, such that  r₁ << r₂, are placed co-axially with centres coinciding. The mutual inductance of the arrangement is:

$$\begin{gathered} 1. \frac{{\mathrm{\mu }}_0\mathrm{\pi }{{\mathrm{r}}_1}^2}{3{\mathrm{r}}_2} \\ 2. \frac{2{\mathrm{\mu }}_0\mathrm{\pi }{{\mathrm{r}}_1}^2}{{\mathrm{r}}_2} \\ 3. \frac{{\mathrm{\mu }}_0\mathrm{\pi }{{\mathrm{r}}_1}^2}{{\mathrm{r}}_2} \\ 4. \frac{{\mathrm{\mu }}_0\mathrm{\pi }{{\mathrm{r}}_1}^2}{2{\mathrm{r}}_2} \end{gathered}$$