Electromagnetic Induction PDF - Physics Questions and Answers

## ELECTROMAGNETIC INDUCTION ### IMPORTANT FORMULAE 1. **Magnetic flux** $B =\overrightarrow{B} \cdot \overrightarrow{A} = BA \cos \theta$ where $\theta$ is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$. 2. **Induced emf in a coil** $\varepsilon=-N \frac{\Delta \phi}{\Delt...

## ELECTROMAGNETIC INDUCTION ### IMPORTANT FORMULAE 1. **Magnetic flux** $B =\overrightarrow{B} \cdot \overrightarrow{A} = BA \cos \theta$ where $\theta$ is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$. 2. **Induced emf in a coil** $\varepsilon=-N \frac{\Delta \phi}{\Delta t}$ 3. **EMF induced in a moving conductor**, $\varepsilon=B v l$ where $B, v, l$ are mutually perpendicular. 4. **Magnetic flux** $\phi=L I$ where $L$ is the coefficient of self-induction. 5. **If $L$ is self inductance, emf induced** $\varepsilon=-L \frac{\Delta I}{\Delta t}$ 6. **Self inductance of a solenoid:** $L=\mu_{r} \mu_{o} n^{2} A l=\mu_{r} \mu_{o} \frac{N^{2} A}{l}$ 7. **Mutual Inductance** $E_{s}=-M \frac{\Delta I}{\Delta t}$ 8. **Mutual inductance of solenoid coil system** $M=\frac{\mu_{o} N_{1} N_{2} A}{l}$ where $N_{1}=$ number of turns/metre in solenoid, $N_{2}=$ number of turns in coil. 9. **Energy stored in inductance** $U_{m}=\frac{1}{2} L I^{2}=\frac{1}{2} \phi I$ **Direction of Current Induced in Some Cases** | System | Primary Current | Induced Current | | :---------------------------------------- | :------------------- | :--------------------- | | 1. Straight wire-coil system | i) Current increasing ii) Current decreasing | Clockwise current Anticlockwise current | | 2. Self inductive circuit 0000000 | i) Key is pressed ii) Key is released | Opposite to direction of main currents In the direction of main current | | 3.Magnetic-coil system Man observing direction of current | i) North pole approaching coil ii) North pole receding coil | Anticlockwise current Clockwise current | *** ### MULTIPLE CHOICE QUESTIONS Choose and write the correct option in the following questions. 1. Whenever the flux linked with a circuit changes, there is an induced emf in the circuit. This emf in the circuit lasts * (a) for a very short duration * (b) for a long duration * (c) forever * (d) as long as the magnetic flux in the circuit changes. 2. The area of a square shaped coil is $10^{-2} m^{2}$. Its plane is perpendicular to a magnetic field of strength $10^{-3} T$. The magnetic flux linked with the coil is * (a) $10^{-1} Wb$ * (b) $10^{-5} Wb$ * (c) $10^{5} \mathrm{~Wb}$ * (d) $100 \mathrm{~Wb}$ 3. An area $A=0.5 m^{2}$ shown in the figure is situated in a uniform magnetic field $B=4.0 Wb/m^{2}$ and its normal makes an angle of $60^{\circ}$ with the field. The magnetic flux passing through the area $A$ would be equal to * (a) $2.0$ weber * (b) $1.0$ weber * (c) $\sqrt{3}$ weber * (d) $0.5$ weber 4. A square of side $L$ meters lies in the X-Y plane in a region, where the magnetic field is given by $\vec{B}=B_{0}(2 \hat{i}+3 \hat{j}+4 \hat{k}) T$, where $B_{0}$ is constant. The magnitude of flux passing through the square is [NCERT Exemplar] * (a) $2 B_{o} L^{2} W b$ * (b) $3 B_{o} L^{2} W b$ * (c) $4 B_{0} L^{2} W b$ * (d) $\sqrt{29} B_{o} L^{2} W b$ 5. 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 $\vec{B}=B_{0}(\hat{i}+\hat{k}) T$ is present in the region. The flux passing through the loop ABCDEFA (in that order) is [NCERT Exemplar] * (a) $B_{0} L^{2} W b$ * (b) $2 B_{0} L^{2} W b$ * (c) $\sqrt{2} B_{o} L^{2} W b$ * (d) $4 B_{0} L^{2} W b$ 6. An emf is produced in a coil, which is not connected to an external voltage source. This can be due to [NCERT Exemplarl * (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) all of the above. 7. 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 [NCERT Exemplar] * (a) a direct current flows in the ammeter A. * (b) no current flows through the ammeter A. * (c) an alternating sinusoidal current flows through the ammeter A with a time period $=2 \pi / \omega$. * (d) a time varying non-sinusoidal current flows through the ammeter A. 8. A copper ring is held horizontally and a magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is * (a) equal to that due to gravity * (b) less than that due to gravity * (c) more than that due to gravity * (d) depends on the diameter of the ring and the length of the magnet 9. 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 counter clockwise. $B$ is kept stationary when $A$ moves. We can infer that [NCERT Exemplar] * (a) there is a constant current in the clockwise direction in $A$. * (b) there is a varying current in $A$. * (c) there is no current in $A$. * (d) there is a constant current in the counterclockwise direction in $A$. 10. Same as the above problem except the coil $A$ is made to rotate about a vertical axis refer to the 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 counterclockwise and the coil $A$ is as shown at this instant, $t=0$, is [NCERT Exemplar] * (a) constant current clockwise. * (b) varying current clockwise. * (c) varying current counterclockwise. * (d) constant current counterclockwise. 11. Lenz's law is essential for * (a) conservation of energy * (b) conservation of mass * (c) conservation of momentum * (d) conservation of charge 12. The self inductance $L$ of a solenoid of length 1 and area of crosssection $A$, with a fixed number of turns $N$ increases as [NCERT Exemplar] * (a) $I$ and $A$ increase. * (b) $I$ decreases and $A$ increases. * (c) $I$ increases and $A$ decreases. * (d) both $I$ and $A$ decrease. 13. A thin circular ring of area $A$ is held perpendicular to a uniform magnetic field of induction $B$. A small cut is made in the ring and a galvanometer is connected across its ends in such a way that the total resistance of the circuit is $R$. When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is * (a) $\frac{B R}{A}$ * (b) $\frac{A B}{R}$ * (c) $A B R$ * (d)$ \frac{B^{2} A}{R^{2}}$ 14. A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of it's sides. A magnetic induction $B$ constant in time and space, pointing perpendicular and into the plane of the loop exists everwhere as in given figure. The current induced in the loop is * (a) $\frac{B l v}{R}$ clockwise * (b) $\frac{B l v}{R}$ anti clockwise * (c) $\frac{2 B l v}{R}$ anticlockwise * (d) zero. 15. Inductance plays the role of * (a)inertia * (b) friction * (c) source of emf * (d) force 16. A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because * (a) the magnetic field is constant. [NCERT Exemplar] * (b) the magnetic field is in the same plane as the circular coil and it may or may not vary. * (c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. * (d) both (b) and (c) 17. When the current in a coil changes from 8 A to 2 A in $3 x 10^{-2}$ second, the emf induced in the coil is 2 volt. The self-inductance of the coil, in millihenry, is * (a) 1 * (b) 5 * (c) 20 * (d) 10 18. The mutual inductance of two coils depends upon * (a) medium between coils * (b) separation between coils * (c) both on (a) and (b) * (d) none of (a) and (b) 19. Due to relative motion of a magnet with respect to a coil, an emf is induced in the coil. Identify the principle involved. * (a) Gauss's law * (b) Biot-Savart law * (c) Ampere's circuital law * (d) Faraday's law 20. In Faraday's experiment of electromagnetic induction, more deflection will be shown by galvanometer, when * (a) magnet is in uniform motion towards the coil * (b) magnet is in accelerated motion towards the coil * (c) magnet is in uniform motion away from the coil * (d) magnet is at rest near the coil 21. If both the number of turns and core length of an inductor is doubled keeping other factors constant, then its self-inductance will be * (a) halved * (b) quadrupled * (c) unaffected * (d) doubled 22. Oscillating metallic pendulum in a uniform magnetic field directed perpendicular to the plane of oscillation * (a) remains unaffected * (b) oscillates with changing frequency * (c) slows down * (d) becomes faster 23. A metallic cylinder is held vertically and then a small magnet is dropped along its axis. It will fall with * (a) acceleration $a=g$ * (c) acceleration $a>g$ * (b) constant velocity $a=0$ * (d) acceleration $a<g$ *** 24. An emf of 200 V is induced in a circuit when current in the circuit falls from 5 Ato 0 A in 0. 1 second. The self-inductance of the circuit is * (a) 3.5 H * (b) 3.9 H * (c) 4 H * (d) 4.2 H 25. A small piece of metal wire is dragged across the gap between the poles of a magnet in 0. 4 s. If change in magnetic flux in the wire is $8 \times 10^{-4} W b$, then emf induced in the wire is\ (a)$8 \times 10^{-3} \mathrm{~V}$\ (b)$6 \times 10^{-3} \mathrm{~V}$\ (c)$4 \times 10^{-3} \mathrm{~V}$\ (d) $2 \times 10^{-3} \mathrm{~V}$ 26. If the number of turns per unit length of the coil of a solenoid is doubled keeping other dimensions same, then its self-inductance will be * (a) four times * (b) eight times * (c) halved * (d) doubled 27. A conducting square loop of side $l$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. A magnetic induction $$ constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced emf is * (a) zero * (b) $\frac{\text { R } v B}{l}$ * (c) $\frac{B l}{R}$ * (d) $v B l$ 28. A wheel with ten metallic spokes each 0.50 m long is rotated with a speed of 120 rev/min in a plane normal to the earth's magnetic field at the place. If the magnitude of the field is 0.4 G the induced emf between the axle and the rim of the wheel is equal to * (a) $1.256 \times 10^{-5} \mathrm{~V}$ * (b) $6.28 \times 10^{-5} \mathrm{~V}$ * (c) $1.256 \times 10^{-4} \mathrm{~V}$ * (d) $6.28 \times 10^{-6} \mathrm{~V}$ 29. In a circuit with a coil of resistance 2 ohms, the magnetic flux changes from $2.0 Wb to 10$. 0 Wb in 0. 2 second. The charge that flows in the coil during this time is * (a) 5.0 coulomb * (b) 0.8 coulomb * (c) 1.0 coulomb * (d) 4.0 coulomb 30. The direction of induced current is such that it opposes the very cause that has produced it. This is the law of * (a) Lenz * (b) Faraday * (c) Kirchhoff * (d) Fleming 31. The magnetic flux through a circuit of resistance $R$ changes by an amount $\Delta \phi$ in time $\Delta$, then the total quantity of electric charge $Q$, passing during this time through any point of the circuit is given by\ (a) $\Delta Q=\frac{\Delta \phi}{\Delta t}$\ (b) $\Delta Q=\frac{\Delta \phi}{R \Delta t}$\ (c) $\Delta Q=\frac{\Delta \phi+R}{\Delta t}$\ (d) $\Delta Q=\frac{\Delta \phi}{\frac{\Delta t}{R}}$ 32. The dimension of magnetic flux is * (a) $M L^{2} T^{-2} A^{-1}$ * (b) $M^{2} L^{3} T^{-3} A^{-1}$ * (c) $M L^{2} T^{-3} A^{-1}$ * (d) $M L T^{-1} A^{-1}$ 33. Lenz's law is a consequence of the law of conservation of * (a) mass * (b) charge * (c) momentum * (d) energy 34. The physical quantity expressed in henry is * (a) magnetic flux * (b) self-inductance * (c) magnetic permeability * (d) magnetic induction 35. When current in a circuit drops from 10 Ato 2 A in 2 seconds, the induced emf developed in the circuit is 16 volts. The self inductance of the circuit is * (a) 16 henry * (b) 8 henry * (c) 6 henry * (d) 4 henry 36. The current passing through a choke coil of self-inductance 5 henry is decreasing at the rate of 2 A/s. The induced emf developed across the coil is * (a) 10 volt * (b) -10 volt * (c) 2.5 volt * (d) -2.5 volt *** 37. Magnetic flux through a coil changes from $0.7 \mathrm{~Wb}$ to $0.2 \mathrm{~Wb}$ in $0.1$ second. The induced emf developed in the coil is * (a) $7 \mathrm{~V}$ * (b) $5 \mathrm{~V}$ * (c) $20 \mathrm{~V}$ * (d) $2 \mathrm{~V}$ 38. The magnetic potential energy stored in a certain inductor is $25 \mathrm{~mJ}$, when the current in the inductor is $60 \mathrm{~mA}$. This inductor is of inductance * (a) $0.138 \mathrm{H}$ * (b) $13 \overline{8} .88 \mathrm{H}$ * (c) $1.389 \mathrm{H}$ * (d) $13.\overline{8} 9 \mathrm{H}$ 39. The magnitude of induced emf in a coil depend on * (a) the amount of magnetic flux linked by the coil. * (b) the amount of electric flux linked by the coil. * (c) the rate of change of magnetic flux linked by the coil. * (d) the rate of change of electric flux linked by the coil. 40. Weber per second is equal to * (a) ampere * (b) volt * (c) ohm * (d) henry 41. Self inductance of a coil delays * (a) the growth of current through it. * (b) the decay of current through it. * (c) both the growth and decay of current through it. * (d) neither the growth nor the decay of current through it. 42. Self inductance of a coil is the mechanical analogue of * (a) energy * (b) momentum * (c) inertia * (d) power 43. An electron moves on a straight line that is moving from point X to Y path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil? * (a) The current will reverse its direction as the electron goes past the coil. * (b) No current induced * (c) abcd * (d) adcb 44. If the number of turns in a coil is doubled, then its self-inductance becomes * (a) double * (b) half * (c) four times * (d) unchanged 45. Whenever the flux linked with a circuit changes, there is an induced emf in the circuit. This emf in the circuit lasts\ (a) for a very short duration\ (b) for a long duration\ (c) forever;\ (d) as long as the magnetic flux in the circuit changes. 46. Two coils of self inductances 2 mH and 8 mH are placed to close to each other that the flux linkage is complete between the coils. The mutual inductance between these coils is: * (a) 4 mH * (b) 6 mH * (c) 10 mH * (d) 16 mH *** 47. A copper ring is held horizontally and a magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is:\ (a) equal to that due to gravity\ (b) less than that due to gravity\ (c) more than that due to gravity\ (d) depends on the diameter of the ring and the length of the magnet 48. The mutual inductance of two coils depends upon * (a) medium between coils * (b) separation between coils * (c) both on (a) and (b) * (d) none of (a) and (b) 49. The core used in transformers and other electromagnetic equipments is laminated because it * (a) prevents rusting of core * (b) increases the magnetic saturation level of the core * (c) decreases the residual magnetism of the core * (d) minimises eddy-current loss in the core 50. If L and R represent inductance and resistance respectively then the dimensions of $L/R$ will be: * (a) $M^{0} L^{0} T^{-1}$ * (b) $M^{0} L^{0} T^{-2}$ * (c) $M^{0} L^{0} T$ * (d) cannot be expressed in terms of M,L and T. 51. When the current through a solenoid increases at a constant rate, the induced current: * (a) is a constant and is in the direction of the inducing current * (b) is a constant and is opposite to the direction of the inducing current * (c) increases with time and is opposite to the direction of the inducing current * (d) zero 52. Figure shows two bulbs $B_1$ and $B_2$, resistor $R$ and inductor $L$. When the switch $S$ is turned off * (a) both $B_1$ and $B_2$ dies out promptly * (b) both $B_1$ and $B_2$ die out with some delay * (c) $B_2$ dies out promptly, but $B_1$ with some delay * (d) $B_1$ dies out promptly, but $B_2$ with some delay 53. A thin semicircular conducting ring of radius $R$ is falling with its plane vertical in horizontal magnetic induction $B$. At the position MNQ the speed of ring is $v$ then the potential difference developed across the ring is: * (a) zero * (b) $\frac{B v \pi R^{2}}{2}$ and $M$ at higher potential * (c) $\pi R B v$ and $Q$ at higher potential * (d) $2 R B v$ and $M$ at higher potential 54. A metallic square loop ABCD is moving in its own plane with a velocity $v$ in a uniform magnetic field perpendicular to plane as shown in fig. An electric field is induced * (a) in $A D$ but not in $B C$ * (b) in $B C$ but not in $A D$ * (c) neither in $A D$ nor in $B C$ * (d) in both $A D$ and $B C$ *** 55. Two identical circular loops $A$ and $B$ of metal wire are lying on a table without touching each other. Loop $A$ carries a current which increases with time. In response the loop B * (a) remains stationary * (b) is attracted by loop $A$ * (c) is repelled by loop $A$ * (d) rotates about its centre of mass with centre of mass fixed 56. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon: * (a) the materials of wires of the coils * (b) the currents in the two coils * (c) the rates at which currents are changing in the two coils * (d) relative position and orientation of the two coils 57. Two coils have inductances $L_{1}=4 \mathrm{mH}$ and $L_{2}=1 \mathrm{mH}$ respectively. The currents in the two coils are increased at the same rate. At a certain instant of time, both coils are given the same power. If $I_{1}$ and $I_{2}$ are the currents in the two coils at that instant of time respectively, then the value of ratio $\frac{I_{1}}{I_{2}}$ is: * (a) $\frac{1}{8}$ * (b) $\frac{1}{2}$ * (c) $\frac{1}{2}$ * (d) 1 58. An infinitely long cylindrical conducting rod is kept along $+z$-direction. A constant magnetic field is also present in $+z$-direction. Then the current induced will be: * (a) 0 * (b) along $+z$-direction * (c) along clockwise as seen from $+z$ direction * (d) along anticlockwise as seen from $+z$ direction 59. The current in a wire $A B$ is increasing in magnitude. The direction of induced current in the loop (if any) will be: * (a) clockwise * (b) anticlockwise * (c) arbitrary * (d) no current is induced 60. A circular loop of radius R carrying current I lies in $x-y$ plane with the centre at origin. The total magnetic flux through $x y$ plane is: * (a) directly proportional to I * (b) directly proportional to R * (c) directly proportional to $R^{2}$ * (d) zero 61. The equivalent inductance of two inductors is 2. 4 H when connected in parallel and 10 H when connected in series. What is the value of inductances of the individual inductors? * (a) 2 H, 8 H * (b) 4 H, 6 H * (c) 3 H, 7 H * (d) 5 H, 5 H *** 62. A square loop of side 20 cm and resistance 2 Ω is moved towards right with speed 2v as shown. The left arm of the loop is in a uniform magnetic field of 0.5 T. The field is perpendicular to plane of paper, pointing downward. The loop is connected to a network of 5 resistors as shown in fig. With what speed should the loop be moved so that a steady current of $$1 m A$$ flows through the loop? * (a) 2 cm/s * (b) 2.5 cm/s * (c) 5 cm/s * (d) 25 cm/s 63. A small square loop of a wire of side 1 is placed inside a large square loop of side L (L >> I). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to: * (a) $\frac{l^{2}}{L}$ * (b) $\frac{l}{L}$ * (c) $\frac{L^{2}}{l}$ * (d) $\frac{L}{l}$ 64. Two circular coils can be arranged in any of the three situations as shown in fig. Their mutual inductance will be: * (a) maximum in situation (i) * (b) maximum in situation (ii) * (c) maximum in situation (iii) * (d) same in all situations 65. The variation of induced emf (E) with time $t$ in a coil if a short bar magnet is moved along its axis with a constant velocity is best represented as: *** 66. A uniform but time varying magnetic field $B(t)$ exists in a circular region of radius ' $a$ ' and is directed into the plane of paper as shown. The magnitude of the induced electric field at point $P$ at a distance $\mathrm{r}$ from the centre of the circular region: * (a) is zero * (b) decreases as $I/r$ * (c) increases as $r$ * (d) decreases as $1 / r^{2}$ 67. A short circuited coil is placed in a time varying magnetic field. Electric power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be: * (a) halved * (b) the same * (c) doubled * (d) quadrupled 68. Figure shows a conducting circular loop of radius ' $a$ ' placed in a uniform, perpendicular magnetic field $B$. A metal rod $O A$ is pivoted at the centre $O$ of the loop. The other end $A$ of the rod touches the loop. The rod $O A$ and the loop are resistanceless but a tungsten wire of resistance $R$ is connected between $O$ and a fixed point $P$ on the loop. The rod $O A$ is made to rotate anticlockwise with a uniform angular velocity $\omega$ by an external source. The current induced in the tungsten wire is * (a) zero * (b) $\frac{B \omega a}{R}$ * (c) $\frac{B \omega a}{2 R}$ * (d) $\frac{B \omega a}{8 R}$ 69. A coil of area $5.0 \times 10^{-3} \mathrm{~m}^{2}$ is a coil placed perpendicular to a time varying magnetic field shown in figure. The value of induced emf in coil in $10 \mathrm{~ms}$ is:\ (a) $0-1 \mathrm{~V}$\ (b) $0.1 \mathrm{mV}$\ (c) $0.5 \mathrm{~V}$\ (d) $0.5 \mathrm{mV}$ 70. When the current changes from + 2A to -2 A in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self-inductance of the coil is\ (a) $0-1 \mathrm{H}$\ (b) $0-2 \mathrm{H}$\ (c) $0-4 \mathrm{H}$\ (d) $0-8 \mathrm{H}$ 71. The effective inductance between $$\mathrm{A}$ and $$\mathrm{B}$ in the fig. shown if $$\mathrm{L}=3$$\mathrm{H}$ is: * (a) 1 H * (c) 0.67 H * (b) 9 H * (d) 1.5H 72. In the given diagram, a line of force of a particular force field is shown. Out of the following options, it can never represent: * (a) an electrostatic field * (b) a magnetostatic field * (c) a gravitational field of a mass at rest * (d) an induced electric field *** 73. Which of the following units denotes the dimensions $\frac{M L^{2}}{Q^{2}}$ ?, where $Q$ denotes the electric charge?\ (a) $Wb m^{2}$\ (b) henry (H)\ (c) $H / m^{2}$\ (d) weber (Wb) 74. A circular loop of radius r, carrying a current I lies in $y-z$ plane with its centre at the origin. The net magnetic flux through the loop is: [CBSE 2020 (55/4/1] * (a) directly proportional to r * (b) zero * (c) inversely proportional to r * (d) directly proportional to I 75. A rectangular, a square, a circular and an elliptical loop, all in the $x-y$ plane are moving out of the uniform magnetic field with a constant velocity $v=v i$. The magnetic field is directed along the negative $z$-direction. The induced emf during the passage of these loops, out of the field region will not remain constant for: * (a) the circular and the elliptical loops * (b) only the elliptical loop * (c) any of the four loops * (d) the rectangular, circular and elliptical loops 76. A conducting circular loop is placed in a uniform magnetic field $0.04 \mathrm{~T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 \mathrm{~mm} / \mathrm{s}$. The induced emf in the loop when the radius is $2 \mathrm{~cm}$ is:\ (a) $4.8 \pi \mu V$\ (b) $0.8 \pi \mu V$\ (c) $1.6 \pi \mu V$\ (d) $3.2 \pi \mu V$ 77. A long solenoid has 500 turns. When a current of $2 \mathrm{~A}$ is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \mathrm{~Wb}$. The self inductance of the solenoid is :\ (a) $2.5 \mathrm{H}$\ (b) $2.0 \mathrm{H}$\ (c) $1.0 \mathrm{H}$\ (d) $40 \mathrm