Chapter 21

A cylindrical bar magnet is kept along the axis of a circular coil. The magnet is rotated about its axis such that north pole faces the coil. The induced current in the coil (a) is zero (b) is clockwise from magnet side (c) may be clockwise or anti-clockwise (d) is anti-clockwise from magnet side

A radio can tune over the frequency range of a portion of MW broadcast bond; \((800 \mathrm{kHz}\) to 1200 \(\mathrm{kHz}\) ). If its LC circuit has an effective inductance of \(220 \mu \mathrm{H}\), what must be the range of its variable capacitor? [Hint For tuning the natural frequency i.e., the frequency of free oscillations of the \(L C\) circuit should be equal to the frequency of the radiowave.] (a) \(87.8\) to \(198 \mathrm{pF}\) (b) 99 to \(190 \mathrm{pF}\) (c) 63 to \(168 \mathrm{pF}\) (d) 44 to \(208 \mathrm{pF}\)

A jet plane is travelling towards west at a speed of \(1800 \mathrm{~km} / \mathrm{h}\). What is the voltage difference developed between the ends of the wing having a span of \(25 \mathrm{~m}\), if the earth's magnetic field at the location has a magnitude of \(5 \times 10^{-4} \mathrm{~T}\) and the dip angle is \(30^{\circ}\). [NCERT] (a) \(2.1 \mathrm{~V}\) (b) \(3.1 \mathrm{~V}\) (c) \(4.1 \mathrm{~V}\) (d) \(5.2 \mathrm{~V}\)

A radio can tune over the frequency range of a portion of MW broadcast bond; \((800 \mathrm{kHz}\) to 1200 \(\mathrm{kHz}\) ). If its LC circuit has an effective inductance of \(220 \mu \mathrm{H}\), what must be the range of its variable capacitor? [Hint For tuning the natural frequency i.e., the frequency of free oscillations of the \(L C\) circuit should be equal to the frequency of the radiowave.] (a) \(87.8\) to \(198 \mathrm{pF}\) (b) 99 to \(190 \mathrm{pF}\) (c) 63 to \(168 \mathrm{pF}\) (d) 44 to \(208 \mathrm{pF}\)

The wing span of an aeroplane is \(36 \mathrm{~m}\). If the plane is flying at \(400 \mathrm{kmh}^{-1}\), the emf induced between the wings tips is (Assume \(V=4 \times 10^{-5} \mathrm{~T}\) ) (a) \(16 \mathrm{~V}\) (b) \(1.6 \mathrm{~V}\) (c) \(0.16 \mathrm{~V}\) (d) \(0.016 \mathrm{~V}\)

The wing span of an aeroplane is \(36 \mathrm{~m}\). If the plane is flying at \(400 \mathrm{kmh}^{-1}\), the emf induced between the wings tips is (Assume \(V=4 \times 10^{-5} \mathrm{~T}\) ) (a) \(16 \mathrm{~V}\) (b) \(1.6 \mathrm{~V}\) (c) \(0.16 \mathrm{~V}\) (d) \(0.016 \mathrm{~V}\)

A square of side \(L\) metres lies in the x-y plane in a region. Where the magnetic field is given by \(\mathbf{B}=B_{0}(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \mathbf{T}\), where \(B_{0}\) is constant. The magnitude of flux passing through the square is [NCERT Exemplar] (a) \(2 B_{0} L^{2} \mathrm{~Wb}\) (b) \(3 B_{0} L^{2} \mathrm{~Wb}\) (c) \(4 B_{0} L^{2}\) Wb (d) \(\sqrt{29} B_{0} L^{2} \mathrm{~Wb}\)

A pair of adjacent coils has a mutual inductance of \(1.5 \mathrm{H}\). If the current in one coil changes from 0 to \(20 \mathrm{~A}\) in \(0.5 \mathrm{~s}\), what is the change of flux linkage with the other coil? (a) \(30 \mathrm{~Wb}\) (b) \(33 \mathrm{~Wb}\) (c) \(23 \mathrm{~Wb}\) (d) \(42 \mathrm{~Wb}\)

An aeroplane in which the distance between the tips of the wings in \(50 \mathrm{~m}\) is flying horizontally with a speed of \(360 \mathrm{kmh}^{-1}\) over a place where the vertical component of earth's magnetic field is \(2 \times 10^{-4} \mathrm{Wbm}^{-2}\). The potential difference between the tips of the wings would be (a) \(0.1 \mathrm{~V}\) (b) \(1.0 \mathrm{~V}\) (c) \(0.2 \mathrm{~V}\) (d) \(0.01 \mathrm{~V}\)

An aeroplane in which the distance between the tips of the wings in \(50 \mathrm{~m}\) is flying horizontally with a speed of \(360 \mathrm{kmh}^{-1}\) over a place where the vertical component of earth's magnetic field is \(2 \times 10^{-4} \mathrm{Wbm}^{-2}\). The potential difference between the tips of the wings would be (a) \(0.1 \mathrm{~V}\) (b) \(1.0 \mathrm{~V}\) (c) \(0.2 \mathrm{~V}\) (d) \(0.01 \mathrm{~V}\)

A solenoid has 2000 turns wound over a length of \(0.30 \mathrm{~m}\). The area of its cross-section is \(1.2 \times 10^{-3} \mathrm{~m}^{2}\). Around its central section, a coil of 300 turns is wound. If an initial current of \(2 \mathrm{~A}\) in the solenoid is reversed in \(0.25 \mathrm{~s}\), then the emf induced in the coil is equal to (a) \(6 \times 10^{-4} \mathrm{~V}\) (b) \(4.8 \times 10^{-2} \mathrm{~V}\) (c) \(6 \times 10^{-2} \mathrm{~V}\) (d) \(48 \mathrm{kV}\)

The two rails of a railway track insulated from each other and the ground are connected to a milli-voltmeter. What is the reading of the \(\mathrm{mV}\), when a train travels at a speed of \(180 \mathrm{kmh}^{-1}\) along the track, given that the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \mathrm{Wbm}^{-2}\) and the rails are separated by \(1 \mathrm{~m}\).(a) \(10^{-2} \mathrm{mV}\) (b) \(10 \mathrm{mV}\) (c) \(10^{2} \mathrm{mV}\) (d) \(1 \mathrm{mV}\)

An axle of truck is \(2.5 \mathrm{~m}\) long. If the truck is moving due north at \(30 \mathrm{~ms}^{-1}\) at a place where the vertical component of the earth's magnetic field is \(90 \mu \mathrm{T}\), the potential difference between the two ends of the axle is (a) \(6.75 \mathrm{mV}\) with west end positive (b) \(6.75 \mathrm{mV}\) with east end positive (c) \(6.75 \mathrm{mV}\) with north end positive (d) \(6.75 \mathrm{mV}\) with south end positive

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 altemating sinusoidal current flows through the ammeter \(A\) with a time period \(T=\frac{2 \pi}{\omega}\). (d) a time varying non-sinosoidal current flows through the ammeter \(A\).

A circular ring of diameter \(20 \mathrm{~cm}\) has a resistance of \(0.01 \Omega\). The charge that will flow through the ring if it is turned from a position perpendicular to a uniform magnetic field of \(2.0 \mathrm{~T}\) to a position parallel to the field is about (a) \(63 \mathrm{C}\) (b) \(0.63 \mathrm{C}\) [c) \(6.3 \mathrm{C}\) (d) \(0.063 \mathrm{C}\)

vA magnet is suspended lengthwise from a spring and while it oscillates, the magnet moves in and out of the coil \(C\) connected to a galvanometer \(G\). Then as the magnet oscillates. (a) \(G\) shows no deflection (b) G shows deflection on one side (c) Deflection of \(G\) to the left and right has constant amplitude [d) Deflection of \(G\) to the left and right has decreasing amplitude

There are two coils \(A\) and \(B\) as shown in 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 \(\quad\) [NCERT Exemplar] (a) there is a constant current in the clockwise direction in \(A\). (b) there is a varying curent in \(A\). (c) there is no current in \(A\). (d) there is a constant current in the counterclockwise direction in \(A\)

The rails of a railway track insulated from each other and the ground are connected to a millivoltmeter. Find the reading of voltmeter, when a train travels with a speed of \(180 \mathrm{~km} / \mathrm{h}\) along the track. Given that the vertical component of earth magnetic field is \(0.2 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^{2}\) and the rails are separated by \(1 \mathrm{~m}\) (a) \(10^{-4} \mathrm{~V}\) (b) \(10^{-2} \mathrm{~V}\) (c) \(10^{-3} \mathrm{~V}\) (d) \(1 \mathrm{~V}\)

The rails of a railway track insulated from each other and the ground are connected to a millivoltmeter. Find the reading of voltmeter, when a train travels with a speed of \(180 \mathrm{~km} / \mathrm{h}\) along the track. Given that the vertical component of earth magnetic field is \(0.2 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^{2}\) and the rails are separated by \(1 \mathrm{~m}\) (a) \(10^{-4} \mathrm{~V}\) (b) \(10^{-2} \mathrm{~V}\) (c) \(10^{-3} \mathrm{~V}\) (d) \(1 \mathrm{~V}\)

A square loop of wire of side \(5 \mathrm{~cm}\) is lying on a horizontal table. An electromagnet above and to one side of the loop is turned on, causing a uniform magnetic field downwards at an angle of \(60^{\circ}\) to the vertical as shown in figure. The magnetic induction is \(0.50 \mathrm{~T}\). The average induced emf in the loop, if the field increases from zero to its final value in \(0.2 \mathrm{~s}\) is (a) \(5.4 \times 10^{-3} \mathrm{~V}\) (b) \(312 \times 10^{-3} \mathrm{~V}\) (c) 0 (d) \(0.25 \times 10^{-3} \mathrm{~V}\)

A coil has an area of \(0.05 \mathrm{~cm}^{2}\) and it has 800 turns. is placed perpendicularly in a magnetic field strength \(4 \times 10^{-5} \mathrm{~Wb} / \mathrm{m}^{2}\), it is rotated through \(90^{\circ} \mathrm{i}\) \(0.1 \mathrm{~s}\). The average emf induced in the coil is (a) \(0.016 \mathrm{~V}\) (b) \(0.032 \mathrm{~V}\) (c) \(0.064 \mathrm{~V}\) (d) \(0.029 \mathrm{~V}\)

Two coils of self-inductances \(2 \mathrm{mH}\) and \(8 \mathrm{mH}\) are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is (a) \(16 \mathrm{mH}\) (b) \(10 \mathrm{mH}\) (c) \(4 \mathrm{mH}\) (d) \(6 \mathrm{mH}\)

A coil is wound on a core of rectangular cross-section. If all the linear dimensions of core are increased by a factor 2 and number of turns per unit length of coil remains same, the self-inductance increases by a factor of (a) 16 (b) 8 (c) 4 (d) 2

Two coils \(X\) and \(Y\) are placed in a circuit such that a current changes by \(2 \mathrm{~A}\) in coil \(X\) and magnetic flux change of \(0.4\) Wb occurs in \(Y\). The value of mutual inductance of the coils is (a) \(0.8 \mathrm{H}\) (b) \(0.2 \mathrm{~Wb}\) (c) \(0.2 \mathrm{H}\) (d) \(5 \mathrm{H}\)

A long solenoid with 15 turns per \(\mathrm{cm}\) has a small loop of area \(2.0 \mathrm{~cm}^{2}\) placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from \(2.0 \mathrm{~A}\) to \(4.0 \mathrm{~A}\) in \(0.1 \mathrm{~s}\), what is the induced emf in the loop while the current is changing? [NCERT] (a) \(7.5 \times 10^{6} \mathrm{~V}\) (b) \(8.5 \times 10^{6} \mathrm{~V}\) (c) \(7.5 \times 10^{4} \mathrm{~V}\) (d) \(7.5 \times 10^{5} \mathrm{~V}\)

Two coils \(X\) and \(Y\) are placed in a circuit such that a current changes by \(2 \mathrm{~A}\) in coil \(X\) and magnetic flux change of \(0.4\) Wb occurs in \(Y\). The value of mutual inductance of the coils is (a) \(0.8 \mathrm{H}\) (b) \(0.2 \mathrm{~Wb}\) (c) \(0.2 \mathrm{H}\) (d) \(5 \mathrm{H}\)

A circular coil of radius \(8.0 \mathrm{~cm}\) and 20 turns is rotated about its vertical diameter with an angular speed of \(50 \mathrm{rad} / \mathrm{s}\) in a uniform horizontal magnetic field of magnitude \(3.0 \times 10^{-2} \mathrm{~T}\). Obtain the maximum and average emf induced in the coil. If the coil forms a closed-loop of resistance \(10 \Omega\), calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. [NCERT] (a) \(2 \mathrm{~W}\) (b) \(0.2 \mathrm{~W}\) [c) \(0.49 \mathrm{~W}\) (d) \(0.018 \mathrm{~W}\)

When current in a coil changes from \(2 \mathrm{~A}\) to \(-2 \mathrm{~A}\) in \(0.05 \mathrm{~s}\), an emf of \(8 \mathrm{~V}\) is induced in the 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) \(0.8 \mathrm{H}\)

When current in a coil changes from \(2 \mathrm{~A}\) to \(-2 \mathrm{~A}\) in \(0.05 \mathrm{~s}\), an emf of \(8 \mathrm{~V}\) is induced in the 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) \(0.8 \mathrm{H}\)

What is self-inductance of a coil which produces \(5 \mathrm{~V}\), when current in it changes from \(3 \mathrm{~A}\) to \(2 \mathrm{~A}\) in one millisecond? (a) \(5000 \mathrm{H}\) (b) \(5 \mathrm{mH}\) (c) \(50 \mathrm{H}\) (d) \(5 \mathrm{H}\)

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 (a) \(l\) and \(A\) increase (b) \(l\) decreases and \(A\) increases (c) \(l\) increases and \(A\) decreases (d) both \(I\) and \(A\) decreases

What is the self-inductance of an air core solenoid \(1 \mathrm{~m}\) long, diameter \(0.05 \mathrm{~m}\), if it has 500 turns? Take \(\pi^{2}=10\) (a) \(3.15 \times 10^{-4} \mathrm{H}\) (b) \(4.8 \times 10^{-4} \mathrm{H}\) (c) \(5 \times 10^{-4} \mathrm{H}\) (d) \(6.25 \times 10^{-4} \mathrm{H}\)

What is the self-inductance of an air core solenoid \(1 \mathrm{~m}\) long, diameter \(0.05 \mathrm{~m}\), if it has 500 turns? Take \(\pi^{2}=10\) (a) \(3.15 \times 10^{-4} \mathrm{H}\) (b) \(4.8 \times 10^{-4} \mathrm{H}\) (c) \(5 \times 10^{-4} \mathrm{H}\) (d) \(6.25 \times 10^{-4} \mathrm{H}\)

A small magnet \(M\) is allowed to fall through a fixed horizontal conducting ring \(R\). Let \(g\) be the acceleration due to gravity. The acceleration of \(M\) will be (a) \(g\) when it is above \(R\) and moving towards \(R\) (c) \(g\) when it is below \(R\) and moving away from \(R\)

A coil of wire of certain radius has 100 turns and a self-inductance of \(15 \mathrm{mH}\). The self-inductance of a second similar coil of 500 turns will be (a) \(75 \mathrm{mH}\) (b) \(375 \mathrm{mH}\) (c) \(15 \mathrm{mH}\) (d) None of these

Two circuits have mutual inductance of \(0.09 \mathrm{H}\). Average emf induced in the secondary by a change of current from 0 to \(20 \mathrm{~A}\) in \(0.006 \mathrm{~s}\) in primary will be (a) \(120 \mathrm{~V}\) (b) \(200 \mathrm{~V}\) (c) \(180 \mathrm{~V}\) (d) \(300 \mathrm{~V}\)

An emf is produced in a coil, which is not connected to an external voltage source. This can be due to [NCERT Exemplar] (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 external spatially varying magnetic field, which does not change with time

If number of turns in primary and secondary coils is increased to two times each, the mutual inductance (a) becomes 4 times (b) becomes 2 times (c) becomes \(1 / 4\) times (d) remains unchanged

The expression for magnetic induction inside a solenoid of length \(L\), carrying a current \(i\) and having \(N\) number of turns is (a) \(\frac{\mu_{0}}{4 \pi} \frac{N}{L} i\) (b) \(\mu_{0} N U\) (c) \(\frac{\mu_{0}}{4 \pi} N L\) (d) \(\mu_{0} \frac{N^{2}}{L} i\)

A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because \(\quad\) [NCERT Exemplar](a) the magnetic field is constant (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) there is a constant magnetic field in the perpendicular (to the plane of the coill direction

A current of \(10 \mathrm{~A}\) in the primary coil of a circuit is reduced to zero. If the coefficient of mutual inductance is \(3 \mathrm{H}\) and emf induced in secondary coil is \(30 \mathrm{kV}\), time taken for the change of current is (a) \(10^{3} \mathrm{~s}\) (b) \(10^{2} \mathrm{~s}\) (c) \(10^{-3} \mathrm{~s}\) (d) \(10^{-2} \mathrm{~s}\)

A \(1.0 \mathrm{~m}\) long metallic rod is rotated with an angular frequency of \(400 \mathrm{rad} / \mathrm{s}\) about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. \(\mathrm{A}\) constant and uniform magnetic field of \(0.5\) 'T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring. [NCERT] (a) \(95 \mathrm{~V}\) (b) \(85 \mathrm{~V}\) (al ian y

A coil of inductance \(0.2 \mathrm{H}\) and \(1.0 \mathrm{~W}\) resistance is connected to a \(90 \mathrm{~V}\) source. At what rate will the current in the coil grow at the instant the coil is connected to the source? (a) \(450 \mathrm{As}^{-1}\) (b) \(4.5 \mathrm{As}^{-1}\) (c) \(45 \mathrm{As}^{-1}\) (d) \(0.45 \mathrm{As}^{-1}\)

A 110 volt \(\mathrm{AC}\) is connected to a transformer of ratio 10\. If resistance of secondary is \(550 \Omega\), current through secondary will be (a) \(10 \mathrm{~A}\) (b) \(2 \mathrm{~A}\) [c) zero (d) \(55 \mathrm{~A}\)

If the rms current in a \(50 \mathrm{~Hz}\) AC circuit is \(5 \mathrm{~A}\), the value of the current \(1 / 300\) seconds after its value \mathrm{\\{} b e c o m e s ~ z e r o ~ i s ~ [NCERT Exemplar] (a) \(5 \sqrt{2} \mathrm{~A}\) (b) \(5 \sqrt{3 / 2} \mathrm{~A}\) (c) \(5 / 6 \mathrm{~A}\) (d) \(5 / \sqrt{2} \mathrm{~A}\)

Two inductors of inductance \(L\) each are connected in series with opposite magnetic fluxes. What is the resultant inductance? (Ignore mutual inductance) (a) Zero (b) \(\underline{L}\) (c) \(2 L\) (d) \(3 L\)

A circular coil of diameter \(21 \mathrm{~cm}\) is held in a magnetic field of induction \(10^{-4} \mathrm{~T}\). The magnitude of magnetic flux linked with the coil when the plane of the coil makes an angle of \(30^{\circ}\) with the field is (a) \(3.1 \times 10^{-6} \mathrm{~Wb}\) (b) \(1.414 \mathrm{~Wb}\) (c) \(1.73 \times 10^{-6} \mathrm{~Wb}\) (d) \(14.14 \mathrm{~Wb}\)

The number of turns of primary and secondary coils of a transformer are 5 and 10 respectively and mutual inductance of the transformer is \(25 \mathrm{H}\). Now, number of turns in primary and secondary are made 10 and 5 respectively. Mutual inductance of transformer will be (a) \(25 \mathrm{H}\) (b) \(12.5 \mathrm{H}\) [c) \(50 \mathrm{H}\) (d) 6. \(25 \mathrm{H}\)

A uniformly wound solenoidal coil of self-inductance \(1.8 \times 10^{-4} \mathrm{H}\) and resistance \(6 \Omega\) is broken up into two identical coils. These identical coils are then connected in parallel across a \(12 \mathrm{~V}\) battery of negligible resistance. The time constant of the current in the circuit and the steady state current through battery is (a) \(3 \times 10^{-5} \mathrm{~s}, 8 \mathrm{~A}\) (b) \(1.5 \times 10^{-5}\) s, \(8 \mathrm{~A}\) (c) \(0.75 \times 10^{-4} s, 4 \mathrm{~A}\) (d) \(6 \times 10^{-5} \mathrm{~s}, 2 \mathrm{~A}\)

The dimension of magnetic flux is (a) \(\left[\mathrm{M}^{2} \mathrm{~L}^{2} \mathrm{~T}^{-2} \mathrm{~A}\right]\) (b) \(\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\) (c) \(\left[\mathrm{ML}^{-2} \mathrm{~A}^{-2} \mathrm{~T}^{-1}\right]\) (d) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{2} \mathrm{~T}^{-1} \mathrm{~A}^{2}\right]\)