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Physics · Textbook solutions

Electromagnetic Induction

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 18 questions

Worked Examples

10 q

Solved Examples

Worked · 10
  1. Eg 6.1
    Consider Experiment 6.2. (a) What would you do to obtain a large deflection of the galvanometer? (b) How would you demonstrate the presence of an induced current in the absence of a galvanometer?
  2. Eg 6.2
    A square loop of side 10 cm10\,\text{cm} and resistance 0.5 Ω0.5\,\Omega is placed vertically in the east-west plane. A uniform magnetic field of 0.10 T0.10\,\text{T} is set up across the plane in the north-east direction. The magnetic field is decreased to zero in 0.70 s0.70\,\text{s} at a steady rate. Determine the magnitudes of induced emf and current during this time-interval.
  3. Eg 6.3
    A circular coil of radius 10 cm10\,\text{cm}, 500 turns and resistance 2 Ω2\,\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∘180^\circ in 0.25 s0.25\,\text{s}. Estimate the magnitudes of the emf and current induced in the coil. Horizontal component of the earth's magnetic field at the place is 3.0×10−5 T3.0 \times 10^{-5}\,\text{T}.
  4. Eg 6.4
    Figure 6.7 shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normal to the plane of the loop away from the reader. Determine the direction of induced current in each loop using Lenz's law.
  5. Eg 6.5
    (a) A closed loop is held stationary in the magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets? (b) A closed loop moves normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop (i) when it is wholly inside the region between the capacitor plates (ii) when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop. (c) A rectangular loop and a circular loop are moving out of a uniform magnetic field region (Fig. 6.8) to a field-free region with a constant velocity v\mathbf{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. (d) Predict the polarity of the capacitor in the situation described by Fig. 6.9.
  6. Eg 6.6
    A metallic rod of 1 m1\,\text{m} length is rotated with a frequency of 50 rev/s50\,\text{rev/s}, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius 1 m1\,\text{m}, about an axis passing through the centre and perpendicular to the plane of the ring (Fig. 6.11). A constant and uniform magnetic field of 1 T1\,\text{T} parallel to the axis is present everywhere. What is the emf between the centre and the metallic ring?
  7. Eg 6.7
    A wheel with 10 metallic spokes each 0.5 m0.5\,\text{m} long is rotated with a speed of 120 rev/min120\,\text{rev/min} in a plane normal to the horizontal component of earth's magnetic field HEH_E at a place. If HE=0.4 GH_E = 0.4\,\text{G} at the place, what is the induced emf between the axle and the rim of the wheel? Note that 1 G=10−4 T1\,\text{G} = 10^{-4}\,\text{T}.
  8. Eg 6.8
    Two concentric circular coils, one of small radius r1r_1 and the other of large radius r2r_2, such that r1≪r2r_1 \ll r_2, are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangement.
  9. Eg 6.9
    (a) Obtain the expression for the magnetic energy stored in a solenoid in terms of magnetic field BB, area AA and length ll of the solenoid. (b) How does this magnetic energy compare with the electrostatic energy stored in a capacitor?
  10. Eg 6.10
    Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a 100 turn coil of area 0.10 m20.10\,\text{m}^2. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of 0.01 T0.01\,\text{T} perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil?

Exercises

8 q
  1. Ex 6.1
    Predict the direction of induced current in the situations described by the following Figs. 6.15(a) to (f).
  2. Ex 6.2
    Use Lenz's law to determine the direction of induced current in the situations described by Fig. 6.16: (a) A wire of irregular shape turning into a circular shape; (b) A circular loop being deformed into a narrow straight wire.
  3. Ex 6.3
    A long solenoid with 15 turns per cm has a small loop of area 2.0 cm22.0\,\text{cm}^2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A2.0\,\text{A} to 4.0 A4.0\,\text{A} in 0.1 s0.1\,\text{s}, what is the induced emf in the loop while the current is changing?
  4. Ex 6.4
    A rectangular wire loop of sides 8 cm8\,\text{cm} and 2 cm2\,\text{cm} with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T0.3\,\text{T} directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s−11\,\text{cm s}^{-1} in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?
  5. Ex 6.5
    A 1.0 m1.0\,\text{m} long metallic rod is rotated with an angular frequency of 400 rad s−1400\,\text{rad s}^{-1} 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. A constant and uniform magnetic field of 0.5 T0.5\,\text{T} parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
  6. Ex 6.6
    A horizontal straight wire 10 m10\,\text{m} long extending from east to west is falling with a speed of 5.0 m s−15.0\,\text{m s}^{-1}, at right angles to the horizontal component of the earth's magnetic field, 0.30×10−4 Wb m−20.30 \times 10^{-4}\,\text{Wb m}^{-2}. (a) What is the instantaneous value of the emf induced in the wire? (b) What is the direction of the emf? (c) Which end of the wire is at the higher electrical potential?
  7. Ex 6.7
    Current in a circuit falls from 5.0 A5.0\,\text{A} to 0.0 A0.0\,\text{A} in 0.1 s0.1\,\text{s}. If an average emf of 200 V200\,\text{V} induced, give an estimate of the self-inductance of the circuit.
  8. Ex 6.8
    A pair of adjacent coils has a mutual inductance of 1.5 H1.5\,\text{H}. If the current in one coil changes from 0 to 20 A20\,\text{A} in 0.5 s0.5\,\text{s}, what is the change of flux linkage with the other coil?