Physics · Textbook solutions

Electromagnetic Induction

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 36 questions

12. Electromagnetic Induction — worked examples

11 q

Solved Examples

Worked · 11
  1. Solved Ex.12.1
    A coil consists of 400 turns of wire. Each turn is a square of side d=20d = 20 cm. A uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.8 s, what is the magnitude of induced emf in the coil while the field is changing?
  2. Solved Ex.12.2
    A long solenoid S, as shown in the figure has 200 turns/cm and carries a current ii of 1.4 A. The diameter DD of the solenoid is 3 cm. A coil C, having 100 turns and diameter dd of 2 cm is kept coaxial to the solenoid. The current in the solenoid is decreased steadily to zero in 20 ms. Calculate the magnitude of emf induced in the coil C when the current in the solenoid is changing.
  3. Solved Ex.12.3
    A rotating armature of a simple generator consists of rectangular section DABC of a conducting wire as shown in the figure, to which connections are made through sliding contacts. The armature is rotated at 1500 rpm in the magnetic field (B⃗)(\vec{B}) of 0.5 N/A.m. Determine the induced emf between the terminals P and Q of the generator at the instant shown in the adjoining figure.
  4. Solved Ex.12.4
    A conducting loop of area 1 m2^2 is placed normal to uniform magnetic field 3 Wb/m2^2. If the magnetic field is uniformly reduced to 1 Wb/m2^2 in a time of 0.5 s, calculate the induced emf produced in the loop.
  5. Solved Ex.12.5
    Derive an expression for the self-inductance of a toroid of circular cross-section of radius rr and major radius RR. Calculate the self inductance (L)(L) of toroid for major radius (R)=15(R) = 15 cm, cross-section of toroid having radius (r)=2.0(r) = 2.0 cm and the number of turns (n)=1200(n) = 1200.
  6. Solved Ex.12.6
    Consider a uniformly wound solenoid having NN turns and length ll. The core of the solenoid is air. Find the inductance of the solenoid of N=200N = 200, l=20l = 20 cm and cross-sectional area, A=5A = 5 cm2^2. Calculate the induced emf eLe_{\mathrm{L}}, if the current flowing through the solenoid decreases at a rate of 60 A/s.
  7. Solved Ex.12.7
    The self-inductance of a closely wound coil of 200 turns is 10 mH. Determine the value of magnetic flux through the cross-section of the coil when the current passing through the coil is 4 mA.
  8. Solved Ex.12.8
    Calculate the self-inductance of a coaxial cable of length ll and carrying a current II. The current flows down the inner cylinder with radius aa, and flows out of the outer cylinder with radius bb.
  9. Solved Ex.12.9
    Mutual inductance of the wireless charging system. In a wireless battery charger, the base unit can be imagined as a solenoid (coil B) of length ll with NBN_{\mathrm{B}} turns, carrying a current iBi_{\mathrm{B}} and having a cross-section area AA. The handle coil (coil HH) has NHN_{\mathrm{H}} turns and surrounds the base solenoid (coil B) completely. The base unit is designed to hold the handle of the charging unit. The handle has a cylindrical hole so that it fits loosely over a matching cylinder on the base unit. When the handle is placed on the base, the current flowing in coil BB induces a current in the coil HH. Thus, the induced current in the coil HH is used to charge the battery housed in the handle.
  10. Solved Ex.12.10
    Two coils having self inductances L1=75L_1 = 75 mH and L2=55L_2 = 55 mH are coupled with each other. The coefficient of coupling (K)(K) is 0.75 calculate the mutual inductance (M)(M) of the two coils.
  11. Solved Ex.12.11
    The mutual inductance (M)(M) of the two coils is given as 1.5 H. The self inductances of the coils are : L1=5L_1 = 5 H, L2=4L_2 = 4 H. Find the coefficient of coupling beween the coils.

Exercises

25 q

Choose the correct option

Practice · 5
  1. Choose the correct option.
    Ex Q.1 (i)
    A circular coil of 100 turns with a cross-sectional area (A) of 1 m2^2 is kept with its plane perpendicular to the magnetic field (B) of 1 T. What is the magnetic flux linkage with the coil?
    1. A.
      1 Wb
    2. B.
      100 Wb
    3. C.
      50 Wb
    4. D.
      200 Wb
  2. Ex Q.1 (ii)
    A conductor rod of length (l) is moving with velocity (v) in a direction normal to a uniform magnetic field (B). What will be the magnitude of induced emf produced between the ends of the moving conductor?
    1. A.
      BLvBL\mathrm{v}
    2. B.
      BLv2BL\mathrm{v}^2
    3. C.
      12Blv\dfrac{1}{2} Bl\mathrm{v}
    4. D.
      2Blv\dfrac{2Bl}{\mathrm{v}}
  3. Ex Q.1 (iii)
    Two inductor coils with inductance 10 mH and 20 mH are connected in series. What is the resultant inductance of the combination of the two coils?
    1. A.
      20 mH
    2. B.
      30 mH
    3. C.
      10 mH
    4. D.
      203\dfrac{20}{3} mH
  4. Ex Q.1 (iv)
    A current through a coil of self inductance 10 mH increases from 0 to 1 A in 0.1 s. What is the induced emf in the coil?
    1. A.
      0.1 V
    2. B.
      1 V
    3. C.
      10 V
    4. D.
      0.01 V
  5. Ex Q.1 (v)
    What is the energy required to build up a current of 1 A in an inductor of 20 mH?
    1. A.
      10 mJ
    2. B.
      20 mJ
    3. C.
      20 J
    4. D.
      10 J

Answer in brief

Practice · 5
  1. Answer in brief.
    Ex Q.2 (i)
    What do you mean by electromagnetic induction? State Faraday's law of induction.
  2. Ex Q.2 (ii)
    State and explain Lenz's law in the light of principle of conservation of energy.
  3. Ex Q.2 (iii)
    What are eddy currents? State applications of eddy currents.
  4. Ex Q.2 (iv)
    If the copper disc of a pendulum swings between the poles of a magnet, the pendulum comes to rest very quickly. Explain the reason. What happens to the mechanical energy of the pendulum?
  5. Ex Q.2 (v)
    Explain why the inductance of two coils connected in parallel is less than the inductance of either coil.

Solve the following

Practice · 15
  1. Ex Q.3
    In a Faraday disc dynamo, a metal disc of radius RR rotates with an angular velocity ω\omega about an axis perpendicular to the plane of the disc and passing through its centre. The disc is placed in a magnetic field BB acting perpendicular to the plane of the disc. Determine the induced emf between the rim and the axis of the disc.
  2. Ex Q.4
    A horizontal wire 20 m long extending from east to west is falling with a velocity of 10 m/s normal to the Earth's magnetic field of 0.5×10−40.5 \times 10^{-4} T. What is the value of induced emf in the wire?
  3. Ex Q.5
    A metal disc is made to spin at 20 revolutions per second about an axis passing through its centre and normal to its plane. The disc has a radius of 30 cm and spins in a uniform magnetic field of 0.20 T, which is parallel to the axis of rotation. Calculate (a) The area swept out per second by the radius of the disc, (b) The flux cut per second by a radius of the disc, (c) The induced emf in the disc.
  4. Ex Q.6
    A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 10 A in 0.2 s, what is the change of flux linkage with the other coil?
  5. Ex Q.7
    A long solenoid has 1500 turns/m. A coil C having cross sectional area 25 cm2^2 and 150 turns (Nc)(N_{\mathrm{c}}) is wound tightly around the centre of the solenoid. If a current of 3.0 A flows through the solenoid, calculate : (a) the magnetic flux density at the centre of the solenoid, (b) the flux linkage in the coil C, (c) the average emf induced in coil C if the direction of the current in the solenoid is reversed in a time of 0.5 s. (μ0=4π×10−7 T.m/A)(\mu_0 = 4\pi \times 10^{-7}\ T.m/A)
  6. Ex Q.8
    A search coil having 2000 turns with area 1.5 cm2^2 is placed in a magnetic field of 0.60 T. The coil is moved rapidly out of the field in a time of 0.2 second. Calculate the induced emf across the search coil.
  7. Ex Q.9
    An aircraft of wing span of 50 m flies horizontally in earth's magnetic field of 6×10−56 \times 10^{-5} T at a speed of 400 m/s. Calculate the emf generated between the tips of the wings of the aircraft.
  8. Ex Q.10
    A stiff semi-circular wire of radius RR is rotated in a uniform magnetic field BB about an axis passing through its ends. If the frequency of rotation of the wire is ff, calculate the amplitude of the alternating emf induced in the wire.
  9. Ex Q.11
    Calculate the value of induced emf between the ends of an axle of a railway carriage 1.75 m long traveling on level ground with a uniform velocity of 50 km per hour. The vertical component of Earth's magnetic field (Bv)(B_{\mathrm{v}}) is given to be 5×10−55 \times 10^{-5} T.
  10. Ex Q.12
    The value of mutual inductance of two coils is 10 mH. If the current in one of the coil changes from 5 A to 1 A in 0.2 s, calculate the value of emf induced in the other coil.
  11. Ex Q.13
    An emf of 96.0 mV is induced in the windings of a coil when the current in a nearby coil is increasing at the rate of 1.20 A/s. What is the mutual inductance (M)(M) of the two coils?
  12. Ex Q.14
    A long solenoid of length ll, cross-sectional area AA and having N1N_1 turns (primary coil), has a small coil of N2N_2 turns (secondary coil) wound about its centre. Determine the Mutual inductance (M)(M) of the two coils.
  13. Ex Q.15
    The primary and secondary coil of a transformer each have an inductance of 200×10−6200 \times 10^{-6} H. The mutual inductance (M)(M) between the windings is 4×10−64 \times 10^{-6} H. What percentage of the flux from one coil reaches the other?
  14. Ex Q.16
    A toroidal ring, having 100 turns per cm of a thin wire is wound on a non-magnetic metal rod of length 1 m and diameter 1 cm. If the permeability of bar is equal to that of free space (μ0)(\mu_0), calculate the magnetic field inside the bar (B)(B) when the current (i)(i) circulating through the turns is 1 A. Also determine the self-inductance (L)(L) of the coil.
  15. Ex Q.17
    A uniform magnetic field B(t)B(t), pointing upward fills a circular region of radius, ss in horizontal plane. If BB is changing with time, find the induced electric field. [Hint : Part of Maxwell's equation, applied to a time varying magnetic flux, leads us to the equation ∮E⃗⋅dl→=−dϕmdt\oint \vec{E} \cdot \overrightarrow{\mathrm{d}l} = \dfrac{-\mathrm{d}\phi_m}{\mathrm{d}t}, where E⃗\vec{E} is the electric field induced when the magnetic flux changes at the rate of dϕmdt\dfrac{\mathrm{d}\phi_m}{\mathrm{d}t}.]