44Electromagnetic induction

📚
ELECTROMAGNETIC INDUCTION
▢ Magnetic Flux:
❖ Symbol: \(\phi\)
❖ Definition: Magnetic field lines passing normally through a surface

Table 1: Flux Formulae

Quantity
Formula
Flux through one turn
\(\phi=BA\cos\theta\)
Flux linkage for \(N\) turns
\(N\phi=NBA\cos\theta\)
Flux linkage and self-inductance
\(N\phi=LI\)
❖ Symbols:
  • •
    \(B\) = magnetic field
  • •
    \(A\) = area
  • •
    \(\theta\) = angle between \(B\) and area vector
  • •
    \(N\) = number of turns
  • •
    \(L\) = self inductance
  • •
    \(I\) = current
▢ Induced EMF:
❖ Law: Faraday-Lenz law

Table 1: Induced EMF Formulae

Condition
Formula
General
\(E=-\frac{d\phi}{dt}\)
Using flux linkage
\(E=-\frac{d(N\phi)}{dt}\)
Using self inductance
\(E=-L\frac{dI}{dt}\)
Changing area / field / angle
\(E=-\frac{d(NBA\cos\theta)}{dt}\)
Rotating coil, \(\theta=\omega t\)
\(E=-\frac{d(NBA\cos\omega t)}{dt}\)
Rotating coil result
\(E=NBA\omega\sin\omega t\)
Maximum induced emf
\(E_0=NBA\omega\)
❖ Negative Sign: Shows Lenz's law: induced emf opposes change in magnetic flux
▢ Induced EMF in Various Cases:
❖ Conducting Rod in Uniform Magnetic Field:

Table 1: Motional EMF in Straight Rod

Condition
Formula
Vector form
\(E=\vec B\cdot(\vec l\times\vec v)\)
General
\(E=Blv\sin\theta\)
\(B,l,v\) mutually perpendicular
\(E=Blv\)
◉ Symbols:
  • •
    \(l\) = length of rod
  • •
    \(v\) = velocity of rod
  • •
    \(B\) = magnetic field
  • •
    \(\theta\) = angle between \(\vec B\) and \((\vec l\times\vec v)\)
❖ Conducting Rod Rotating in Uniform Magnetic Field:

Table 1: Rotating Rod EMF

Condition
Formula
Rod of length \(l\), angular velocity \(\omega\)
\(E=\frac{1}{2}Bl^2\omega\)
Using \(v=l\omega\)
\(E=\frac{Blv}{2}\)
Using frequency \(f\)
\(E=B\pi l^2f\)
Using swept area \(A=\pi l^2\)
\(E=BAf\)
▢ Self Inductance:
❖ Definition: Property of a coil by which change of current in it induces emf in the same coil

Table 1: Self Inductance Formulae

System
Self inductance
General
\(L=\frac{N\phi}{I}\)
Circular coil
\(L=\frac{\mu_0N^2A}{2r}\)
Solenoid of length \(l\)
\(L=\frac{\mu_0N^2A}{l}\)
❖ Induced EMF: \(E=-L\frac{dI}{dt}\)
▢ Mutual Inductance:
❖ Definition: Property by which change of current in one coil induces emf in nearby coil
❖ _*table:
    ❖ Induced EMF: \(E=-M\frac{dI}{dt}\)
    ▢ Energy Stored in Inductor:

    Table 1: Energy Stored

    Condition
    Formula
    In self-inductor
    \(U=\frac{1}{2}LI^2\)
    Using mutual inductance notation
    \(U=\frac{1}{2}MI^2\)
    ▢ Transformer:
    ❖ Definition: Device used to change AC voltage using mutual induction

    Table 1: Ideal Transformer Relations

    Relation
    Formula
    Voltage ratio
    \(\frac{E_s}{E_p}=\frac{N_s}{N_p}\)
    Inductance ratio
    \(\frac{E_s}{E_p}=\sqrt{\frac{L_s}{L_p}}\)
    Current ratio
    \(\frac{E_s}{E_p}=\frac{I_p}{I_s}\)
    Transformation ratio
    \(K=\frac{E_s}{E_p}=\frac{N_s}{N_p}=\sqrt{\frac{L_s}{L_p}}=\frac{I_p}{I_s}\)
    ❖ Symbols:
    • •
      \(E_p\) = primary emf / voltage
    • •
      \(E_s\) = secondary emf / voltage
    • •
      \(N_p\) = number of primary turns
    • •
      \(N_s\) = number of secondary turns
    • •
      \(I_p\) = primary current
    • •
      \(I_s\) = secondary current
    • •
      \(L_p\) = self inductance of primary coil
    • •
      \(L_s\) = self inductance of secondary coil
    • •
      \(K\) = transformation ratio
    ❖ Types:

    Table 1: Transformer Types

    Type
    Condition
    Effect
    Step-up transformer
    \(N_s>N_p\), \(K>1\)
    Increases voltage, decreases current
    Step-down transformer
    \(N_s
    Decreases voltage, increases current
    ▢ High-Yield Recall:

    Table 1: Electromagnetic Induction One-Liners

    Fact
    Formula
    Flux through one turn
    \(\phi=BA\cos\theta\)
    Flux linkage
    \(N\phi=NBA\cos\theta=LI\)
    Faraday's law
    \(E=-\frac{d\phi}{dt}\)
    Self-induced emf
    \(E=-L\frac{dI}{dt}\)
    Rotating coil emf
    \(E=NBA\omega\sin\omega t\)
    Maximum emf
    \(E_0=NBA\omega\)
    Moving rod emf
    \(E=Blv\sin\theta\)
    Moving rod perpendicular case
    \(E=Blv\)
    Rotating rod emf
    \(E=\frac{1}{2}Bl^2\omega\)
    Rotating rod using frequency
    \(E=BAf\)
    Circular coil self inductance
    \(L=\frac{\mu_0N^2A}{2r}\)
    Solenoid self inductance
    \(L=\frac{\mu_0N^2A}{l}\)
    Circular coil mutual inductance
    \(M=\frac{\mu_0N_1N_2A}{2r}\)
    Solenoid mutual inductance
    \(M=\frac{\mu_0N_1N_2A}{l}\)
    Energy in inductor
    \(U=\frac{1}{2}LI^2\)
    Transformer ratio
    \(K=\frac{E_s}{E_p}=\frac{N_s}{N_p}=\frac{I_p}{I_s}\)
    Transformer inductance relation
    \(\frac{E_s}{E_p}=\sqrt{\frac{L_s}{L_p}}\)
    Q1.
    In a metal block, eddy current is due to
    📅CEE MBBS 2025
    Q2.
    SI unit of magnetic flux is:
    📅CEE Nursing 2024
    Q3.
    Unit of self inductance is:
    📅CEE MBBS 2024B
    Q4.
    A coil of area 10 m² is placed perpendicular to a uniform magnetic field of 0.1 T. The magnetic flux linked with the coil is:
    📅CEE MBBS 2024a
    Q5.
    A step-down transformer has primary voltage 200 V and 5 A current. If the ratio of turns is 1:3, then secondary voltage will be:
    📅CEE MBBS 2024a
    Q6.
    Current of a 12 V battery having 3 Ω resistance and 4 H inductance initially at t = 0 is:
    📅CEE MBBS 2024a
    Q7.
    Current in a circuit falls steadily from 5.0 A to 0.0 A in 10 ms. If the self-inductance of the circuit is 10 mH, the induced emf is:
    📅CEE MBBS 2023
    Q8.
    Self-inductance of a coil is independent of:
    📅CEE MBBS 2022
    Q9.
    If the rate of change of current is 1 A/s, the induced emf in a coil is equal to its:
    📅CEE MBBS 2021
    Q10.
    A coil of area 0.04 m² having 1000 turns is suspended perpendicular to a magnetic field of magnitude \(5 imes10^{-5}\, ext{Wb/m}^2\). If rotated through 180° in 0.1 s, the average induced emf is:
    📅CEE MBBS 2021
    Q11.
    In an inductor of self inductance L = 2 mH, I changes with time according to the relation I = t²e⁻ᵗ. The time at which the emf becomes zero is:
    📅CEE BDS 2024
    Q12.
    Mutual inductance of two coils is 5mH. The current changes from 3A to 2 A in 0.01 sec, then the emf produced is
    📅BP 2014
    Q13.
    Eddy currents are induced within a bulk conductor principally by:
    📅BP 2013
    Q14.
    A bar magnet falls vertically toward a horizontal conducting plate. Neglecting air resistance, how is its downward acceleration affected by induced eddy currents?
    📅BP 2013/ 2016
    Q15.
    The core of transformer is made up to:
    📅BP 2011
    Q16.
    Two coils are at fixed locations. When coil I has no current in coil 2 increases at the 15.0 A/s, the emf in coil I is 25 mV, when coil 2 has no current and coil I has a current of 3.6 A, the flux linkage in coil 2 is ?
    Q17.
    In a dynamo, voltage is 6V. current 0.5A. What is the power generated?
    📅IOM 2013
    Q18.
    A uniform metal disc of radius R lies in XY - plane and rotates with uniform angular velocity ω about the Z - axis. If a constant field B is parallel to the Z- axis, the total induced EMF between the center and the rim of the disc is equal to:
    📅KU 2011
    Q19.
    A transformer is designed to work from 220 volts AC mains to give a supply at 11 volts AC to run a device. The primary coil has 480 turns. The number of turns in the secondary coil should be-
    Q20.
    A straight conducting rod of length 0.4 m is moving perpendicular to magnetic flux density of 0.9 Wb/m² with a speed of 7m/s. The emf developed in the rod is :
    📅IE 2014
    Q21.
    A charged particle undergoes uniform circular motion in a constant magnetic field. Which vector quantity has zero average over one complete orbit?
    📅IE 2013
    Q22.
    A stationary closed conducting coil is kept in a magnetic field that is spatially nonuniform but does not change with time. What is induced in the coil?
    📅BP 2014
    Q23.
    When a motor car starts, the brightness of bulb is decreased then after some time its brightness increases due to:
    📅BP 2014
    Q24.
    Lenz's law is a consequence of the law of conservation of
    📅MOE 09/ KU 2017
    Q25.
    Two parallel conductors carrying current in same direction.
    📅KU 08
    Q26.
    A transformer is employed to reduce 220 V to 11 V. The primary coil draws a current of 5 A and secondary draws 90 A. The efficiency of transformer is
    Q27.
    The two parallel wires carrying current in opposite direction
    📅Bangladesh Emb
    Q28.
    An electron enters a field of 1 Tesla with a velocity of 1000 m/s parallel the field. The force experienced by it is
    📅 Bangladesh Emb
    Q29.
    A freely falling magnet passes lengthwise through a horizontal circular coil of conductor. The correct expression relating the acceleration of the falling magnet a and the acceleration due to gravity (g) is
    📅MOE 2054, BP 2014, KU 2013
    Q30.
    Laminated cores are used in a transformer in order to:
    📅MOE
    Q31.
    If the flux associated with a coil varies a the rate of 1 Weber per minute, the induced emf is
    📅MOE 2000
    Q32.
    The two conductors carrying current in same direction attract each other due to the existence of:
    📅MOE 2063
    Q33.
    Transformer is a device to
    📅IOM 1995
    Q34.
    A rectangular current loop lies in the same plane as a long straight current-carrying wire. Its closest side is parallel to the wire and carries current in the same direction. What is the net force on the loop?
    📅IE-08
    Q35.
    If a wire of resistance 10Ω is moving in a non-uniform magnetic field in such a way that decrease in K.E. is 10J/s. What is current induced in wire ?
    📅IE-06
    Q36.
    A rectangular current loop lies in the same plane as a long straight current-carrying wire. Its closest side is parallel to the wire and carries current in the same direction. What is the net force on the loop?
    Q37.
    The magnetic resonance imaging (MRI) based on; the phenomenon of:
    📅BPKIHS-08
    Q38.
    An electron travels perpendicular to a uniform magnetic field of magnitude \(B\) at speed \(v\), in a circular path of radius \(r\). If electron mass is \(m\) and charge magnitude is \(e\), then \(r\) is:
    📅BPKIHS 02
    Q39.
    A single-turn circular coil of radius \(0.1\,\mathrm m\), carrying \(10\,\mathrm A\), has its plane parallel to a uniform \(0.1\,\mathrm T\) magnetic field. What is its torque magnitude?
    📅BPKIHS 05
    Q40.
    The magnetic field at a point at a large distance r at the axis of a current carrying circular coil of small radius is proportional to
    📅BPKIHS-06
    Q41.
    A circular coil is moving parallel to magnetic field then value of emf is
    📅IE-02
    Q42.
    The phenomenon of acquiring temporary electrification under the influence of a charged body is called
    📅IOM 98
    Q43.
    The energy per unit volume in a magnetic field is given by:
    📅MOE 2060
    Q44.
    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.
    Q45.
    A helicopter rises vertically at \(10\,\mathrm{m/s}\). Its nose-to-tail conducting length of \(10\,\mathrm m\) is oriented along \(\mathbf v\times\mathbf B\), with the horizontal Earth magnetic field \(B=1.5\times10^{-3}\,\mathrm T\). What is the motional potential difference?
    Q46.
    A magnetic flux 5 x \(10^{-5}\) Wb is passing through a coil of 1000 turns. If the e.m.f induced through coil is 5 volt, the time interval will be
    Q47.
    A coil of cross-sectional area \(10^{-2}\)\(m^{2}\) is placed in the magnetic field, which changes to \(4x10^{-3}\)Wb/\(m^{2}\) within 5 sec. What will be induced emf across the coil?
    Q48.
    A coil having 500 square loops each of side 10cm is placed normal to a magnetic field which increases at the rate of 1 Wb/\(m^{2}\)s. The induced e.m.f is
    Q49.
    A long straight wire runs horizontally from A on the left to B on the right. Its current increases from A to B. A small closed loop lies in the plane of the page below the wire. Viewed looking at the page, what is the induced current direction?
    Q50.
    A coil of area \(100cm^{2}\) having 50 turns is perpendicular to a magnetic field of intensity 0.02 weber/m². The resistance of the coil is 2ohm. If it is removed in 1sec from the magnetic field, the induced charge produced is
    Q51.
    The current passing through a choke coil of 5H is decreasing at the rate of \(2As^{-1}\). The emf developed across the coil is
    Q52.
    A coil of mean area \(500cm^{2}\) and having 1000 turns is held perpendicular to a uniform field of 0.4 gauss. The coil is turned through 180° in 1/10 second, the induced e.m.f. is
    Q53.
    A circular coil and a bar magnet placed nearby are mode to move in the same direction. If the coil covers a distance of 1m in 0.5sec and the magnet a distance of 2m in 1sec, the induced e.m.f. produced in the coil is
    Q54.
    Two solenoids of same cross-sectional area have their lengths and number of turns in the ratio of 1:2. The ratio of self-inductance of two solenoids is
    Q55.
    Two coils, a primary of 100 turns and a secondary of 20 turns are wound over an iron core of length 20cm and cross-section of 2cm radius. If \(μ_{r}\) = 800, then coefficient of mutual induction is approximately
    Q56.
    Two coils A and B have 200 and 400 turns. A current of 1 A in A links flux per turn \(10^{-3}\,\mathrm{Wb}\) through A and \(0.8\times10^{-3}\,\mathrm{Wb}\) through B. Find the ratio self-inductance of A to mutual inductance of A and B.
    Q57.
    Magnetic flux φ in Weber in a closed circuit of resistance 10Ω varies with time t (sec) as φ = \(6t^{2}\) - 5t + 1. The magnitude of induced current at t = 0.25s is
    Q58.
    When a wire loop is rotated in a magnetic field, the direction of induced e.m.f. changes in every
    📅IE 2008
    Q59.
    Two identical, tightly coupled windings are connected in series opposition on the same core. If their mutual inductance equals the self-inductance of either winding, their equivalent self-inductance is:
    Q60.
    A magnet is moved towards a coil through a certain distance slowly in one case and quickly in second case. The emf induced is
    Q61.
    A coil of area A and resistance R is kept inside a uniform magnetic field B normal to plane of coil, then charge induced in the coil if it is revolved end for end is
    Q62.
    The current in an inductor decreases linearly from 10 A to zero in 2 s. If its self-inductance is 5 H, what is the magnitude of the change in its total flux linkage?
    Q63.
    A circular loop of wire of radius \(r\) lies in a uniform magnetic field \(B\) perpendicular to its plane. It is reshaped into a square of the same wire length over time \(t\), maintaining its orientation. What is the magnitude of the average induced emf?
    Q64.
    A coil and an incandescent bulb are connected in series across an ideal DC supply. After a soft-iron core is fully inserted into the coil and all transient effects have ended, what happens to the bulb brightness?
    Q65.
    The number of turns of primary and secondary coils of transformer are 5 and 10 respectively and mutual inductance of the transformer is 25H. Now number of turns in primary and secondary are 10 and 5 respectively. Mutual inductance of the transformer will be
    Q66.
    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 coll remains same, then self-inductance increases by a factor of
    Q67.
    A coil of wire of a certain radius has 10 turns and a self inductance of 15mH. The self inductance of second similar coil of 500 turns will be
    Q68.
    A d.c. circuit contains 10Ω of resistance in series with 10H coil. The impedence of the circuit is
    Q69.
    The charge which will flow through a 20Ω galvanometer connected to a 400Ω circular coil of 100 turns wound on a wooden stick 20mm in diameter, if B = 0.012T parallel to the axis of the stick decreased suddenly to zero is
    Q70.
    The induced emf of a generator when the flux of poles is doubled and speed is doubled
    Q71.
    The armature of a shunt wound motor can withstand current upto 8A before it overheats and is damaged. If the armature resistance is 0.5Ω, minimum back e.m.f that must be generated to avoid motor damage, when the motor is connected to a 120V line is
    📅BPKIHS
    Q72.
    A DC motor draws 10 A while operating from 120 V with back emf 115 V. Neglecting armature inductance, what would its initial current at switch-on be before the rotor starts moving?
    Q73.
    A circuit has a self inductance of 1H and carries a current of 2A. To prevent sparking, when the circuit is broken, a capacitor which can withstand 400 V is used. The least capacitance of the capacitor is
    Q74.
    A 5cm long solenoid having 10ohm resistance and 5mH inductance is joined to a 10V battery. At steady state, current through solenoid is
    Q75.
    In a noiseless transformer, an a.c. of 2A is flowing in the primary coil. The number of turns in the primary and secondary coils are 100 and 20 respectively. The current in the secondary coil is
    Q76.
    The number of turns in a secondary coil is twice the number of turns in primary. A Leclanche cell of 1.5 V is connected across the primary. The voltage across the secondary is
    Q77.
    The number of turns in primary and secondary coils are 500 and 5000 respectively. Input voltage is 20V and frequency is 50Hz. Then in output we have
    Q78.
    A transformer is used to light 140W, 24V lamp from 240V a.c. mains. The current it the mains is 0.7A. The efficiency of the transformer is nearest to
    Q79.
    A step-up transformer raises 120 V AC to 2400 V AC. If its primary has 75 turns, how many turns should its secondary have?
    Q80.
    The primary winding of a transformer has 200 turns and its secondary winding has 50 turns. If the current in the secondary winding is 40A, the current in the primary is
    Q81.
    The power loss in transformer working on 220V a.c. supply is 30%. The ratio of primary to secondary current when output voltage is 110V is
    Q82.
    A transformer is used to reduce, the mains supply of 220V to 11V. If the current in the primary and secondary coil are 5A and 90A respectively, efficiency of transformer is
    Q83.
    For a finite straight conductor that forms part of a closed electrical circuit, self-inductance is generally:
    Q84.
    If the length of a solenoid is doubled and no. of turns doubled, keeping the area constant, then inductance becomes
    📅IOM 2015
    Q85.
    For a coil rotating uniformly in a constant magnetic field, the induced emf magnitude is greatest when the angle between the plane of the coil and the magnetic field is:
    📅IOM 2016