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Text lesson

Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire

Physics

Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire

Overview

Overview

🌳 Concept tree

Lesson 1→Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire

├── Faraday's experiment

├── Faraday's law

├── Lenz's rule

  • ├── Fleming's right-hand rule (induced current in a moving straight wire)
  • └── Induced emf in a straight wire moving in a magnetic field
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 1 / 7
Faraday’s experiment

Faraday’s experiment

  • Faraday made a cylindrical coil of insulated copper wire (the turns separated from each other so that they do not short-circuit) and joined its ends to a sensitive galvanometer with its zero at the middle of the scale, so that the pointer can swing either way.
Comparison aspectMain ideaKeywords
Plunging a bar magnet into the coilthe pointer deflects momentarily in one directionpointerdeflectsmomentarilydirection
Pulling the magnet outthe pointer deflects momentarily in the opposite directionpointerdeflectsmomentarilyopposite
Holding the magnet still, inside or outside the coil
  • no deflection
  • whatever the strength of the magnet
deflectionwhateverstrength
•
  • Moving the magnet faster gives a bigger deflection
  • a coil with more turns gives a bigger deflection
  • an iron core in the coil gives a bigger deflection (it concentrates the flux)
Movingmagnetfastergives
•Keeping the magnet still and moving the coil gives the same effect: only the relative motion mattersKeepingmagnetstillmoving
  • Conclusion an emf and a current are induced in the coil whenever the magnetic flux linked with it changes with time.
  • This phenomenon is electromagnetic induction.
  • The induced current exists only while the flux is changing.
  • Faraday explained it by saying that the induced emf and current appear because the magnetic field lines are cut by the turns of the coil as the magnet moves.
  • Also, the coil reacts against the motion of the magnet when the magnet is pushed in, the induced field opposes it (repels it); when pulled out, the induced field tries to keep it in (attracts it).
  • You can feel this resistance if the coil has many turns and is short-circuited: it is harder to push the magnet in quickly.
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 2 / 7
Faraday’s law

Faraday’s law

  • From his observations Faraday concluded that:
  1. A relative motion between a conductor and a magnetic field that changes the magnetic flux linked with the conductor induces an emf in it. Its direction depends on the direction of the relative motion.
  2. The magnitude of the induced emf is proportional to the rate of change of the magnetic flux (the rate at which the conductor cuts the flux lines): emf ∝ ΔΦm / Δt.
  3. It is also proportional to the number of turns N of the coil that link the flux (each turn contributes the same emf, and they are in series): emf ∝ N.
  • Combining these:

emf = − N ΔΦm / Δt

  • Φm = B A cos(angle) is the magnetic flux (weber, Wb = T·m2); Δt in seconds.
  • The flux is the product of the field and the area that is perpendicular to it, so the flux can change in three ways: B changes, the area A changes, or the angle between the coil and the field changes.
  • The factors that increase the induced emf: more turns, a stronger magnet (or field), a faster motion (smaller Δt), an iron core.
Comparison aspectMain ideaKeywords
Practical check of Faraday’s law (the usual essay)connect a coil of N turns to a galvanometer and move a magnet through itconnectcoilturnsgalvanometer
(i) Move the magnet slowly, then quicklythe quicker motion (greater rate of change of flux) gives a larger deflectionquickermotiongreaterrate
•
  • (ii) Repeat with coils of different numbers of turns
  • keeping the speed constant: the deflection is proportional to N
Repeatcoilsdifferentnumbers
(iii) Use a stronger magnetthe deflection increasesdeflectionincreases
Example 1a.A coil of 120 turns and area 0.01 m2 has the field through it (perpendicular to the coil) fall from 0.5 T to 0.1 T in 0.04 s. ΔΦ = (0.5 − 0.1) × 0.01 = 4×10−3 Wb. |emf| = 120 × 4×10−3 / 0.04 = 12 V. If the circuit resistance is 24 Ω the induced current is 12 / 24 = 0.5 Acoilturnsareafield
Example 1b.→A coil of 60 turns and area 0.05 m2 is turned in a 0.4 T field from the position where its plane is perpendicular to the field to the position where it is parallel, in 0.1 s. The flux falls from BA = 0.02 Wb to zero, so |emf| = 60 × 0.02 / 0.1 = 12 V.
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 3 / 7
Lenz’s rule

Lenz’s rule

  • The negative sign in Faraday’s law expresses Lenz’s rule:
  • The direction of the induced current (and induced emf) is such that its magnetic effect opposes the change in flux that produces it.
  • Applications (this is the use of Fig 3-2 in the book):
Comparison aspectMain ideaKeywords
North pole of a magnet approaching a coilthe end of the coil facing the magnet becomes a north pole (repels the magnet). The induced current is anticlockwise as seen from the magnet side. The repulsion resists the motion of the magnet towards the coilfacingbecomesrepelsinduced
North pole moving awaythe near end becomes a south pole (attracts the magnet and tries to keep it). The attraction resists the motion of the magnet away from the coilnearbecomessouthattracts
Lenz’s rule is a statement of conservation of energy
  • the work done against the opposing force by the person moving the magnet is the source of the electrical energy. If the induced effect helped the change
  • energy would be created from nothing
  • and a tiny push would produce a growing current for ever
workdoneagainstopposing
How to use it
  • (1) decide whether the flux through the coil is increasing or decreasing
  • (2) the induced field must point in the opposite sense to the change (against the original field if the flux is increasing
  • along it if the flux is decreasing)
  • (3) use the right-hand screw rule on the coil to find the direction of the current that gives that field
decidewhetherfluxthrough
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 4 / 7
Fleming’s right-hand rule (induced current in a moving straight wire)

Fleming’s right-hand rule (induced current in a moving straight wire)

  • Stretch the thumb, forefinger and middle finger of the right hand at right angles to each other.
  • If the thumb points in the direction of motion of the wire and the forefinger in the direction of the field (N → S), the middle finger gives the direction of the induced current (emf).
  • Compare left hand → motor (current + field → force); right hand → generator (motion + field → current). A useful memory trick: "left for motor, right for generator" — the word "generator" has the letter "r" for right.
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 5 / 7
Induced emf in a straight wire moving in a magnetic field

Induced emf in a straight wire moving in a magnetic field

  • A straight wire of length L is perpendicular to a uniform field B and moves with velocity v perpendicular to both the field and the wire.
  • In a time Δt it moves a distance Δx = v Δt and sweeps an area ΔA = L Δx = L v Δt, so the flux it cuts is ΔΦ = B ΔA = B L v Δt.

By Faraday’s law (one turn),

emf = B L v

  • The negative sign (Lenz’s rule) only tells the direction.
  • If the velocity makes an angle θ with the field (wire still perpendicular to the velocity), only the component v sin θ perpendicular to the field cuts the flux lines:

emf = B L v sin θ

Comparison aspectMain ideaKeywords
•
  • The emf is maximum when the wire moves perpendicular to the field (θ = 90°) and zero when it moves along the field (θ = 0°)
  • because then it does not cut any lines
maximumwiremovesperpendicular
•
  • If the wire is part of a closed circuit of resistance R
  • the induced current is I = emf / R
wirepartclosedcircuit
Example 1.A 0.6 m metal rod moves at 3 m/s perpendicular to a 0.25 T field. emf = 0.25 × 0.6 × 3 = 0.45 Vmetalmovesperpendicularfield
Example 2.A coil of 50 turns has its flux changed from 0.04 Wb to 0.01 Wb in 0.1 s. |emf| = 50 × 0.03 / 0.1 = 15 Vcoilturnsfluxchanged
Example 2a.A rod of length 45 cm moves at 2 m/s in a direction making 30° with a field of 0.5 T. emf = 0.5 × 0.45 × 2 × sin 30° = 0.225 Vlengthmovesdirectionmaking
Example 2b.
  • An aircraft with a wingspan of 40 m flies horizontally at 250 m/s where the vertical component of the Earth’s field is 4×10−5 T. The emf between the wing tips is 4×10−5 × 40 × 250 = 0.40 V. (It cannot light a lamp
  • because no complete circuit exists.)
aircraftwingspanflieshorizontally
Example 2c — finding the speed.A 25 cm rod in a 0.4 T field has an emf of 0.15 V between its ends when moved perpendicular to the field. v = emf / (B L) = 0.15 / (0.4 × 0.25) = 1.5 m/sfieldbetweenendsmoved
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 6 / 7
Part 7

Part 7

  • 📖

🔍 In-Depth Explanations, Deductions & Multi-Book Insights:

Physics (Thanaweya Amma 2026/2027)

  • Lesson 1 – Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire
  • Electromagnetic induction is the generation of an induced electromotive force (EMF) and induced electric current in a closed circuit when exposed to a varying magnetic flux.
  • Faraday's Law states emf = -N (ΔΦm / Δt), where the negative sign embodies Lenz's Law of opposition.

🌳 Conceptual Hierarchy Tree

Electromagnetic Induction Fundamentals

├── 1. Faraday's Induction Experiment

  • │ ├── Moving magnet relative to solenoid coil induces transient galvanometer deflection
  • │ └── Faraday's Law emf = -N · (ΔΦm / Δt) = -N · A · (ΔB / Δt)

├── 2. Lenz's Law (Direction of Induced Current)

  • │ ├── Principle Induced current always flows in a direction opposing the magnetic flux change producing it
  • │ ├── Approaching North Pole → Face becomes North Pole (Repulsion)
  • │ └── Receding North Pole → Face becomes South Pole (Attraction)
  • └── 3. Induced EMF in a Straight Conductor (Length L, Velocity v)

├── emf = -B · L · v · sin θ

  • ├── Direction determined by Fleming's Right-Hand Rule
  • └── Maximum when wire moves perpendicular to field; Zero when parallel

📋 Master Teacher's Blackboard Secrets

Comparison aspectMain ideaKeywords
RULE 1Lenz's Law embodies the Law of Conservation of Energy: External mechanical work done to overcome repulsive/attractive forces converts into electrical energyLenzembodiesConservationEnergy
RULE 2
  • Fleming's RIGHT-Hand Rule is for INDUCED current in a moving generator wire
  • Fleming's LEFT-Hand Rule is for MAGNETIC FORCE in a motor
FlemingRIGHTHandINDUCED
RULE 3If a loop is rotated in a magnetic field: ΔΦm = 2 B A when rotated 180° (reversed) from perpendicular positionlooprotatedmagneticfield
EXAM TRAP
  • The induced EMF depends on the RATE of change of magnetic flux (ΔΦm / Δt)
  • NOT the absolute value of flux Φm itself!
induceddependsRATEchange
📊 MatrixComparative Analysis: Lenz's Law Magnetic Opposition ResponsesComparativeAnalysisLenzMagnetic
Magnet Relative Motion Flux Change (ΔΦm) Induced Coil Pole Formed Direction of Induced Current
North Pole Approaching Increasing (+ΔΦm) North Pole (Repulsive force) Counter-Clockwise
North Pole Receding Decreasing (-ΔΦm) South Pole (Attractive force) Clockwise
South Pole Approaching Increasing (+ΔΦm) South Pole (Repulsive force) Clockwise
South Pole Receding Decreasing (-ΔΦm) North Pole (Attractive force) Counter-Clockwise
Magnet Stationary Inside Coil Zero change (ΔΦm = 0) No pole formed Zero induced current (I = 0)
Lesson 1: Faradays Law of Induction, Lenzs Law and EMF in a Moving Wire · 7 / 7