Faraday and Lenz at GCSE β generating current by moving a magnet, and how the AC generator works
β‘ Explain what electromagnetic induction is and the conditions needed for it to occur
𧲠Describe how moving a magnet into a coil induces an EMF and current
π State and apply Faraday's Law β EMF depends on the rate of change of magnetic flux
π State and apply Lenz's Law β the induced current opposes the change that caused it
βοΈ Describe the structure and operation of a simple AC generator (alternator)
π Interpret and sketch graphs of induced EMF against time for an AC generator
π What is Electromagnetic Induction?
Electromagnetic induction is the process by which a changing magnetic field creates (induces) an electromotive force (EMF) β and if the circuit is complete, a current flows. This was discovered independently by Michael Faraday and Joseph Henry in 1831 and is one of the most important discoveries in physics, forming the basis of every electrical generator.
Electromagnetic Induction: The production of an EMF (and possibly a current) in a conductor when there is a change in the magnetic flux linking that conductor.
The critical word is change. A stationary magnet near a stationary coil produces no EMF. Induction only occurs when:
A magnet is moved towards or away from a coil
A coil is moved towards or away from a magnet
The current in a nearby coil changes (mutual induction)
No relative movement (or change) = no induced EMF. It is the rate of change of magnetic flux that matters, not the flux itself.
The induced EMF can be detected using a sensitive galvanometer (a centre-zero ammeter). When the magnet moves in, the needle deflects one way; when the magnet moves out, it deflects the other way; when the magnet is stationary, the reading is zero.
π Faraday's Law
Faraday's Law tells us the size of the induced EMF. In simple terms for GCSE:
Induced EMF β rate of change of magnetic flux
This means the induced EMF is larger when:
The magnet moves faster (greater rate of flux change)
A stronger magnet is used (more flux, so bigger change per second)
There are more turns on the coil (each turn contributes its own EMF, and they add together)
The area of the coil is larger (more flux links each turn)
Magnetic flux (Ξ¦): The amount of magnetic field passing through a given area. At GCSE you need to understand this concept qualitatively β the field lines "threading through" the coil.
In summary: anything that increases the rate at which field lines are cut will increase the induced EMF. You can think of the conductor "cutting through" magnetic field lines β the faster the cutting, the greater the EMF.
Doubling the speed of the magnet doubles the rate of flux change, which doubles the induced EMF and therefore doubles the induced current (assuming resistance is constant).
π Lenz's Law
Lenz's Law tells us the direction of the induced current. It is a consequence of the law of conservation of energy.
Lenz's Law: The direction of the induced current is always such that it opposes the change in magnetic flux that caused it.
In practice, this means:
When a north pole approaches a coil, the induced current flows to make the near face of the coil a north pole β repelling the approaching magnet. You must do work to push the magnet in.
When the north pole is withdrawn, the induced current reverses to make the near face a south pole β attracting the retreating magnet. Again, you must do work to pull it out.
Lenz's Law is really just conservation of energy in disguise. If the induced current helped the magnet move, you would be getting electrical energy for free β which is impossible. The opposing force means you always have to do work, and that work is converted into electrical energy.
You can use the right-hand grip rule to find which way the current flows: curl the fingers of your right hand around the coil in the direction of current flow, and your thumb points in the direction of the magnetic north pole created by that current.
Remember: Lenz's Law means the induced effects always act to resist change. This is analogous to Newton's third law β every action has an equal and opposite reaction.
βοΈ The AC Generator (Alternator)
An AC generator (alternator) converts kinetic energy into electrical energy using electromagnetic induction. It is the basis of all power station generators and bicycle dynamos.
Key Components:
Component
Description
Function
Coil (armature)
Rectangular coil of wire, many turns
Rotates in the magnetic field; EMF is induced in it
Magnet (field magnet)
Permanent magnet or electromagnet
Provides the magnetic field the coil rotates in
Slip rings
Two metal rings attached to the axle
Rotate with the coil; maintain contact with brushes
Carbon brushes
Fixed contacts pressing on slip rings
Transfer current from the rotating coil to the external circuit
How it works:
As the coil rotates in the magnetic field, each side of the coil cuts through the field lines. This induces an EMF in each side, and the two sides add together. The EMF varies sinusoidally:
When the coil is parallel to the field (sides cutting field lines at 90Β°) β EMF is at its maximum
When the coil is perpendicular to the field (sides moving parallel to field lines, cutting nothing) β EMF is zero
Because slip rings are used (not a split-ring commutator), the output alternates in direction every half turn. This produces alternating current (AC) β the current reverses direction periodically.
Increasing the output EMF:
Rotate the coil faster β increases frequency AND peak EMF
Use a stronger magnet β increases peak EMF
Use a coil with more turns β increases peak EMF
Use a coil with a larger area β increases peak EMF
For a UK mains supply: frequency = 50 Hz, peak voltage β 325 V, RMS voltage = 230 V
π EMFβTime Graphs for AC Generators
The output of an AC generator is a sinusoidal wave. Understanding the graph is essential for exam questions.
Peak EMF (Ξ΅β): The maximum value of the induced EMF, occurring when the coil is parallel to the magnetic field (sides cutting field lines at maximum rate).
Period (T): The time for one complete rotation of the coil (one complete cycle of the AC output). Measured in seconds (s).
frequency (f) = 1 Γ· period (T) | f in Hz, T in s
Key features of the graph to identify in exams:
Peaks and troughs β maximum positive and negative EMF values
Zero crossings β coil is perpendicular to field at these moments
Period β time between two identical points on the wave
Effect of changes on the graph:
Faster rotation: higher peaks (greater peak EMF) AND shorter period (higher frequency) β the wave is taller and more compressed
Stronger magnet only: higher peaks, same period β wave is taller but same width
More turns only: higher peaks, same period
Only changing the rotation speed affects the frequency. Changing magnet strength or number of turns only affects the peak EMF (amplitude) β the frequency stays the same as long as the rotation speed is unchanged.
Example 1: A student pushes a bar magnet (north pole first) into a coil connected to a galvanometer. The needle deflects to the right. Describe what happens to the galvanometer reading when: (a) the magnet is held stationary inside the coil, (b) the magnet is pulled out slowly, (c) the magnet is pulled out quickly. Explain each using Faraday's and Lenz's Laws.
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Part (a) β Stationary inside: When the magnet is stationary, the magnetic flux through the coil is not changing. By Faraday's Law, EMF β rate of change of flux. If the rate of change is zero, the induced EMF is zero. Therefore the galvanometer reads zero.
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Part (b) β Pulled out slowly: Now the flux through the coil is decreasing (the magnet is moving away). By Faraday's Law, an EMF is induced. By Lenz's Law, the induced current must oppose this change β it must try to maintain the flux, so the near face of the coil becomes a south pole (to attract the retreating north pole). This means the current flows in the opposite direction to when the magnet was pushed in. The galvanometer needle deflects to the left. Because the magnet moves slowly, the rate of change of flux is small, so the deflection is small.
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Part (c) β Pulled out quickly: The direction of the induced current is the same as in (b) β the galvanometer still deflects to the left. However, the rate of change of flux is much greater because the magnet moves faster. By Faraday's Law, a greater rate of flux change induces a larger EMF. Therefore the galvanometer shows a larger deflection to the left, but only briefly (the magnet exits faster).
(a) Reads zero β no change in flux. (b) Deflects left (small) β EMF induced, current opposes flux decrease. (c) Deflects left (large) β greater rate of flux change β larger EMF.
Example 2: An AC generator produces a peak EMF of 240 V and completes 50 full rotations per second. (a) State the frequency of the AC output. (b) Calculate the period of the output. (c) Describe what happens to the peak EMF and the period if the rotation speed is doubled.
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Part (a) β Frequency: The coil completes 50 full rotations per second. Each full rotation produces one complete cycle of AC. Therefore: frequency f = 50 Hz.
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Part (b) β Period: Use the equation: T = 1 Γ· f
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T = 1 Γ· 50 = 0.02 s (20 ms)
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Part (c) β Doubling rotation speed: Doubling the speed means the coil now completes 100 rotations per second. The sides of the coil cut field lines at twice the rate, so the peak EMF doubles: new peak EMF = 240 Γ 2 = 480 V. The frequency also doubles to 100 Hz, so the new period = 1 Γ· 100 = 0.01 s (the period halves).
(a) f = 50 Hz | (b) T = 0.02 s | (c) Peak EMF doubles to 480 V; period halves to 0.01 s
Example 3: A student sets up an AC generator with a coil of 200 turns rotating at 25 Hz in a magnetic field. The peak EMF is 120 V. She then changes the coil to one with 400 turns, keeping everything else the same. (a) What is the new peak EMF? (b) What is the new frequency of the output? Explain your reasoning.
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Part (a) β New peak EMF: By Faraday's Law, the induced EMF is proportional to the number of turns in the coil. Doubling the number of turns from 200 to 400 doubles the contribution of each turn to the total EMF.
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New peak EMF = 120 Γ (400 Γ· 200) = 120 Γ 2 = 240 V
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Part (b) β New frequency: The rotation speed has NOT been changed β the coil still completes 25 full rotations per second. The frequency of the AC output equals the number of complete rotations per second. Therefore the frequency remains 25 Hz.
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Key distinction: changing the number of turns affects the amplitude (peak EMF) but not the frequency. Only the rotation speed determines the frequency of the output.
(a) New peak EMF = 240 V (doubled) | (b) Frequency remains 25 Hz (rotation speed unchanged)
Example 4: An AC generator's EMFβtime graph shows a sinusoidal wave with a peak EMF of 180 V and a period of 0.04 s. (a) Calculate the frequency. (b) At what positions in the rotation is the EMF equal to zero? (c) The magnet is replaced with a stronger one. Sketch how the graph changes.
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Part (a) β Frequency from period: f = 1 Γ· T = 1 Γ· 0.04 = 25 Hz
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Part (b) β Zero EMF positions: The EMF is zero when the rate of cutting field lines is zero β i.e., when the sides of the coil move parallel to the field lines rather than cutting through them. This occurs when the plane of the coil is perpendicular to the magnetic field (the coil faces the magnet directly). This happens twice per full rotation β once at the start of each half-cycle.
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Part (c) β Stronger magnet effect: A stronger magnet increases the magnetic flux density. At any given moment, the rate of change of flux is greater, so the peak EMF increases. However, the rotation speed is unchanged, so the period and frequency remain the same. The graph shows a taller sinusoidal wave (peak EMF greater than 180 V) with the same period of 0.04 s.
(a) f = 25 Hz | (b) EMF = 0 when coil is perpendicular to field (sides moving parallel to field) | (c) Graph: same period (0.04 s), larger peak EMF β taller wave, same width
Question 1: A bar magnet is held stationary inside a coil connected to a galvanometer. What does the galvanometer read?
Question 2: According to Lenz's Law, when a north pole is pushed towards a coil, the near face of the coil becomesβ¦
Question 3: An AC generator produces an output with a period of 0.025 s. Calculate the frequency of the output in Hz.
Question 4: Which change to an AC generator would increase the peak EMF but NOT change the frequency of the output?
Question 5: In an AC generator, what is the purpose of the slip rings and carbon brushes?
Challenge 1: A student investigates electromagnetic induction using a coil of 150 turns and a bar magnet. She records the galvanometer deflection when the magnet is moved at different speeds. She then replaces the coil with one of 300 turns and repeats the experiment at the same speeds.
(a) Explain, using Faraday's Law, why the deflection is larger when the magnet is moved faster. [2 marks]
(b) Explain why the deflection is larger with 300 turns than with 150 turns at the same speed. [2 marks]
(c) Explain, using Lenz's Law and conservation of energy, why the student must always do work to move the magnet. [3 marks]
(a) Moving the magnet faster increases the rate of change of magnetic flux through the coil. By Faraday's Law, the induced EMF is proportional to the rate of change of flux, so a higher rate gives a larger EMF and therefore a larger current/deflection. [2]
(b) Each turn of the coil has an EMF induced in it. With 300 turns (double), there are twice as many turns each contributing to the total EMF. The total induced EMF is proportional to the number of turns, so it doubles, giving a larger deflection. [2]
(c) By Lenz's Law, the induced current creates a magnetic field that opposes the motion of the magnet (e.g. repelling an approaching north pole). This means a force opposes the student's movement of the magnet β she must exert a force to overcome this. Work done = force Γ distance. This work done by the student is the source of the electrical energy generated. If the induced current had aided the motion instead, energy would be created from nothing, violating conservation of energy. [3]
Challenge 2: An AC generator has a coil rotating at 60 Hz in a magnetic field. It produces a peak EMF of 300 V.
(a) Calculate the period of the AC output. [1 mark]
(b) The rotation speed is reduced so that the coil now rotates at 30 Hz. State and explain the effect on (i) the peak EMF and (ii) the period. [4 marks]
(c) Instead of changing speed, the original generator (60 Hz, 300 V peak) has its coil replaced with one of the same dimensions but double the number of turns. State the new peak EMF and frequency. [2 marks]
(a) T = 1 Γ· f = 1 Γ· 60 = 0.0167 s (β 16.7 ms) [1]
(b)(i) Peak EMF: Halving the rotation speed halves the rate at which the coil cuts through field lines. By Faraday's Law, the induced EMF is proportional to rate of flux change, so the peak EMF halves: new peak EMF = 300 Γ· 2 = 150 V. [2] (b)(ii) Period: Frequency = rotations per second = 30 Hz. New period T = 1 Γ· 30 = 0.033 s (period doubles). [2]
(c) Doubling the turns doubles the peak EMF: new peak EMF = 600 V. The rotation speed is unchanged (still 60 Hz), so the frequency remains 60 Hz. [2]
Challenge 3 (Extended answer): A simple AC generator consists of a rectangular coil rotating between the poles of a magnet, connected to an external circuit via slip rings and carbon brushes. The generator produces a sinusoidal EMF output.
(a) Describe the positions of the coil in the magnetic field at which (i) the EMF is maximum and (ii) the EMF is zero. Explain why in each case. [4 marks]
(b) Explain why slip rings are used in an AC generator rather than a split-ring commutator. [2 marks]
(c) A power station generator produces an output at 50 Hz with a peak voltage of 25 000 V. Calculate the period of this output and explain what physical motion in the generator this period corresponds to. [2 marks]
(a)(i) Maximum EMF: When the plane of the coil is parallel to the magnetic field (the coil lies flat relative to the field). At this position, the sides of the coil are moving perpendicular to the field lines and cutting through them at the maximum rate. By Faraday's Law, maximum rate of flux change β maximum induced EMF. [2] (a)(ii) Zero EMF: When the plane of the coil is perpendicular to the magnetic field (the coil faces the poles directly). At this position, the sides of the coil move parallel to the field lines and do not cut through them at all. The rate of change of flux is zero, so by Faraday's Law, the induced EMF is also zero. [2]
(b) Slip rings are continuous metal rings that rotate with the coil. They allow the current to flow out to the external circuit in the same direction as it flows in the coil at any given moment, producing an alternating (AC) output. A split-ring commutator reverses the connections every half-turn, which would convert the output to DC. Since we want AC, slip rings are used. [2]
(c) T = 1 Γ· f = 1 Γ· 50 = 0.02 s. This period corresponds to the time taken for the generator coil (or turbine) to complete one full rotation. Every rotation produces one complete cycle of AC. [2]
Challenge 4 (Synoptic): A student says: "If I use a stronger magnet in my AC generator, both the peak EMF and the frequency of the output will increase." Evaluate this statement, correcting any errors and explaining your reasoning with reference to the relevant laws. [4 marks]
The student is partially correct but partially wrong. [1]
Peak EMF β correct: A stronger magnet increases the magnetic flux density. At any given instant, the sides of the coil cut through more field lines per second (greater rate of flux change). By Faraday's Law, a greater rate of change of magnetic flux induces a greater EMF. So the peak EMF does increase. [1]
Frequency β incorrect: The frequency of the AC output is determined solely by the number of complete rotations per second (the rotation speed of the coil). Using a stronger magnet does not change the rotation speed β the coil still completes the same number of full turns per second. Therefore the frequency remains unchanged. [2]
Correction: Using a stronger magnet increases the peak EMF (amplitude of the wave) but does not change the frequency. To increase the frequency, the rotation speed of the coil must be increased.