Describe an experiment to demonstrate electromagnetic induction

Cambridge IGCSE Physics 0625 – Topic 4.5.1 Electromagnetic Induction

Learning Objective (AO1)

Describe an experiment that clearly demonstrates electromagnetic induction.

Syllabus wording (AO1)

• Electromagnetic induction – the production of an emf (and hence a current) in a closed circuit when the magnetic flux through the circuit changes.
• Faraday’s law – \(\displaystyle \mathcal{E}= -\,N\frac{d\Phi}{dt}\)
• Lenz’s law – The induced current produces a magnetic field that **opposes the change in magnetic flux** which produced it.
• Four factors that affect the magnitude of the induced emf (exact syllabus wording):
  • “Number of turns in the coil” (\(N\))
  • “Speed of relative motion between the magnet and the coil” (\(v\))
  • “Magnetic field strength” (\(B\))
  • “Area of the coil” (\(A\))

Key Concepts (AO1)

• Magnetic flux through one turn: \(\Phi = B\,A\cos\theta\) (for a coil whose plane is perpendicular to the field, \(\cos\theta = 1\)).
• Induced emf magnitude is proportional to each of the four factors above:
\[ \boxed{\mathcal{E}\;\propto\;N\,B\,A\,v} \]
• Direction of the induced current is given by Lenz’s law – the current creates a magnetic field that opposes the increase or decrease of flux.

Apparatus

Item	Purpose
Coiled copper wire (≈ 100 turns, known area \(A\))	Secondary circuit in which the emf is induced
Strong bar magnet	Source of a changing magnetic field when moved
Galvanometer (or sensitive ammeter) with internal resistance \(R_g\)	Detects and measures the induced current
Connecting leads with crocodile clips	Complete the circuit between coil and galvanometer
Ruler or measuring scale	Measure the distance the magnet travels (used to estimate speed)
Stopwatch (optional) / Photogate (recommended)	Measure the time taken for the magnet to travel the measured distance → speed \(v\)
Known resistor (e.g. 10 Ω) – optional	Allows calculation of emf from \(\mathcal{E}=IR\) without relying on the galvanometer’s scale

Pre‑lab Checklist (AO3)

1. Check that the coil is not damaged and note its resistance \(R_{\text{coil}}\) (use an ohmmeter).
2. Zero the galvanometer by briefly short‑circuiting its terminals; record the zero‑adjustment.
3. Verify that all crocodile‑clip connections are tight and that the leads are free from loose strands.
4. Confirm the magnet is clean, free of cracks and that the north and south poles are clearly marked.
5. Ensure the ruler or photogate is aligned with the coil’s central axis.
6. Read the safety notes (magnet handling, electrical connections, etc.) and sign‑off.

Experimental Procedure (AO2 & AO3)

1. Connect the coil leads to the galvanometer (or to the resistor‑galvanometer combination). Make sure the polarity is noted.
2. Record the coil’s area \(A\) (measure the diameter and calculate \(A=\pi r^{2}\)) and the exact number of turns \(N\).
3. Hold the bar magnet vertically with the north pole pointing toward the centre of the coil.
4. Insert the magnet **quickly** (aim for a travel time of ≈ 0.05 s) through the coil and immediately note:
   • Deflection of the galvanometer needle (direction and magnitude).
   • Time taken for the magnet to travel a measured distance \(d\) (use a stopwatch or photogate) → calculate speed \(v = d/t\).
5. Withdraw the magnet rapidly and record the needle deflection (direction should be opposite).
6. Repeat the above steps for:
   • Two different speeds (slow vs. fast) – keep the distance \(d\) constant and vary the time.
   • Two different numbers of turns (e.g., use a second coil with 200 turns).
   • Both magnet orientations (north‑first and south‑first).
7. For each trial write down:
   • Speed \(v\) (m s\(^{-1}\))
   • Number of turns \(N\)
   • Magnet pole first (N or S)
   • Galvanometer current \(I_g\) (A) or needle deflection
   • Calculated emf \(\mathcal{E}\) (V)

Data‑Table Template (AO2)

Trial	Speed \(v\) (m s\(^{-1}\))	Turns \(N\)	Magnet pole (first)	Current \(I_g\) (A)	Calculated \(\mathcal{E}\) (V)
1	2.0	100	N	0.018
2	1.0	100	N	0.009
3	2.0	200	N	0.036
4	2.0	100	S	0.018 (opposite direction)

Quick‑Calc Box – Estimating \(\mathcal{E}\) Directly (AO2)

When a bar magnet of length \(\ell\) passes completely through a coil of area \(A\) at a constant speed \(v\), the change in flux is approximately \(\Delta\Phi \approx B\,A\). The time for the magnet to travel its own length is \(t = \ell/v\). Substituting into Faraday’s law gives

\[ \boxed{\mathcal{E}\;\approx\;N\,\frac{\Delta\Phi}{t}\;=\;N\,B\,A\,\frac{v}{\ell}} \]

This relation shows the expected proportionalities \(\mathcal{E}\propto N,\;B,\;A,\;v\). It is useful for a quick comparison between measured and theoretical values.

Sample Calculation (AO2)

Assume:

• Galvanometer internal resistance \(R_g = 10\;\Omega\)
• Measured current for Trial 1: \(I_g = 0.018\;\text{A}\)

Then

\[ \mathcal{E}=I_g R_g = 0.018 \times 10 = 0.18\;\text{V} \]

Using the Quick‑Calc formula with \(N=100\), \(B=0.35\;\text{T}\) (average field measured with a gauss‑meter), \(A=4.0\times10^{-4}\;\text{m}^2\), \(\ell=0.05\;\text{m}\) and \(v=2.0\;\text{m s}^{-1}\):

\[ \mathcal{E}_{\text{theory}} \approx 100 \times 0.35 \times 4.0\times10^{-4} \times \frac{2.0}{0.05}=0.224\;\text{V} \]

The measured value (0.18 V) is reasonably close, the difference being due to the non‑uniform field of a real bar magnet and timing uncertainties.

Worksheet‑style Question (AO2)

Using the data you have recorded, plot the induced emf \(\mathcal{E}\) against the speed \(v\) for a fixed number of turns (e.g., \(N=100\)). From the straight‑line graph determine the gradient and compare it with the theoretical gradient \(\displaystyle \frac{NBA}{\ell}\). Comment on any discrepancy.

Observations (AO1)

• A sudden deflection of the galvanometer needle occurs whenever the magnet moves relative to the coil.
• Insertion and withdrawal give deflections in opposite directions – a direct illustration of Lenz’s law.
• Higher speed \(v\) produces a larger deflection (greater \(\mathcal{E}\)).
• Doubling the number of turns roughly doubles the deflection.
• Reversing the magnet’s polarity reverses the direction of the needle movement.

Explanation Using Faraday’s & Lenz’s Laws (AO1)

The magnetic flux through one turn is \(\Phi = B A\) (coil perpendicular to field). While the magnet is moving, \(\Phi\) changes, giving an induced emf

\[ \mathcal{E}= -\,N\frac{d\Phi}{dt}. \]

The negative sign embodies Lenz’s law: the induced current creates a magnetic field that **opposes the change in flux**.

• Insertion (north pole first): Flux through the coil increases. The induced current produces a north pole on the coil’s near face, repelling the approaching magnet. The galvanometer needle deflects, say, to the right.
• Withdrawal (north pole first): Flux decreases. The coil now produces a south pole on the near face, attracting the retreating north pole. The needle deflects to the left.
• Reversing the magnet’s polarity simply reverses the direction of the induced current, because the sign of \(\Delta\Phi\) changes.

Evaluation, Sources of Error and Suggested Improvements (AO3)

Source of error	Effect on results	Suggested improvement (purpose)
Timing with a handheld stopwatch	Reaction‑time uncertainty → inaccurate speed \(v\)	Use a photogate or motion sensor (reduces timing uncertainty, giving a more reliable \(v\)‑relationship).
Magnet not travelling along the coil’s central axis	Effective area \(A\) varies → scattered data	Guide the magnet with a non‑magnetic tube (ensures a constant \(A\) and improves repeatability).
Internal resistance of the galvanometer loading the circuit	Measured current lower than true value → under‑estimates \(\mathcal{E}\)	Insert a known external resistor and calculate \(\mathcal{E}=I(R_{\text{ext}}+R_g)\) (gives a more accurate emf).
Magnetic field of the bar magnet is not uniform	Quick‑calc assumes uniform \(B\); quantitative prediction becomes inaccurate	Measure the field at the coil centre with a gauss‑meter and use the average value in calculations (makes the theoretical estimate realistic).
Friction or air resistance on the moving magnet	“Fast” and “slow” speeds become ill‑defined	Mount the magnet on a motor‑driven carriage with a controllable speed setting (provides precise, repeatable velocities).

Safety and Precautions

• Handle the bar magnet with care – strong magnets can pinch fingers and attract metal objects.
• Never connect the galvanometer to a separate voltage source while the coil is open; this can damage the instrument.
• Check all connections before each trial to avoid spurious readings.
• Keep the set‑up away from credit cards, pacemakers, or other sensitive electronic devices.
• Do not place the magnet near magnetic storage media (e.g., hard drives) as it may erase data.

Extension / Challenge Questions (AO2)

1. Predict how the induced emf would change if the coil were rotated at a constant angular speed \(\omega\) in a uniform magnetic field instead of moving the magnet. Explain using \(\mathcal{E}= -N\frac{d\Phi}{dt}\).
2. If the coil is connected to a resistor of known resistance \(R\), write the expression for the induced current and show how you would calculate \(\mathcal{E}\) from the galvanometer reading.
3. Describe how the principle demonstrated in this experiment is employed in a practical electric generator.