Difficulty: Intermediate | Prerequisites: Faraday's Law theory (see companion notes), vector components, familiarity with the iOLab device and its high gain sensor.
This set of notes covers the experimental side of Faraday's Law: how to measure an induced voltage using only Earth's magnetic field and a wire coil, and how to squeeze the largest possible EMF out of that setup. It walks through calibrating the magnetometer, understanding the high gain offset, and the design reasoning behind coil geometry and rotation strategy. If you have the theory down but are unsure how the lab measurement works, start here.
To maximise the induced EMF from Earth's field, you want the largest possible coil area, the most turns of wire, alignment with the strongest component of the local field, and the fastest rotation you can manage reliably. Subtract the high gain offset from every reading, and report the average of three reproducible trials.
High gain sensor (G+ / G−)
The sensitive voltage input on the iOLab, used to detect small induced EMFs in the millivolt range. It has a ceiling of about 1.07 mV; readings that hit this value are clipped and you must switch to the A1/GND inputs instead.
High gain offset
A small, constant voltage the sensor reports even when nothing is happening. You find it by highlighting a flat region of your voltage-vs-time graph (away from any bump) and reading the average. This value is subtracted from your peak measurements.
Magnetometer calibration
The process of zeroing the iOLab's three-axis magnetic field sensor. Done via the gear icon, selecting "Calibration" then "Accel – magn – gyro." Must be performed away from magnets and large metal objects. If readings exceed roughly 50–55 μT total, recalibrate.
iOLab axis convention
The x, y, and z labels on the iOLab correspond to physical directions that depend on how you orient the device. You must record which axis points north, east, and up so that your magnetometer data is interpretable.
Place the iOLab on a flat, horizontal surface with one axis pointing north.
After calibration, the magnetometer outputs Bx, By, and Bz at 80 Hz.
Typical total field strength is 25–65 μT depending on your latitude and local environment.
Record which component is largest. That tells you the dominant direction of the local field, which you will align your coil rotation axis against.
When you record voltage with G+ and G−, the baseline is not exactly zero.
To measure the offset: look at a flat portion of your graph (no magnet motion, no coil rotation), highlight it, and note the average voltage. That average is your offset.
Every peak EMF reading must have this offset subtracted before you report it.
Corrected EMF = |peak reading| − |offset|
Faraday's Law (ε = −N dΦ_B / dt) tells you exactly which knobs to turn:
Increase N (number of turns):
Use all the wire available from one E&M kit.
Wind it into as many complete, tightly packed loops as possible.
Each full turn adds to the total EMF proportionally.
Increase A (loop area):
A larger loop encloses more flux.
There is a trade-off: using wire for a bigger loop means fewer turns if your total wire length is fixed. The optimum depends on the specific wire length available.
Maximise B · cos θ (effective field component):
You cannot change Earth's field strength, but you can choose which component of it your coil "sees."
Orient the coil so that the area vector sweeps through the direction of the strongest field component.
For example, if the vertical (downward) component of the field is largest at your location, rotate the coil about a horizontal axis so the area vector swings from pointing down to pointing up.
Maximise dΦ/dt (rate of change):
Rotate or flip the coil as quickly as you can while still being reproducible.
A 180° flip changes the flux from +BAcos0° to +BAcos180° = −BA, giving a total change of 2BA per turn. This is the maximum single-flip change.
Speed matters: the same total flux change crammed into a shorter time window gives a taller voltage spike.
Start with the high gain inputs (G+ and G−) for their sensitivity.
If your peak EMF clips at 1.07 mV (the reading appears "stuck" at that value), the amplifier is saturating.
Switch your wires to A1 and GND, which have a wider voltage range but lower sensitivity. This only becomes necessary if your coil design is producing large EMFs, which is a good problem to have.
The lab requires three trials whose peak values agree within about 25%.
If your results vary wildly, the rotation speed or coil positioning is inconsistent. Consider building a physical jig or guide (using available materials) to make each flip as uniform as possible.
Report the average of the three corrected peak values.
What you control | How it enters ε = −N (dΦ_B / dt) | Practical lever |
|---|---|---|
Number of turns, N | Directly multiplies EMF | Wind more loops with available wire |
Loop area, A | Inside Φ_B = B A cos θ | Make the loop as large as wire length allows (trade-off with N) |
Alignment angle, θ | cos θ factor in flux | Rotate so the area vector sweeps through the strongest B component |
Rotation speed | Determines dt | Flip faster for a larger peak voltage |
For a 180° flip of an N-turn coil in a uniform field B, aligned so θ goes from 0° to 180°:
Total flux change = 2 N B A
The peak EMF depends on how quickly that change occurs (the shape of dΦ/dt during the flip).
This experiment mirrors, on a tiny scale, how a simple AC generator works: a coil rotates in a magnetic field and a voltage appears at its terminals. Industrial generators use powerful electromagnets instead of Earth's field and spin at precise speeds (50 or 60 Hz) to produce mains electricity. The same optimisation logic applies: more turns, bigger area, stronger field, faster rotation all increase output voltage.
"The spring from the iOLab kit would be fine to use." It is explicitly banned. It can produce large but unreliable EMFs, which defeats the reproducibility requirement.
"A bigger coil is always better than more turns." Not necessarily. With a fixed length of wire, enlarging the loop reduces the number of turns. There is an optimal balance; blindly maximising area at the expense of N may reduce total EMF.
"The sign of the voltage spike matters." Only the magnitude is reported. The sign reflects the direction of the induced current, which depends on which way you flipped and how G+/G− are connected.
"If my three trials don't match, I just pick the best one." The lab requires the average of three trials that are within 25% of each other. Inconsistent trials indicate a reproducibility problem with your method, not bad luck.
⚠️ Be able to explain, using Faraday's Law, why each design choice (more turns, bigger area, faster flip, field alignment) increases the induced EMF.
⚠️ Know how to correct for the high gain offset and why it matters.
⚠️ Understand the physical meaning of each axis on the magnetometer graph and how to determine the dominant direction of Earth's field at your location.
⚠️ Be prepared to discuss the trade-off between loop area and number of turns for a fixed wire length.
True or false: Flipping a coil 180° produces twice the flux change of rotating it 90° from the aligned position. (True: 0° to 180° gives ΔΦ = 2BA; 0° to 90° gives ΔΦ = BA.)
Fill in the blank: If the high gain sensor clips at 1.07 mV, you should switch to the ______ and ______ inputs. (A1 and GND)
True or false: You should subtract the high gain offset before reporting your peak EMF. (True)
Fill in the blank: The lab requires the average of ______ reproducible trials. (three)
True or false: Using materials other than the E&M kit wires to build a frame for the coil is prohibited. (False, you may use almost any available materials for the geometry/frame.)
Q: A student has 2 metres of wire and can wind it into either a single loop of large area or multiple smaller loops. Using Faraday's Law, explain the trade-off.
A: EMF = N · (dΦ_B / dt) and Φ_B = B · A · cos θ. A single large loop has N = 1 but maximum A. Multiple loops increase N but each loop has a smaller A (since the same total wire length is divided among more turns). The product N × A determines the total flux linkage; for a circular coil of fixed wire length L, N × A = N × π(L / 2πN)² = L² / (4πN), which increases as N decreases. So for circular loops, fewer larger turns actually win, but practical constraints (keeping the coil rigid, fitting it in the lab) may shift the optimum.
Q: Why is it important to know which component of Earth's magnetic field is strongest at your location?
A: You want to rotate the coil so the area vector sweeps through the direction of the largest field component. If the vertical component is dominant, you rotate about a horizontal axis. Aligning with the wrong component wastes potential flux change and produces a smaller EMF.
Q: A student measures peak voltages of 0.38 mV, 0.41 mV, and 0.36 mV, with a high gain offset of 0.015 mV. What corrected average EMF should they report?
A: Corrected values: 0.365 mV, 0.395 mV, 0.345 mV. Average = (0.365 + 0.395 + 0.345) / 3 = 0.368 mV (or about 0.37 mV).
Q: Explain why rotating the coil faster produces a larger peak EMF, even though the total flux change is the same.
A: Faraday's Law involves dΦ_B / dt. The total change in flux (numerator) is fixed by N, B, A, and the angle swept. A faster rotation compresses that change into a shorter time interval (smaller dt), so the instantaneous rate of change is larger, producing a higher peak voltage.
Q: What does it mean physically when the high gain sensor reads a constant non-zero value with no changing flux?
A: That constant value is the high gain offset, an artefact of the amplifier electronics. It does not represent a real induced voltage and must be subtracted from all measurements.
This connects to experimental design and error analysis skills used across all physics labs: controlling variables, averaging repeated trials, and correcting for systematic offsets. The rotation strategy links directly to AC circuits and generators covered later in the course, where a continuously spinning coil produces sinusoidal voltage. The magnetometer calibration also reinforces vector decomposition of fields into components, a skill used throughout electromagnetism.
Faraday's Law experiment, maximising induced EMF, Earth's magnetic field, iOLab magnetometer, high gain offset, high gain sensor, coil turns vs area trade-off, magnetic flux change, 180-degree flip, AC generator principle, G+ G− sensor, A1 GND input, magnetometer calibration, PHYS 142, Physics 142 Lab 7, electromagnetic induction lab, reproducible EMF measurement