Biot-Savart law

This activity allows students to experimentally verify the relationship between the intensity of the electric current and the magnetic field produced. It develops the ability to establish a relationship between physical quantities and to deduce a law.

In April 1820, Hans Christian Ørsted noticed that a compass needle deflected when placed near a wire carrying electric current, revealing an unexpected connection between electricity and magnetism that would transform physics. Just months later, Jean-Baptiste Biot and Félix Savart quantified this relationship, establishing the law that bears their names: the magnetic field produced by a current-carrying wire is proportional to the current intensity and inversely proportional to the distance from the wire. This discovery laid the foundation for electromagnetism and ultimately for technologies that define modern life, from electric motors and generators to MRI scanners and magnetic data storage. The remarkable precision of smartphone magnetometers, capable of detecting fields as small as 0.1 microtesla, now makes it possible to verify the Biot-Savart law using equipment no more sophisticated than a coil of wire, a battery, and a phone. In this experiment, students recreate one of the foundational experiments of electromagnetic theory, directly measuring how the magnetic field produced by a coil varies with the current flowing through it.

Learning objectives:

The student uses the FizziQ magnetometer to measure the magnetic field created by a coil carrying a current. By gradually varying the intensity of the current and recording the Y component of the magnetic field, the student draws a graph making it possible to determine the relationship between these two quantities and verifies the linearity predicted by the Biot-Savart law.

Level:

High school

FizziQ

Author:

Duration (minutes) :

45

What students will do :

- Measure the magnetic field produced by a current-carrying coil using the smartphone magnetometer
- Vary the current intensity and record the corresponding magnetic field values
- Plot the graph B = f(I) and verify the linear relationship predicted by the Biot-Savart law
- Determine the proportionality constant and relate it to the coil geometry and µ₀
- Identify and evaluate experimental sources of error in magnetometric measurements

Scientific concepts:

- Magnetic field
- Electromagnetism
- Biot-Savart law
- Relationship of proportionality
- Coils and solenoids

Sensors:

- Magnetometer (magnetic field sensor, Y-component or total field)

What is required:

- Smartphone with the FizziQ application
- A coil or solenoid
- An adjustable direct current generator
- Connection wires
- A multimeter (optional) to measure precise intensity
- FizziQ experience notebook

Experimental procedure:

Assemble the circuit: connect the coil (or solenoid) to the adjustable DC power supply using connection wires. Insert an ammeter (or multimeter in current mode) in series to measure the current precisely.
Open FizziQ and select the Magnetometer sensor. Choose the Y-component of the magnetic field (the component aligned with the coil axis).
Before powering on the circuit, calibrate the magnetometer by recording the baseline reading. This accounts for the Earth's magnetic field and any nearby magnetic sources. Note this as B₀.
Position the smartphone so that its Y-axis is aligned with the axis of the coil, with the sensor at the center of the coil. Secure the phone so it does not move during the experiment.
Set the power supply to the lowest current setting (e.g., 0.1 A). Turn on the circuit and wait 5 seconds for the reading to stabilize. Record both the current (I) and the magnetic field reading (B).
Calculate the net field produced by the coil: B_coil = B - B₀ (subtract the baseline).
Increase the current by 0.1 A increments (or appropriate steps for your power supply), recording B and I at each step. Collect at least 8-10 data points.
Do not exceed the maximum recommended current for your coil to avoid overheating. If the coil becomes warm, pause between measurements.
Enter all data pairs (I, B_coil) in the FizziQ notebook and plot the graph B_coil vs. I.
Use the FizziQ curve fitting tool to fit a straight line to the data: B = kI. Record the slope k.
Compare the measured slope with the theoretical prediction: for a solenoid, k = µ₀ × n, where µ₀ = 4π×10⁻⁷ T·m/A and n is the number of turns per unit length.
Discuss the quality of the linear fit, identify any outliers, and evaluate whether the Biot-Savart law is confirmed by your data.

Expected results:

The graph of B_coil versus I should be a straight line passing through or very near the origin, confirming the proportionality predicted by the Biot-Savart law. The slope of the line depends on the coil geometry: for a solenoid with n turns per meter, the theoretical slope is µ₀n. For example, a solenoid with 1000 turns/m would produce a slope of about 1.26 × 10⁻³ T/A = 1.26 mT/A. The typical magnetic field values measured will range from a few microtesla (at low currents) to a few hundred microtesla (at higher currents). The coefficient of determination R² should exceed 0.98 for careful measurements. Deviations from perfect linearity may occur at high currents (due to coil heating changing resistance) or at very low currents (where the coil field is comparable to environmental magnetic noise). Students should expect measurement uncertainty of ±0.5-1 µT from the magnetometer and ±0.01 A from the ammeter.

Scientific questions:

- Why is the magnetic field at the center of a coil proportional to the current? What happens if the current doubles?
- How would the results change if you used a coil with twice as many turns?
- What are the main sources of error in this experiment, and which one contributes most to the uncertainty?
- Why is it important to calibrate the magnetometer before starting the measurements?
- How is the Biot-Savart law applied in the design of MRI machines or electric motors?
- What would happen if you measured the magnetic field at a point off the axis of the coil?

Scientific explanations:

The Biot-Savart law, established in 1820 by French physicists Jean-Baptiste Biot and Félix Savart, is one of the fundamental laws of electromagnetism. It describes how an electric current generates a magnetic field.

For a coil or a solenoid, this law predicts that the magnetic field B at the center is directly proportional to the intensity of the current I passing through it, according to the relation B = µ₀nI, where µ₀ is the magnetic permeability of the vacuum (4π×10⁻⁷ T·m/A) and n the number of turns per unit length. The smartphone's magnetometer measures the magnetic field along three orthogonal axes with a sensitivity of approximately 0.1 µT.

By aligning the Y axis of the magnetometer with the axis of the coil and calibrating the sensor to subtract the Earth's magnetic field, we can measure only the field created by the coil. The main experimental difficulties include: 1) Precise alignment of the smartphone relative to the coil; 2) Surrounding magnetic interference; 3) Heating of the coil for high currents which can slightly modify its resistance.

By drawing the graph B = f(I), we should obtain a line whose slope corresponds to the factor µ₀n. Verification of this linearity confirms the validity of the Biot-Savart law for this configuration.

This experiment provides an accessible introduction to electromagnetism and illustrates how an electric current can generate a magnetic field, a fundamental principle underlying many modern technologies such as electric motors, transformers or MRIs.

Extension activities:

Frequently asked questions:

Q: The magnetic field reading fluctuates a lot even when the current is stable. What can I do?
R: Magnetic interference from nearby electronic devices, metal furniture, or structural steel can cause fluctuations. Move the experiment away from computers, monitors, and metal objects. Take multiple readings and average them. Also ensure the smartphone is positioned stably and does not move.

Q: My measured slope does not match the theoretical value of µ₀n. Why?
R: Verify the number of turns and the length of your coil carefully. The theoretical formula applies to an ideal infinite solenoid; for a short coil, the field at the center is reduced by a geometry-dependent factor. Also ensure the magnetometer is truly at the center of the coil.

Q: The graph does not pass through the origin. Is this a problem?
R: A small y-intercept can result from imperfect baseline subtraction (the Earth's field may have shifted slightly due to the phone moving) or from residual magnetization of the coil core. Ensure you subtract the baseline value B₀ carefully and that the phone has not moved between the calibration and the measurements.

Q: What type of coil should I use for this experiment?
R: Any coil or solenoid with a known number of turns will work. A physics lab solenoid with 500-2000 turns is ideal. If unavailable, you can wind your own coil around a cardboard tube using insulated copper wire. Count the turns carefully and measure the coil length to calculate n.