Magnetic ruler
Measure the speed of a moving object using magnets placed at regular intervals and the smartphone magnetometer.
How can you measure the speed of a moving object without a camera or stopwatch? The smartphone magnetometer offers an elegant solution: by placing magnets at regular intervals along the path, each passage past a magnet creates a sharp peak in the magnetic field signal. The time between peaks, combined with the known spacing, directly gives the speed. This technique is the basis of many industrial speed sensors and even some speedometers.
Learning objectives:
The student places magnets at regular intervals along a path and records the magnetic field from a smartphone attached to a moving object. Speed is calculated from the time intervals between magnetic field peaks.
Level:
High School
FizziQ
Author:
Duration (minutes) :
30
What students will do :
- Measure a magnetic field with the smartphone magnetometer
- Calculate average speed from distance and time measurements
- Distinguish instantaneous speed from average speed
- Trace position and speed graphs from magnetic peak data
- Understand the 1/r³ decay of dipole magnetic fields
Scientific concepts:
- Magnetic field
- Dipole field decay (1/r³)
- Instantaneous and average velocity
- Rectilinear kinematics
- Magnetic detection
- Signal processing
Sensors:
- Magnetometer
What is required:
- Smartphone or tablet with FizziQ
- Small magnets (neodymium or refrigerator magnets)
- A straight track (toy train rails, gutter, table edge)
- A moving object (toy train, cart)
- Tape measure and adhesive tape
Experimental procedure:
Choose a straight track: toy train rail, gutter, curtain rod, or table edge.
Place magnets at regular intervals along the track (for example every 10 or 20 cm). Use a tape measure for precise placement.
Measure and note the distance d between two consecutive magnets.
Attach your smartphone to the moving object (toy train, cart). The magnetometer must pass close to the magnets. Identify which side of the phone has the sensor.
Open FizziQ and select the Magnetometer instrument. Ideally, use remote control from a second device.
Start the recording while the smartphone is stationary at the starting point.
Set the object in motion along the rail. The phone must pass at the same distance from each magnet.
Stop the recording at the end of the track, before removing the phone.
Observe the magnetic field versus time graph. You should see sharp peaks corresponding to each magnet passage.
From the time intervals between peaks and the known distance d, calculate the average speed in each interval: v = d/Δt. Plot speed versus time to analyze acceleration or deceleration.
Expected results:
The magnetic field graph shows sharp, regularly spaced peaks corresponding to each magnet. For a toy train at constant speed, the intervals between peaks are equal. For an accelerating cart on an inclined plane, the intervals decrease as the object speeds up. Speed precision is typically ±2-5% depending on the regularity of magnet placement and motion.
Scientific questions:
- How does the shape of the peaks change if you modify the distance between the sensor and the magnets?
- Why does the 1/r³ decay allow precise detection of individual magnets?
- What is the difference between average speed and instantaneous speed in this experiment?
- How could you use this technique to measure acceleration?
- Why are neodymium magnets better than ferrite magnets for this experiment?
- What industrial applications use a similar magnetic detection principle?
Scientific explanations:
The smartphone magnetometer is an extremely sensitive magnetic field sensor, capable of detecting fields as small as 0.1 µT. Near a small neodymium magnet, the field can reach several hundred µT.
The magnetic field of a dipole (small magnet) decays as 1/r³. This very rapid decay means each magnet creates a sharp, localized peak in the signal, with minimal overlap from neighboring magnets.
The average speed between two magnets is calculated by v = d/Δt, where d is the distance between magnets and Δt is the time between corresponding peaks.
The precision depends on the magnet placement and the constancy of the phone-magnet distance. On a guided rail, one can achieve 1-2% precision on the speed measurement.
Caution: electric motors (in a toy train) also generate a parasitic magnetic field. Keep the phone sensor away from the motor to avoid interference.
Extension activities:
- How does the shape of the peaks change if you modify the distance between the sensor and the magnets?
- Why does the 1/r³ decay allow precise detection of individual magnets?
- What is the difference between average speed and instantaneous speed in this experiment?
- How could you use this technique to measure acceleration?
- Why are neodymium magnets better than ferrite magnets for this experiment?
- What industrial applications use a similar magnetic detection principle?
Frequently asked questions:
Q: Some magnets are not detected.
R: The phone-magnet distance is probably too large or the magnets too weak. Bring the phone closer to the magnets. Neodymium magnets give the strongest signal.
Q: The peaks overlap and are hard to distinguish.
R: Increase the spacing between magnets or use weaker magnets. Also ensure the phone passes at a constant distance from each magnet.
Q: The baseline drifts during the recording.
R: Earth's magnetic field and local sources create a slowly varying baseline. This does not affect the peak detection. Focus on the sharp variations, not the absolute values.
Q: Can I use this on a bicycle?
R: Yes! Mount the phone on the frame and attach magnets to the wheel spokes. Each spoke passage creates a peak, giving wheel rotation speed and hence the bicycle speed.