Learning Exercise
Helmholtz coils: measuring magnetic-field uniformity
A 30–40 minute investigation using two coaxial current loops. Students hold coil separation fixed, vary both loop radii, sample the magnetic field along the common axis, and distinguish field uniformity from field strength.
- Material:
- Magnetism 3D Lab
- Date last modified:
- September 6, 2026
- Created by:
- Nima Bigdely Shamlo
- License:
-
Magnetism 3D Lab is a free, browser-based interactive magnetic-field simulator for high-school and introductory... see more
Exercise
Work in pairs. Open https://electromagnetism3d.com/try?example=helmholtz and select 2D View. Keep the two loop centers at their preset positions, approximately x = -4 mm and +4 mm on y = 0; their separation d is 8 mm. Do not drag the loops. Double-click a loop to open Object Properties; confirm Current (A) = 20 and Radius (m) = 0.008, then close the dialog. Check the second loop as well.
1. Predict how uniform the field is near the midpoint. Distinguish uniformity (small spatial variation) from strength (large magnitude).
2. For the initial R = 8 mm configuration, compute a Heatmap or Vectors display. Move the pointer along the horizontal axis and use POSITION and FIELD |B| in the status bar to record approximate readings at x = -2, -1, 0, +1, and +2 mm, keeping y as close to zero as possible. Record the actual coordinates and units; small pointer-placement errors and rounded readings limit precision.
3. Change the radius of BOTH loops to 0.016 m using Object Properties > Radius (m) > Save. Keep currents and centers unchanged. This gives d/R = 0.5. Recompute the field display, then measure the same five positions.
4. Change BOTH radii to 0.004 m, giving d/R = 2. Recompute and repeat the measurements.
5. For each configuration, calculate U = (largest measured |B| - smallest measured |B|) / mean measured |B| across the five positions. A smaller U indicates greater uniformity over this sampled interval. Plot |B| divided by the center value against x for all three configurations. Compare the curves and support your conclusion with the measurements. Do not interpret rounded identical readings as proof of a perfectly uniform field.
6. Restore both radii to 0.008 m, so d = R. Switch to 3D View and select Compute Field to inspect the geometry. Explain why an approximately uniform central region is useful in a laboratory. Does the field remain uniform arbitrarily far from the center?
Extension: return to 2D View and reverse ONE loop's current from +20 A to -20 A. Predict the field at the midpoint using superposition, recompute the display, then inspect the field readout near the midpoint. Explain why this is no longer the Helmholtz configuration.
Disciplines
Audience
Technical Notes
Modern desktop or Chromebook browser with JavaScript enabled; WebGL support for the optional 3D step. A mouse or trackpad is useful for sampling. No account or installation is required. Recompute the visualization after changing object properties. Field canvases are visual-only; students needing an accessible alternative should receive an instructor-prepared numerical data table and equivalent analysis questions. Accessibility information: https://electromagnetism3d.com/accessibility/.
Requirements
Basic understanding of magnetic fields produced by electric currents and the principle of superposition. Ability to read coordinates, convert meters to millimeters, compute an average and a ratio, and plot data. A calculator and spreadsheet or graph paper are sufficient. Calculus is not required.
Topics
Magnetic fields of current loops; superposition; Helmholtz coils; field uniformity; normalized data analysis; measurement uncertainty.
Type of Task
Learning Objectives
Measure the magnetic field along the axis of a coil pair; compare normalized field variation for different coil geometries; identify the locally uniform Helmholtz configuration; distinguish field strength from uniformity; explain how superposition changes the field when one current is reversed; evaluate the limits imposed by pointer placement and rounded readings.
Assessment
Submit a table of 15 field readings with actual coordinates and units; three normalized-variation calculations; one graph comparing the three normalized field profiles; and a short conclusion identifying the most uniform configuration over the sampled interval. Discuss pointer-placement and display-rounding uncertainty. Explain the distinction between a zero field at one point and a uniform nonzero field over a region.