About This Lesson
A 30–40 minute investigation using two coaxial current loops in Magnetism 3D Lab. Students hold coil separation fixed, vary both loop radii, sample the magnetic field along the common axis, and distinguish field uniformity from field strength. Suitable for grades 11–12 and introductory college physics.
Launch: Open the Helmholtz-coil simulation. Free to use; no account or installation required.
Learning objectives
- Measure the magnetic field along the axis of a coil pair and compare normalized field variation for different geometries.
- Identify the locally uniform Helmholtz configuration and distinguish uniformity from field strength.
- Explain the effect of reversing one current using superposition.
- Evaluate uncertainty from pointer placement and rounded readings.
Prerequisites and materials
Basic understanding of magnetic fields produced by electric currents and superposition. Students should be able to read coordinates, convert meters to millimeters, compute an average and a ratio, and plot data. Calculus is not required. Work in pairs with a desktop or Chromebook browser, a mouse or trackpad, and a calculator plus a spreadsheet or graph paper.
Set up the investigation
Open the simulation 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.
Student activity
- Predict how uniform the field is near the midpoint. Distinguish uniformity (small spatial variation) from strength (large magnitude).
- 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.
- 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.
- Change BOTH radii to 0.004 m, giving d/R = 2. Recompute and repeat the measurements.
- 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.
- 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.
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.
Technology and accessibility
A modern browser with JavaScript enabled is required; WebGL is needed for the optional 3D step. 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. See the accessibility information.
Attribution and software terms
By Nima Bigdely-Shamlo. Adapted in formatting from Helmholtz coils: measuring magnetic-field uniformity on MERLOT, published under CC BY 4.0. This Share My Lesson copy is additionally offered under CC BY-NC-SA. The lesson license does not apply to the simulator software, which is proprietary and governed by its separate terms.
