Physics IA · D · Fields · topic 22 of 30

Two magnets: how does the force fall with distance? · IB Physics IA idea: guide, sample graph and step-by-step plan

easy to build badly, great to build well

Point charges follow an inverse square law. Real magnets don't, and you're going to measure exactly how they break the rules.

Difficulty●●○ Medium
KitStandard: balance or force sensor, neodymium magnets
TimeAbout 10 hours
FitsSL and HL (the dipole model is beyond the course)
  • ✓ you like finding a power law
  • ✓ you can build a rig that does not wobble
  • ✓ you enjoy testing a model that is only half right

The big idea

← the bend is the interesting bit!

Far from two small magnets, theory for magnetic dipoles predicts a force that falls off much faster than an inverse square, roughly as 1/d⁴. Close up, the magnets are not point-like, so the real law is different. A graph that starts as a power law and then bends is a gift: you can test which model fits where and explain why. Measuring force against gap with a balance is simple in principle and unforgiving in practice.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Find the exponent

Fit a power law to force against separation, using the distance between magnet centres, not faces.

→ Your key result becomes the exponent with its uncertainty, compared with the dipole-model value; the offset between face and centre becomes part of the analysis.
Compare magnet shapes

Discs, cubes or spheres of similar strength.

→ Tests whether the shape changes how closely the point-dipole model works at a given distance.
Attraction versus repulsion

Measure both, same gaps, same magnets.

→ Are the forces equal in size? Any difference points to the other magnet's field changing the first magnet's magnetisation, a nice evaluation point.
Use a force sensor or a lever

Replace the balance with a force sensor, or a beam balance made from a ruler.

→ Different resolution and different systematic errors; you can compare two methods.
Stack the magnets

Repeat with two, then three magnets stacked to make a longer magnet.

→ How does the force depend on the magnet's length? Extends the investigation into a second variable, so keep one of them as the main one.
Add a shield

Place a thin sheet of different materials between the magnets.

→ Changes the independent variable to the material. Choose sheets that are not magnetic steel or you will be measuring the sheet.

Your Physics IA research question: run the check

write it FIRST, then check it

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable with its range (which separations, measured from where, how many values).
  • Names the dependent variable and how you will get it (a balance reading converted to force, or a force sensor).
  • Says what stays fixed: the pair of magnets, the orientation, the alignment on one axis.
  • Says what you will compare your results with (a power law, the dipole model, or a model you derive).
  • Is narrow enough for about 10 hours, with enough values at the small and large ends of your range.

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The set-up

A balance does the hard work: the pan reads the change in mass caused by the force. Draw your own version, with real distances, for the Method.

BAdheld by a plastic rodmagnet A on a wood spacerbalance shows Δmstand is steel:keep it well awaylike poles face each other

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question, where magnetic forces matter (maglev, motors, magnetic latches) and what you expect the graph to do.
Background physics~450
Magnetic poles and dipoles, the model you will test and its assumptions, and why a real magnet breaks them at short range.
Variablestable
Independent, dependent and controlled variables with how each is set and kept constant.
Method~400
How you hold and align the magnets, how you set and measure each gap, how you zero and read the balance, and how you keep steel away.
Safety, ethics, environment~70
Pinching and flying magnets, swallowing risk, keeping magnets away from phones, cards and implanted medical devices.
Raw datatable
Gap and balance readings with units and resolution; zero readings recorded.
Processing~250
Converting mass change to force, handling the offset between face gap and centre separation, and uncertainties; worked examples.
Graphs and analysis~400
Force against separation, and a graph that turns your model into a straight line; what the gradient and intercept mean.
Conclusion~400
What law your data follows, over what range, compared with the model; where it stops working and why.
Evaluation~650, the biggest part!
Weaknesses ranked by effect on your result, linked to specific improvements.
Referencesnot counted
Sources for the model and for any magnet specifications.

What your Physics IA graph could look like

two models on one graph ✓

Made-up data, to show the form of a strong graph, not the answer. Yours will look different. example only

812162024283236400100200300400500600700800900Gap between magnet faces d / mm (± 1 mm)Force F / mN (± 5 mN)dipole model, F ∝ 1/(d + 5 mm)⁴inverse square, for comparisonyour data, with error barssmall forces at large gaps:the error bars get big in % termsILLUSTRATIVE · MADE-UP DATA
  • The gap is measured between faces, but the theory uses centre-to-centre. Show how you handled the difference.
  • Error bars in both directions. A 1 mm error in gap matters far more at small gaps, where the force changes quickly.
  • Two models drawn so the reader can see which one the data follows, and where.
  • On a linear scale the large-gap data are squashed against the axis. Say so, and choose a second graph to show them.
  • Another graph to consider: ln F against ln(d + offset). If a power law holds, the gradient is the exponent.

Which uncertainty matters most?

Rank by the effect on your result, here the force at a gap of 20 mm. For a steep law, a small error in distance is a large error in force.

Reading the gap (±1 mm)16%Gap drift (±0.5 mm)8%Balance (±0.01 g)0.2%biggest effect: discuss this first!% uncertainty in F at a 20 mm gap (assuming F ∝ 1/(d + 5 mm)⁴)ILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

the trial run will find your steel!

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictFind the dipole-model prediction and the assumptions behind it. Sketch what you expect force against gap to look like, and where you expect the model to fail.
  2. Trial run (1 lesson)Hang one magnet and read the balance at five gaps. Does the reading drift? Does the magnet twist or slide sideways? Does anything steel change the reading?
  3. Build the rigMake the holder from wood, plastic or brass, with a way to set and repeat a gap precisely (spacers or a lab jack). Check the magnets stay on one axis.
  4. Choose the rangeChoose at least 7 gaps, with more at small distances where the force changes quickly. Decide how many repeats and write down why.
  5. Collect the dataZero the balance before each reading. Record raw readings with units. Note any sudden changes, they become evaluation evidence.
  6. ProcessConvert mass change to force, deal with the face-to-centre offset, and work out the uncertainty in each force.
  7. Graph and fitPlot force against gap, then a graph that makes your model a straight line. Add error bars and compare with the model.
  8. Compare with theoryOver what range does the model work? What does the exponent come out as, with its uncertainty?
  9. EvaluateRank the sources of uncertainty by their effect on your conclusion. Link every improvement to a specific weakness.
  10. Check before your teacher's draftRun the checklist above, then get your RQ or draft checked. Your teacher reads one draft only.

Physics you'll need

Traps to avoid in this Physics IA

  • Measuring from the face of the magnet but using a centre-to-centre formula.
  • Steel nearby: a clamp stand, a bench leg or a steel pan changes the field and the reading.
  • The magnets twisting or sliding sideways as they get close, so the force is no longer along one axis.
  • Too few points at small gaps, where the force changes fastest.
  • Forgetting that a balance reads mass: showing no conversion to force, or no zero check.
  • Calling a curve "inverse square" because it falls, without testing the exponent.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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