OPOpenPithMake curiosity visiblePhysics lab / Fields

About this lab

Five experiments, one thread: you cannot see a field, but you can measure what it does.

The first two look at electric fields: the probe shows that field strength and potential are different things, and the capacitor shows what sets the field between its plates. The third shows how a magnetic field pushes on a moving charge. The last two turn it round: how a changing magnetic field drives a current, and how a turning coil makes alternating current.

Every reading, curve and table row comes from the same physics model, not from a pre-drawn animation. Change one parameter and all of it is recalculated together.

Five results

Run the experiments and you will arrive at these five statements.

  1. On the perpendicular bisector of equal and opposite charges the potential is zero everywhere, yet the field is not. At the midpoint between equal like charges the field is zero, yet the potential is highest. A zero in one does not mean a zero in the other.
  2. Charge the capacitor, disconnect it, and triple the gap: C falls to a third, U triples, and the field between the plates stays the same. Only with the supply left connected does the field fall to a third.
  3. In a uniform magnetic field the electron keeps its speed and circles with radius r = mv/(eB). At 200 V and 1.4 A the diameter is about 8.7 cm, giving e/m ≈ 1.78 × 10¹¹ C/kg, about 1 % from the accepted 1.759 × 10¹¹ C/kg.
  4. With the magnet resting in the middle of the coil the flux is largest and the current is zero. Double the speed and the peak current doubles, while the charge that flows stays the same (about 86 μC with 400 turns).
  5. In the neutral plane the generator coil has the largest flux and zero EMF. With 100 turns at 120 r/min the peak EMF is about 0.50 V and the RMS value about 0.36 V.

Model and sources

Model and sources

  • Field and potential: outside each metal sphere the field is that of a point charge; induction between the spheres is ignored. The probe only scans outside the spheres, so it never meets the point-charge singularity. Field lines and equipotentials are traced numerically from the field direction and are a picture only.
  • Capacitor: ideal parallel plates with edge effects ignored; 20 cm square plates, charged to 200 V, gap pulled from 2 cm to 6 cm.
  • e/m apparatus: at the centre of the Helmholtz pair B = (4/5)^{3/2} μ₀NI/R, with 130 turns per coil and radius 15 cm; the diameter is read to 1 mm.
  • Induction: the magnet is modelled as a pair of magnetic poles; the 400-turn coil is wound evenly on a tube 8 cm long and 2.5 cm in radius, and the flux linkage has a closed form.
  • Generator: B = 0.2 T, a 5 cm × 4 cm coil turning steadily from the neutral plane.

Constants are the CODATA 2018 recommended values. The coil turns and radius follow common teaching e/m tubes; the magnet moment of 1.5 A·m², the 60 Ω galvanometer and the 0.2 T generator field are teaching assumptions for comparing size and direction, not measurements of a real instrument. Arrow lengths are schematic only.

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