Electromagnetic induction
Slide a rod along rails through a magnetic field: ε = BLv, and Lenz’s law brings it to a stop.
Fields — Action at a distance: gravitational, electric and magnetic fields and the paths in them.
Experiments already set up on it
emf against speed
Hold the rod at a steady speed: ε against v is a straight line of gradient BL.
- ε = BLv
- Getting B from the gradient when L is known
emf against field strength
At a fixed speed, ε against B is a straight line of gradient Lv.
- ε = BLv
- Every term in the relation can be checked separately
Lenz’s law brings it to a stop
Let the rod coast: the time to slow to 1/e of its speed is mR/B²L².
- The induced current opposes the change that made it
- τ = mR/B²L², so doubling B brakes four times as hard
- The kinetic energy goes into heating the resistance
Watching it slow down
Record the speed, the emf and the current as the rod coasts to a halt.
- Exponential decay
- Kinetic energy becoming heat
What you can measure
Each of these can be recorded over time, aggregated over a run, or read at the moment something happens — through an instrument that carries its own uncertainty.
- Timet (s)
- Predicted time constantτ (s)
- Distance alongx (m)
- Speedv (m/s)
- Accelerationa (m/s^2)
- Induced emfε (V)
- Induced currentI (A)
- Force opposing the motionF_B (N)
- Power dissipatedP (W)
- Flux through the circuitΦ (T*m^2)
- Charge movedQ (C)
- Kinetic energyE_k (J)
- Energy turned to heatQ_h (J)
What you can change
Any of these can be the thing you vary, and every combination of the ones you choose is run as its own trial.
- Magnetic flux densityB (T)
- Length of the rodL (m)
- Length of the trackd (m)
- Resistance of the circuitR (ohm)
- Resistance of the rodr (ohm)
- Mass of the rodm (kg)
- Speed it is launched atv_0 (m/s)
- Steady push along the railsF (N)
- Frictionb (N*s/m)
The equations behind it
What electromagnetic induction is built on. Every one of these is in the lab's formula reference too, where it copies straight into a write-up.
Magnetic effects
- Force on a current-carrying wire
- Force on a moving charge
- Radius of a charged particle’s path
- Field around a straight wire
Electromagnetic induction
- Magnetic flux
- Faraday’s law — The minus sign is Lenz’s law: it opposes the change.
- EMF across a moving rod
- EMF from a rotating coil
- Root mean square current
- Root mean square voltage
- Ideal transformer
Also in Fields
Orbits & gravitation
Put a satellite in orbit and measure its period against its radius, for Kepler’s third law.
Charged particle in a field
Fire a charge through electric and magnetic fields and watch the path bend, for E = V/d and r = mv/qB.
AC generator
Spin a coil in a magnetic field and measure the alternating emf: ε = NBAω sin ωt.
Electric charges & fields
Arrange point charges, map the field and the potential, then let a charge go and watch it fly.
Parallel-plate capacitor
Two plates whose size, spacing and filling you choose: C against 1/d gives ε₀, and pushing the voltage too far breaks the material down.