AC generator

Spin a coil in a magnetic field and measure the alternating emf: ε = NBAω sin ωt.

Fields — Action at a distance: gravitational, electric and magnetic fields and the paths in them.

Open it in The Lab The equations behind it

Experiments already set up on it

Peak-to-peak emf against angular speed
The full swing against ω is a straight line of gradient 2NBA.
- ε = NBAω sin ωt
- Getting NBA from the gradient
- Peak against r.m.s.
Peak-to-peak emf against turns
Twice the turns, twice the emf.
- Each turn adds its own emf in series
Peak-to-peak emf against field strength
The last term in NBAω, checked on its own.
- Each factor in ε₀ = NBAω can be tested separately
The shape of the output
Record the flux and the emf together: the emf is the rate the flux changes.
- ε = −dΦ/dt: the emf peaks where the flux changes fastest
- The emf is zero when the flux is greatest

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)
Angle turnedθ (°)
Frequencyf (Hz)
Measured periodT (s)
emf right nowε (V)
Peak emfε_0 (V)
r.m.s. emfε_{rms} (V)
CurrentI (A)
Power deliveredP (W)
Flux linkageΦ (T*m^2)
Energy deliveredE (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.

Number of turnsN (1)
Magnetic flux densityB (T)
Width of the coilw (m)
Height of the coilh (m)
Angular speedω (rad/s)
Angle at the startθ_0 (°)
Resistance of the loadR (ohm)
Resistance of the coilr (ohm)

The equations behind it

What ac generator 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

$F = B I L sin θ$
Force on a current-carrying wire
$F = q v B sin θ$
Force on a moving charge
$r = \frac{m v}{q B}$
Radius of a charged particle’s path
$B = \frac{μ _{0} I}{2 π r}$
Field around a straight wire

Electromagnetic induction

$Φ = B A cos θ$
Magnetic flux
$ε = - N \frac{ΔΦ}{Δ t}$
Faraday’s law — The minus sign is Lenz’s law: it opposes the change.
$ε = B v l$
EMF across a moving rod
$ε = N B A ω sin (ω t)$
EMF from a rotating coil
$I_{rms} = \frac{I _{0}}{2}$
Root mean square current
$V_{rms} = \frac{V _{0}}{2}$
Root mean square voltage
$\frac{N _{p}}{N _{s}} = \frac{V _{p}}{V _{s}} = \frac{I _{s}}{I _{p}}$
Ideal transformer

Also in Fields

Experiments already set up on it

Peak-to-peak emf against angular speed

The full swing against ω is a straight line of gradient 2NBA.

ε = NBAω sin ωt
Getting NBA from the gradient
Peak against r.m.s.

Peak-to-peak emf against turns

Twice the turns, twice the emf.

Each turn adds its own emf in series

Peak-to-peak emf against field strength

The last term in NBAω, checked on its own.

Each factor in ε₀ = NBAω can be tested separately

The shape of the output

Record the flux and the emf together: the emf is the rate the flux changes.

ε = −dΦ/dt: the emf peaks where the flux changes fastest
The emf is zero when the flux is greatest

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)

Angle turnedθ (°)

Frequencyf (Hz)

Measured periodT (s)

emf right nowε (V)

Peak emfε_0 (V)

r.m.s. emfε_{rms} (V)

CurrentI (A)

Power deliveredP (W)

Flux linkageΦ (T*m^2)

Energy deliveredE (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.

Number of turnsN (1)

Magnetic flux densityB (T)

Width of the coilw (m)

Height of the coilh (m)

Angular speedω (rad/s)

Angle at the startθ_0 (°)

Resistance of the loadR (ohm)

Resistance of the coilr (ohm)

The equations behind it

What ac generator 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

$F = B I L sin θ$
Force on a current-carrying wire
$F = q v B sin θ$
Force on a moving charge
$r = \frac{m v}{q B}$
Radius of a charged particle’s path
$B = \frac{μ _{0} I}{2 π r}$
Field around a straight wire

Electromagnetic induction

$Φ = B A cos θ$
Magnetic flux
$ε = - N \frac{ΔΦ}{Δ t}$
Faraday’s law — The minus sign is Lenz’s law: it opposes the change.
$ε = B v l$
EMF across a moving rod
$ε = N B A ω sin (ω t)$
EMF from a rotating coil
$I_{rms} = \frac{I _{0}}{2}$
Root mean square current
$V_{rms} = \frac{V _{0}}{2}$
Root mean square voltage
$\frac{N _{p}}{N _{s}} = \frac{V _{p}}{V _{s}} = \frac{I _{s}}{I _{p}}$
Ideal transformer

AC generator

Experiments already set up on it

Peak-to-peak emf against angular speed

Peak-to-peak emf against turns

Peak-to-peak emf against field strength

The shape of the output

What you can measure

What you can change

The equations behind it

Magnetic effects

Electromagnetic induction

Also in Fields

Orbits & gravitation

Charged particle in a field

Electromagnetic induction

Electric charges & fields

Parallel-plate capacitor

AC generator

Experiments already set up on it

Peak-to-peak emf against angular speed

Peak-to-peak emf against turns

Peak-to-peak emf against field strength

The shape of the output

What you can measure

What you can change

The equations behind it

Magnetic effects

Electromagnetic induction

Also in Fields

Orbits & gravitation

Charged particle in a field

Electromagnetic induction

Electric charges & fields

Parallel-plate capacitor