Physics · Electricity and magnetism · Grade 10

Shake torch

How does a torch light up without a battery?

The situation

Shake a battery-free “shake torch” for a few seconds and it lights up. Inside is a transparent tube with a strong magnet that slides freely in it, and a copper-wire coil wound around the middle of the tube. Every time the magnet passes through the coil, a current appears in the wire. The faster you shake it, the brighter it glows — why?

Topic

Electromagnetic induction. Shake-to-charge torch and bicycle dynamo

Key ideas

Faraday's law
Lenz's law
Magnetic flux

Formulas

Φ = B S \cos α

Magnetic flux: the “amount” of field passing through a surface, in webers (Wb).

ℰ = - N \frac{Δ Φ}{Δ t}

Faraday's law: the emf equals the rate of change of flux; the minus sign is Lenz's law.

\oint \vec{E} \cdot d \vec{l} = - \frac{d Φ}{d t}, ℰ = B l v

Vortex electric field: a changing magnetic field creates an electric field with closed field lines. In a moving wire the emf equals $B l v$ .

Φ (z) = \frac{μ_{0} m a^{2}}{2 {(a^{2} + z^{2})}^{3 / 2}}

Flux through a loop of radius $a$ when a magnet (a dipole of moment $m$ ) is at distance $z$ along the axis.

I = \frac{ℰ}{R}, F_{t} = \frac{ℰ I}{v}

Current in the circuit (in the bulb $P = I^{2} R_{l}$ ) and magnetic braking: the current slows the magnet or the wire, and its kinetic energy turns into heat. For a moving wire $F_{b} = B^{2} l^{2} v / R$ .

Theory

When the flux changes, a current appears

As the magnet approaches the coil, the number of magnetic field lines passing through the turns increases; as it moves away, it decreases. Where there is change, there is an emf: if the magnet stays still inside the coil, there is no current, even though the flux is large.

Lenz's law

The induced current flows in such a direction that its magnetic field opposes the change in flux. When the magnet enters, the coil pushes it away; when it leaves, the coil pulls it back. That is why the emf has opposite signs on entering and on leaving.

Why two peaks?

As the magnet enters the coil, $Φ$ increases ( $ℰ < 0$ ); after it passes the middle, the flux decreases ( $ℰ > 0$ ). When the magnet is exactly in the middle, $d Φ / d z = 0$ — at that moment the current is zero. A falling magnet moves faster lower down, so the second peak is higher.

Where does the energy come from?

The energy to light the bulb comes from your hand: as you shake, you do work against the magnetic braking force. Check this in “Drop” mode: the mechanical energy lost, $m g h - \frac{1}{2} m v^{2}$ , turns out to equal the heat in the circuit, $\int I^{2} R d t$ .

Vortex electric field and eddy currents

What sets the electrons in a stationary coil moving? A magnetic field does not act on a charge at rest. Maxwell explained that a changing magnetic field creates an electric field in space, whose field lines do not start on charges — they are closed loops (a vortex field): $\oint \vec{E} \cdot d \vec{l} = - d Φ / d t$ . This field exists even without a wire; the wire only “shows” the current. In a solid piece of metal this field drives circular eddy currents: they heat the metal (an induction hob) and brake its motion (damping a galvanometer needle, magnetic brakes on trains). When a changing current in a coil induces an emf in the coil itself, this is self-induction (the “Self-induction” experiment); when it induces one in a neighbouring coil, it is mutual induction (the “Power transmission line” experiment). The $E$ in the HUD is the field along the turn: $E = | ℰ | / (N \cdot 2 π a)$ .

Moving wire: electron theory and the relativity of fields

In “Moving wire” mode a copper wire slides along rails in a uniform field. The electrons inside the wire also move with it at speed $v$ , so the Lorentz force $F = e v B$ acts on them along the wire: the electrons are pushed towards one end, and an emf $ℰ = B l v$ appears across the ends of the wire. This is Faraday's law itself: the area of the circuit changes by $Δ S = l v Δ t$ , so $Δ Φ / Δ t = B l v$ . The Ampère force acting on the induced current opposes the motion (Lenz): to pull the wire at constant speed, a power $F v = ℰ I$ must be supplied. For an observer moving with the wire, the wire is at rest and the electrons are pushed by an electric field $E^{'} = v B$ : what one observer calls a “magnetic force”, another calls an “electric force” — electric and magnetic fields are relative. The general law is the same for moving conductors: $ℰ = \oint (\vec{E} + \vec{v} \times \vec{B}) \cdot d \vec{l} = - d Φ / d t$ .

Did you know?

Electromagnetic induction was discovered in 1831 by the English scientist Michael Faraday: he experimented with two coils wound on an iron ring and with a moving magnet.
The bicycle dynamo, generators in power stations and induction hobs all work on this same law, $ℰ = - N Δ Φ / Δ t$ .

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Electric current in metals — Grade 8
Electrolysis, Faraday's laws — Grade 8
Electric current in vacuum and gases — Grade 8
Magnetic field — Grade 8
Electromagnet and relay — Grade 8
Self-induction — Grade 10
Magnetic properties of matter — Grade 10
Plasma — the fourth state — Grade 10
Power transmission line — Grade 11
Microwaves and Wi-Fi — Grade 11