ElectromagnetismElectromagnetism

Topic Topic 12.112.1 Electromagnetic Electromagnetic InductionInduction

Induced Electromotive Force Induced Electromotive Force (e.m.f.)(e.m.f.)

What is What is electromagnetic electromagnetic induction?induction?

The diagram The diagram shows a copper shows a copper rod connected to rod connected to an ammeter: an ammeter:

There is no battery There is no battery in the circuit. in the circuit.

What happens when you move the What happens when you move the copper rod downwards, to cut copper rod downwards, to cut across across the the horizontal magnetic field?horizontal magnetic field?

The pointer on the meter makes a brief The pointer on the meter makes a brief `flick' to the right, showing that an electric `flick' to the right, showing that an electric current has been current has been induced.induced.

What happens when you move the rod What happens when you move the rod upwards? upwards?

The meter again gives a `flick', but this The meter again gives a `flick', but this time to the left.time to the left.

You have now induced a current in the You have now induced a current in the opposite direction.opposite direction.

If you hold the rod stationary, or if you If you hold the rod stationary, or if you move the rod move the rod along along the field lines, there is the field lines, there is no induced current.no induced current.

Why does electromagnetic Why does electromagnetic induction occur?induction occur?

When you move the copper rod, its free When you move the copper rod, its free electrons move with it.electrons move with it.

But when a charge moves in a magnetic field it But when a charge moves in a magnetic field it experiences a force on itexperiences a force on it

(the B Q v force).(the B Q v force). You can use Flemings Left hand Rule to show You can use Flemings Left hand Rule to show

that the force on each electron is to the left as that the force on each electron is to the left as shown in the diagramshown in the diagram

(Remember that an electron moving down has to (Remember that an electron moving down has to be treated like a positive charge moving up.be treated like a positive charge moving up.

So electrons accumulate at one end of the rod, So electrons accumulate at one end of the rod, making it negative.making it negative.

This leaves the other end short of electrons and This leaves the other end short of electrons and therefore positive.therefore positive.

There is now a There is now a voltage (potential difference) voltage (potential difference) across the ends of the moving rod.across the ends of the moving rod.

If the ends of the moving rod are joined to form a If the ends of the moving rod are joined to form a complete circuit, the induced voltage causes a complete circuit, the induced voltage causes a current to flow round the circuit as shown by the current to flow round the circuit as shown by the flick of the ammeter.flick of the ammeter.

The induced voltage is a source of The induced voltage is a source of electrical energy ‑ an electrical energy ‑ an e.m.f e.m.f

When a conductor is moving in a magnetic When a conductor is moving in a magnetic field like this, field like this, an e.m.f is induced, an e.m.f is induced, even if even if there isn't a complete circuit for a current there isn't a complete circuit for a current to flow.to flow.

Formula for a Straight Formula for a Straight ConductorConductor

Consider a Consider a conductor of length l conductor of length l that moves with that moves with velocity v velocity v perpendicular to a perpendicular to a magnetic flux density magnetic flux density or induction B as or induction B as shown in the figure.shown in the figure.

When the wire conductor moves in the When the wire conductor moves in the magnetic field, the free electrons magnetic field, the free electrons experience a force because they are experience a force because they are caused to move with velocity v as the caused to move with velocity v as the conductor moves in the field.conductor moves in the field.

F = e v BF = e v B

This force causes the electrons to drift This force causes the electrons to drift from one end of the conductor to the from one end of the conductor to the other, and one end builds‑up an excess other, and one end builds‑up an excess of electrons and the other a deficiency of electrons and the other a deficiency of electrons.of electrons.

This means that there is a potential This means that there is a potential difference or difference or emfemf between the ends. between the ends.

Eventually, the Eventually, the emfemf becomes large becomes large enough to balance the magnetic force enough to balance the magnetic force and thus stop electrons from moving.and thus stop electrons from moving.

evB = eE ( from F = evB and F = eE)evB = eE ( from F = evB and F = eE)Therefore E = BvTherefore E = Bv If the potential difference (emf) between If the potential difference (emf) between

the ends of the conductor is the ends of the conductor is εε then then εε = E L (from E = V/d) = E L (from E = V/d)By substitution we haveBy substitution we haveεε = B v L = B v L

Magnetic FluxMagnetic Flux

The The magnetic flux (magnetic flux (ΦΦ)) through a region is a through a region is a measure of the number of lines of magnetic measure of the number of lines of magnetic force passing through that region.force passing through that region.

ΦΦ = AB cos = AB cos θθ where A is the area of the region and where A is the area of the region and θθ is the is the

angle of movement between the magnetic field angle of movement between the magnetic field and a line drawn perpendicular to the area swept and a line drawn perpendicular to the area swept out.out.

The The unit of magnetic flux unit of magnetic flux is theis the weber weber Wb.Wb.

For a single conductor in the magnetic flux For a single conductor in the magnetic flux density, it can be seen thatdensity, it can be seen that

εε = - = - ΔΦΔΦ/ / ΔΔt t (the rate of change of flux density)(the rate of change of flux density) For N number of conductors as in the case for For N number of conductors as in the case for

a solenoid, the term a solenoid, the term flux‑linkageflux‑linkage is used. is used. ThenThen εε = - N = - N Δ Δ ((ΦΦ/ / ΔΔt)t) This is Faraday’s LawThis is Faraday’s Law The minus sign shows us that the emf is The minus sign shows us that the emf is

always produced so as to oppose the change always produced so as to oppose the change in flux.in flux.

Time-changing Magnetic FluxTime-changing Magnetic Flux

Therefore the production of an emf is Therefore the production of an emf is produced by a time changing magnetic produced by a time changing magnetic flux.flux.

This could be due to the wire or coil This could be due to the wire or coil moving through a magnetic fieldmoving through a magnetic field

Or by an increasing or decreasing Or by an increasing or decreasing magnetic field of an electromagnet next to magnetic field of an electromagnet next to a wire or coil.a wire or coil.

Faraday’s LawFaraday’s Law

We know that an e.m.f. is induced when there is We know that an e.m.f. is induced when there is a change in the flux linking a conductor.a change in the flux linking a conductor.

Faraday's law makes the connection between Faraday's law makes the connection between the size of the induced e.m.f. and the the size of the induced e.m.f. and the rate rate at at which the flux is changing.which the flux is changing.

It states that: It states that: the magnitude of the induced e.m.f is directly the magnitude of the induced e.m.f is directly

proportinonal to the rate of change of magnetic proportinonal to the rate of change of magnetic flux or flux linkage.flux or flux linkage.

LinkingLinking

For a single conductor in the magnetic flux For a single conductor in the magnetic flux density, it can be seen thatdensity, it can be seen that

εε = - = - ΔΦΔΦ/ / ΔΔt t (the rate of change of flux (the rate of change of flux density)density)

And And εε = B v l = B v lTherefore Therefore - - ΔΦΔΦ/ / ΔΔt = B v lt = B v l

Lenz’s LawLenz’s Law

Faraday's law tells us the size of the Faraday's law tells us the size of the induced e.m.f., but we can find its direction induced e.m.f., but we can find its direction using using Lenz's lawLenz's law

The direction of the induced e.m.f is such The direction of the induced e.m.f is such that it will try to that it will try to oppose oppose the change in flux the change in flux that is producing it.that is producing it.

Lenz's law is illustrated in the diagrams: As you Lenz's law is illustrated in the diagrams: As you move the N‑pole move the N‑pole into into the coil, an e.m.f. is the coil, an e.m.f. is induced which drives a current round the circuit induced which drives a current round the circuit as shown.as shown.

Now use the right‑hand grip ruleNow use the right‑hand grip rule Can you see that the current produces a Can you see that the current produces a

magnetic field with a N‑pole at the end of the coil magnetic field with a N‑pole at the end of the coil nearest to the magnet?nearest to the magnet?

So the coil So the coil repels repels the incoming magnet, and in the incoming magnet, and in this way the induced current this way the induced current opposes opposes the the change in flux.change in flux.

Why is the current reversed as you move Why is the current reversed as you move the N‑pole the N‑pole out?out?

By Lenz's law, the coil needs to attract the By Lenz's law, the coil needs to attract the receding N‑polereceding N‑pole

Lenz's law is a result of the conservation Lenz's law is a result of the conservation of energy. If you move the magnet into the of energy. If you move the magnet into the coil, you feel the repulsive force.coil, you feel the repulsive force.

You have to You have to do work do work to move the magnet to move the magnet against this force.against this force.

And so energy is transferred from you (or And so energy is transferred from you (or the system that is moving the magnet) to the system that is moving the magnet) to the electrical energy of the current.the electrical energy of the current.