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Electromagnetism

Magnetic FieldsMagnetic field: a region where another magnet (or magnetic material) feels a forceField lines show direction of force on a N poleMagnetic field strength aka Magnetic Flux density, BA vector quantityunit: TeslaIndicated by density of field lines

Direction of field given by Maxwells Right Hand grip rule (or think of a screw thread).Reminder: Magnetic field around a wire carrying current

A reminder of some B fields

Demo: rolling rod or jumping wire in magnetic fieldWhy do we get movement?Because a force is acting. Motor Effect.NOT because of magnetic attraction (non-magnetic material)Direction of force relative to:Current?Magnetic field?Flemings LH rule (Motor effect, motor cars drive on the left). (FBI)

Force on a current in a magnetic field

Magnetic force on moving chargesAn electrical charge moving in a magnetic field experiences a force.This is true for electrons moving in a wire in a magnetic field the motor effect.Demo

Flemings Left Hand Rule

Motor Effect QuestionsA wire carries a current horizontally between the poles of a magnet, as shown below. The direction of the force on the wire is:A from N to SB from S to NC opposite to the current directionD In the direction of the currentE vertically upwards?current

Motor Effect QuestionsIn the figure below, AB is a copper wire hanging from a pivot at A and dipping into mercury in a copper dish at B. It is suspended between the poles of a powerful magnet. (a) Copy the diagram and add the magnetic field lines(b) Mark in the direction of the conventional current(c) What will happen when the switch is closed?AB

Force on a current-carrying wireDo the Experiment

Force on a current-carrying wireExperimentally we find the force is proportional to:The magnetic flux density (B)The current flowing in the wire (I)The length of wire (l)We can write:

(Only true for current and field perpendicular. More generally: F=BIlsin)

Definition of the Tesla1T is defined as the magnetic flux density which produces a force of 1N on a 1m length of wire carrying a current of 1A at right angles to the field.1T=1 NA-1m-1

Definition of the AmpereParallel wires carrying currents will exert forces on each other. Each wire produces a magnetic field, which influences the other wire. The ampere is defined as the constant current which, if flowing in two straight parallel conductors placed 1 metre apart in a vacuum, would produce between these conductors a force equal to 2107 newtons per metre of length [Not examinable]

Sometimes appears in exam questionsMake sure you can apply Flemings left hand rule for the two cases:

the length of wire in a magnetic field is 0.05 m. When a current of 2.5 A flows, a force of 0.01 N is shown. What is the magnetic field strength? B = 0.08 T

TAP 412-4

Couple on a coilForce on each side of coil with n turns: F=BILnPair of forces form a coupleTorque of couple=Force x distance between them

But when coil is not perpendicular to field, the effective width is wcosa:

awB

Electric motorDC MotorAC Motor

Force on a moving chargeConsider a charge Q moving at a speed v:

Force always 90 to velocity circular motion

An electron accelerated to 6.0 106 ms1 is deflected by a magnetic field of strength 0.82 T. What is the force acting on the electron? Would it be any different for a proton?F= 7.9 1013 N The value of the force would be the same but the direction would be opposite.

The Hall ProbeUsed to measure magnetic field strengthCurrent flows through a slice of semiconductorForce on moving charges due to magnetic field deflects chargesPotential difference between top and bottom of slice resultsHall voltage a B field strength

An electron passes through a cathode ray tube with a velocity of 3.7 107 m/s. It enters a magnetic field of flux density 0.47 mT at a right angle. What is the radius of curvature of the path in the magnetic field?F = Bqv and F = mv2/r so r=mv/Bqr=44 cm

Note that radius of track depends on the charge/mass ratio of particlesThis is how a mass spectrometer works

Velocity selectorForce on ions due to electric field

Force on ions due to magnetic field

Only particles with certain velocity so forces cancel can pass through

Mass SpectrometerVelocity selectorIt can be shown that only particles with velocity v=E/B pass through the velocity selectorR=mv/qB=mE/qB2If we know the charge (ionisation state), we can find the mass of the particles from the radius of their pathThis enables us to analyse the constituents of complex materials.

Application: cyclotronA cyclotron is a compact particle accelerator

Lawrences CyclotronParticles are repeatedly accelerated when passing between deesVelocity increasesRadius increasesTime for an orbit remains constantConstant frequency drive signal

The first CyclotronAccelerated protons to 80keV

Electromagnetic inductionAny conductor experiencing a changing magnetic field (or moving across a steady magnetic field) will have a p.d. induced across it.If a closed circuit is made, a current will flow.This is the basis of almost all electricity generation.1820 rsted discovers B field of current1831 Faraday discovers induction

Demo: eclipse magnet, wire and centre spot galvoPhET simulation

The right hand ruleNot to be confused with the left hand rule...

Electromagnetic induction

Electromagnetic inductionThe direction of the induced voltage can be reversed by:Reversing the magnetMoving the magnet in the opposite direction

Electromagnetic inductionThe size of the induced voltage can be increased by:Moving the magnet fasterIncreasing the number of turns on the coilUsing a stronger magnetAdding a soft iron core

Magnetic FluxA useful quantity when considering electromagnetic induction

F=BA if area is at 90 to field (F=BAcosq otherwise)(Loosely) total magnetic field experienced by something of a given areaUnit: Weber (Wb)1 Wb = 1T x 1 m2

Faradays LawFaraday found that for an emf to be induced, a conductor must cut field lines.The induced emf is equal to the rate at which the circuit cuts magnetic fluxemf (V)Rate of change of fluxLenzs LawNumber of turns in circuitNF flux linkage

Lenzs LawThe direction of the induced emf is always such that it opposes the change inducing itReally just the principle of conservation of energyWhat would happen if it did not oppose it?Denoted by the minus sign in the formula.

Induction demos, 414-11 (diff tubes?)Magnet falling through a coil

Generating electricityConsider a conducting rod of length L moving at a steady speed v perpendicular to a field with a flux density B:electrons will experience a force Bev along the rod, creating a separation of chargeElectrostatic repulsion opposes this.

Induced emf

Note: area A swept out in time Dt = LvDt, so:

Faradays Lawemf=flux swept out per secondHow to increase e?

Calculate...

Faradays discWhen the disc turns at frequency f an emf is induced between its axle and rimThink of a thin strip:Flux swept out/s=e=BpR2fWith a load have braking system

WindmillsThe blade of a wind turbine has a radius 12 m and rotates every 6 seconds. The turbines axis is aligned N-S, so the blade cuts the horizontal component of the Earths magnetic field, which is 20 mT. Calculate the emf induced across the blade.Flux swept out/s=e=BpR2f=0.0015V

Flux linkageFlux linkage = NF = NBAN is number of turns on a coil, A is the areaThis is for a coil perpendicular to the fieldIf the coil is parallel to the field, flux linkage = 0Emf = rate of change of flux linkage

Generators / dynamosTo generate a continuous voltage we need a constantly changing magnetic field.This is achieved by rotating a magnet in or near a coil of wire.

An ALTERNATINGCURRENT is produced.

Alternating outputMagnet position

Dynamos

More usually...AC generator is a coil rotating in a magnetic fieldAC motor run in reverse...peak e=BANwcoilFigure 1(b)

AC generationFlux linkage through coil:

If the coil is spun with an angular frequency w:

Induced emf=0 when coil edges moving parallel to B fieldInduced emf is max/min when coil edges cut perpendicularly across B field How would you design a higher voltage generator?

Increasing generator outputThis can be done by:Using a stronger rotating magnet or electromagnetRotating the magnet fasterUsing fixed coils with more turnsPutting an iron core inside the fixed coil

Real generators

Battersea Power Station, 1933

Mutual inductionRemember electromagnets?When a current flows in a coil of wire a magnetic field is producedIf an alternating current flows, then an alternating magnetic field is producedIf a second coil of wire experiences this changing field, a voltage is induced in itRun this simulation and click in the transformer tab

TransformersA transformer consists of two coil mounted on a common iron coreAn alternating current flowing in the primary coil induces a changing magnetic fieldThe iron core concentrates the field through the centre of the secondary coilThe alternating magnetic field induces an alternating current in the secondary coilThis happens even though there is no direct electrical connection between the two coils

- Transformer actionA transformer can change the voltage.The size of the voltage induced in