P4.4 Electromagnetic induction FLAP COPYRIGHT © 1998 THE ...

FLAP P4.4 Electromagnetic inductionCOPYRIGHT © 1998 THE OPEN UNIVERSITY S570 V1.1

Note: 11µT = 10−61T


Permeability of free spaceµ0 = 4π × 10−71T1m1A−1


Proton charge e = 1.602 × 10−191C


These demonstrations work best with asensitive centre-zeroed ammeter and, forthose in Figure 2, a strong magnet isdesirable. In Figure 3, the power supplyshould be a battery, not a low-voltage unitso that current changes can be very rapid.

Experiments similar to these wereperformed first by Michael Faraday (1791–1867). Following Oersted’s discovery in1820 that a current carrying wire had amagnetic field (it could deflect a compassneedle), Faraday was convinced that thesymmetry of nature demanded thatmagnetism must somehow produceelectricity. After many failures andextraordinary persistence, he finallysucceeded in 1831, using arrangementsvery like those of Figures 2 and 3.


The electrical potential difference betweentwo points is the difference in electricalpotential energy per unit charge movingbetween those points. The SI units ofpotential difference are volts.

1 volt (V) = 1 joule per coulomb (11J1C0−1).Further discussion may be found elsewherein FLAP. See the Glossary for details.


Strictly speaking, the voltage developedhere is like the open circuit voltageproduced by a voltage generator. Theseideas are developed elsewhere in FLAP.


You can demonstrate the action of amicrophone by connecting its output to they-plates of a cathode ray oscilloscope.

Mike Tinker


The principle of energy conservation tellsus that in an isolated system the totalenergy is constant. Energy conservation isdiscussed elsewhere in FLAP. See theGlossary for details.


The magnetic energy associated with acurrent is discussed more fully elsewherein FLAP.

Mike Tinker


Unless you are generating a large currentthe repulsion is very small, so you wouldprobably not notice it if you carried out theexperiments in Subsection 2.1.


This law was first stated in 1834 by theRussian physicist Heinrich Lenz (1804–1865).


φ is the lower-case Greek letter phi.


The word flux generally implies a flow. Inthis case, nothing is actually movingthrough the loop. There are situations,though, (not discussed in this module)when it is useful to draw comparisonsbetween magnetic flux and the actual flowof a fluid.


θ is the lower-case Greek letter theta.


Wilhelm Weber (1804 – 1891) was aGerman physicist. He spent most of hiscareer working on electromagnetism,although his early research concernedacoustics.


In Section 5, you will see that Faraday’slaw can be derived for the case of amoving conductor via the Lorentz force ona moving charged particle. However, itcannot be derived from the Lorentz forcein the absence of such motion, such asoccurs when the magnetic field variesaround a stationary conductor, and so itmust be considered to be an independentlaw.


dφ0/dt means ‘the rate of change of flux φwith respect to time t’.

Some authors would write Faraday’s lawas Vind = −dφ1/ dt where the minus sign isin recognition of Lenz’s law. We do not dothis since our equation gives the magnitudeof the induced voltage. The polarity of thevoltage and the direction of any inducedcurrent must be established separately as inQuestion T2.


Φ is the upper-case Greek letter phi.


Some texts do not use Φ, and haveEquation 4

|Vind | = dφdt

(Eqn 4)

as their most general expression ofFaraday’s law.


An alternating (a.c.) current or voltage isone whose direction is repeatedly reversed.A direct (d.c.) current or voltage does notchange direction.

In this module, when we quote an a.c.voltage or a.c. current it should be takenthat this is the rms (root-mean square)value of the voltage or current. These ideasare discussed fully elsewhere in FLAP.See the Glossary for details.


Transformers are discussed in Section 4 ofthis module.


The term dynamo is used for both a.c. andd.c. generators (e.g. a bicycle dynamogenerates a.c.), whereas alternator alwaysmeans the a.c. version.


If you are familiar with differentiation thenyou will see that this confirms Answer T6;if not, then you will still appreciate theconclusion, on the basis of the graphicalargument presented in Answer T6.


The symbol ∆ (Greek capital delta) means‘a change in’.


Angular brackets ⟨ 11⟩ are used to indicatedthe average value of something.


The meter can be calibrated by dischargingthrough it a known capacitor, charged to aknown voltage. Capacitors and storedcharge are discussed elsewhere in FLAP.


If the direction of a field is unknown, bothmagnitude and direction can be found bymeasuring its components in threeperpendicular directions and then addingthem vectorially.


The moving-coil galvanometer is describedelsewhere in FLAP. It consists of a coilsuspended in a fixed magnetic field suchthat when a current flows through the coilthe magnetic forces on the coil form acouple which twists the coil on itssuspension. The coil settles down at anangle determined by the balance betweenthe magnetic torque and the restoringtorque of the suspension; this angle is usedto indicate the size of the current flowing.


The relative permeability µr is defined asthe factor by which the permeability of thematerial is increased relative to thepermeability of free space µ0. The effect isto increase the magnetic field within thematerial by the factor µr relative to thatproduced in vacuum by the same currentdistribution.


The low voltage and high voltage a.c.power units, common in physicslaboratories and mains substations, all usetransformers to change a.c. voltages.


Since we are dealing with alternatingcurrent, the voltages, currents and powershere are rms (root-mean square) valueswhich are related to each other in the sameway as in d.c. circuits. a.c. circuits aretreated in more detail elsewhere in FLAP.


In a d.c. circuit the dissipated power P isrelated to current I and voltage V by:P = VI. In an a.c. circuit we have:P = Vrms 1Irms 1cos1δ, where δ is the phasedifference between the current and voltage.

For an ideal transformer, since V ∝ d0I/dt

the difference is π/2, so power istransferred but not dissipated.


The topic of a.c. impedance is discussedmore fully in the FLAP module dealingwith a.c. circuits.


Notice the symbol for an inductor1—1a coilwith the (optional) parallel lines above itrepresenting the core


Notice that the voltage VL here is the backvoltage due to the coil’s inductance.Any coil will also have another voltagedrop across it due to the current flowthrough its resistance, VR = IR.This voltage drop differs from VL in that it

is proportional to I not to d0I/dt. Thevoltage drop due to resistance is discussedmore fully elsewhere in FLAP.


The American physicist Joseph Henry(1797–1878) discovered electromagneticinduction in 1830, independently ofFaraday, who published his work first.In 1832 Henry published his discovery ofself induction. Henry also developed thefirst practical electric motor.


Equation 18

B =µ0 NI

l(Eqn 18)

is introduced in the FLAP module thatdeals with magnetic fields of currents andwas also used in Answer R2. In thiscontext ‘long’ means that the length ismany times the radius.

µr is a dimensionless factor.


Equation 22

L =µ rµ0 AN 2

l(Eqn 22)

shows that µ0, the permeability of free

space, can be expressed in units of H1m−1.These units are exactly equivalent toT1m1A−1, i.e.

µ0 = 4π × 10−7 T1m1A−1 = 4π × 10−71H1m−1.


A similar derivation can in principle becarried out for any coil, provided we havean expression for its magnetic field.


The direction of the force on the movingelectrons can be found using alternativemethods, such as Fleming’s right-hand rule(or the generator rule), rather than by usingthe vector product definition incorporatedinto the Lorentz force law, as here. InFLAP we prefer the vector route for tworeasons. First, it is all too easy to confuseFleming’s right-hand rule with Fleming’sleft-hand rule (or the motor rule).Secondly, and more importantly, the vectorapproach is a more powerful technique andis also used in more advancedelectromagnetism.


Conventional current is always in theapparent direction of motion of positivecharge, i.e. in the opposite direction to themovement of electrons.


Mach 5 means a speed 5 times the (local)speed of sound.


‘homopolar’ means ‘single polarity’, i.e.the current flows only in one direction, i.e.it is direct current.


Data for exit questions:µ0 = 4π × 10−71H1m−1


✧

We know that the induced current mustrepresent an increase in electrical energy inthe circuit since it will produce heating ofthe wires through which it flows. There isalso energy associated with the magneticfield which results from the current ☞.The principle of energy conservation,applied to the system of the magnet andcircuit, tells us that this gain in energy ofthe circuit and magnetic field must beaccompanied by a reduction in kineticenergy of the moving magnet1—1so theremust be repulsion between the coil and themagnet. If the magnet were moving awayfrom the coil then the same argument leadsto the magnet being slowed down by anattractive force.4❏


✧

Increasing Ns increases Φs. For a given B,

this increases Vs. Since Φs ∝ Ns, and

Vs ∝ dΦs/d0t ∝ Ns, then Vs ∝ Ns.4❏


✧

Before the switch is opened, the current inthe coil flows from A to B. Lenz’s law tellsus that the induced voltage opposes thechange that causes it. The self inducedvoltage must therefore be ‘trying’ tomaintain the magnetic flux within the coilby continuing to drive current through thecoil from A to B (i.e. anticlockwise aroundthe top loop of the circuit). Since the selfinduced voltage always opposes thechange that is causing it, it is sometimescalled a back voltage.4❏


✧

As more and more electrons are pushed toQ a net negative charge would build up atQ, with a net positive charge at P.The increasing negative charge at Q willtend to repel further electron flow.Alternatively, we can say that as the chargeseparation develops, an electric field in thewire will grow in the direction PQ.This electric field will oppose furtherelectron motion towards Q. As the electricfield grows it will eventually reach asteady state situation in which the electricforce on an electron will be equal andopposite to the magnetic force and so nofurther charge separation will occur.4❏

P4.4 Electromagnetic induction FLAP COPYRIGHT © 1998 THE ...

Documents

Transcript of P4.4 Electromagnetic induction FLAP COPYRIGHT © 1998 THE ...