HSC Physics: Notes

HSC Physics: Notes2007

Motors and Generators 1.1: Discuss the effect on the magnitude of the force on a current-carrying conductor of variations in: the strength of the magnetic field in which it is located

the magnitude of the current in the conductor

the length of the conductor in the external magnetic field

the angle between the direction of the external magnetic field and the direction of the length of the conductor A charge placed in a magnetic field experiences a force when moved perpendicularly to the field Wires carrying current perpendicular to the magnetic field experience a force Thus: the Motor Effect: (the force produced on a current carrying wire when it is placed in a magnetic field)

The magnitude of the motor effect force (F) in Newtons (N) is proportional to The strength of the magnetic field (B) measured in Tesla (T) The magnitude of the current in the conductor (I) measured in Amperes (A) The length of the conductor in the field (L) measured in metres (m) The angle between the conductor and the magnetic field

=0, no force, =90, maximum force (sin90=1) Therefore:

Right hand slap/palm rule Thumb = current, fingers = magnetic field, palm = force (FID) Also note right-hand thumb rule

1.2: Describe qualitatively and quantitatively the force between long parallel current-carrying conductors: or

Current carrying wires create a magnetic field according to the right hand thumb rule When two current carrying wires run in parallel these fields interfere with each other. Two parallel current carrying wires running in the same direction will attract

Two parallel current carrying wires running in different directions will repel

The relationship of the force between these two wires is expressed by or

Where force is in Newtons (N), I1 and I2 (the currents of the wires) are in Amperes (A), d ( the distance between the two wires (m), L is the length of the wires that are parallel (m) k is a constant, k = 2 * 10-7 N A-2 1.3: Define torque as the turning moment of a force using:

Torque is the turning force (turning moment) Defined as: the force applied to turn and object multiplied by the perpendicular distance between the line of action and the pivot

Ie:

d in metres, force in newtons, torque is measured in N m so therefore, an equation for use when the force is not parallel:

In terms of motors, DC electric motors convert electrical energy to mechanical energy using the motor effect Producing torque on a coil If the coil rotates in a magnetic field, this formula to calculate torque can be used or (depending on the angle) where t=torque in N m, n = the number of coils, B = the magnetic field strength in T I = the current in A

A = the cross sectional area in m2 = the angle between the plane of the coil and the magnetic field

1.4: Identify that the motor effect is due to the force acting on a current-carrying conductor in a magnetic field

When a current carrying conductor is in a magnetic field, due to the right hand slap rule, the motor effect causes a force to be experienced at right angles to the direction of the current and the direction of the magnetic field 1.5: Describe the forces experienced by a current-carrying loop in a magnetic field and describe the net result of the forces

A current carrying loop is the basis for an electric motor In a magnetic field, one side of the loop will experience an opposite force to that of the other side, and thus bring about a net force causing a rotation As seen in the diagram: different current direction causes different force direction, and therefore rotation around an axle, the force on each side can be found with

1.6: Describe the main features of a DC electric motor and the role of each feature

An electrical motor is a device that transforms electrical potential energy into rotational kinetic energy by means of the motor effect

Stator (field structure): the non-rotating part of the motor (stationary magnets or electromagnets) Often is the magnets fixed to the motor casing and providing an external magnetic field The ends of the pole pieces of magnets are curved ensuring the coil is parallel to the field for as long as possible to maximise the torque. Coil: the current carrying wire that carries the direct current Armature: the frame onto which the coil of wire is wound Rotates in the motors magnetic field on an axle protruding from the casing to allow use Often made of a ferromagnetic material The coil and the armature together are known as the rotor Brushes: the conducting contact connecting the split ring commutator to the DC power source Graphite is commonly used because it conducts electricity and acts as a dry lubricant Commutator: a device for reversing the direction of a current flowing through an electric circuit Split ring commutator: a switch used to reverse the direction of the current in the rotating coil of a DC motor every half cycle

As the coil rotates, first one ring then one the other make contact with the brush, thus reversing the current every half turn and keeping the motor spinning in the same direction [see diagrams]

1.9: Increasing the speed of a DC motor

Increasing the force acting on the sides

Force can be increased by:

Increasing the current

Number of loops in the wire

Stronger magnetic field

Soft iron core in the loops centre (acts as an electromagnet)

Addition of another coil, armature and split ring commutator

Increasing the width of the coil

Using more than one coil1.7: Identify that the required magnetic fields in DC motors can be produced either by current-carrying coils or permanent magnets Either permanent magnets or electromagnets can be used to create the external magnetic field for a DC motor Electromagnets can be turned on and off, and the strength of the field controlled

Reversing the current will reverse the electromagnets polarity Strong permanent magnets may attract objects even when the current is turned off 1.8: Applications of the motor effect: the galvanometer, the loudspeaker

Galvanometer A device used to measure the magnitude and direction of DC currents Consists of a coil of wire around an iron core to create an electromagnet, and connected in series to the circuit When current passes through this coil, due to the motor effect, the resulting torque causes the coil to rotate Uses magnets that are shaped to ensure a maximised magnetic field for any rotation of the coil A spring balances the coil and opposes the torque created by the motor effect This allows various levels of torque to be measured, and thus the current observed

Loudspeaker Devices that transform electrical energy into sound energy Consists of a circular magnet with one pole in the centre and the other surrounding it A coil of wire (the voice coil) sits between the poles, and is connected to the output of an amplifier Amplifier provides variations of current due to the sound being converted to electrical energy, thus creating different directions in the voice coil Diaphragm connected to the coil moves in or out due to the motor effect Thereby vibrating the air, and with the help of the speaker cone, creates sound waves in the air that are detected by our ears

2.1: Outline Michael Faradays discovery of the generation of an electric current by a moving magnet

In 1820, Hans Christian Oersted discovered that an electric current produces a magnetic field 1831, Michael Faraday discovered that a current currying conductor in a magnetic field experiences a force 10 years later, he discovered electromagnetic induction the generation of an electromotive force and/or electric current through the use of a magnetic field Faradays first experiment used a block of wood, around which coils connected to a battery, and coils connected to a galvanometer were wrapped Faraday observed that when he turned the current on or off, there was a small, temporary current detected To test this thesis, he moved a permanent magnet near a coil of wire and showed that increasing or decreasing the magnetic field in the coil induced a current in the coil Through later experimentation, he found that the voltage producing the current was dependent on the rate of change of the magnetic flux

2.2: Define magnetic field strength B as magnetic flux density

Electromagnetic induction is the creation of electromotive force in a conductor when it is in motion relative with a magnetic field This is an induced emf, creating an induced current Induction: process whereby one object with magnetic or electrical properties can produce the same properties in another object without physical contact The strength of the magnetic field (B, measured in Teslas T) is also known as the magnetic flux density Magnetic flux density is measured in tesla (T) or weber per square metre (Wb m-2) 2.3: Describe the concept of magnetic flux in terms of magnetic flux density and surface area

Magnetic flux () is the amount of magnetic field lines passing through a given area Measured in weber (Wb) If the particular area A is in a constant magnetic field, the magnetic flux is proportional to the area, and to the magnetic field strength = BA (magnetic flux, measured in weber, weber = 1 tesla m2) B (magnetic field strength (Tesla, or Wb m-2)) A (surface area affected (m2)

Note: the magnetic flux passing through the area is reduced if its not perpendicular Thus: = BA cos (or = Bperpendicular component A), if parallel, cos=0, therefore no magnetic flux density 2.4: Describe generated potential difference as the rate of change of magnetic flux through a circuit

Faraday also showed that the potential difference induced in the coil of wire is equal to the rate of change of magnetic flux

t is time in seconds V is potential difference in volts The implications of this are that if The strength of the magnetic field is changed, or The area of the coil perpendicular to the field is changed A voltage will be induced in the coil during the change Thus, to continually produce an electrical energy, the magnetic flux in a coil must constantly be changed This can be done by changing the magnetic field (B) or surface area (A) 2.5: Account for Lenzs Law in terms of conservation of energy and relate it to the production of back emf in motors

Lenzs law: An induced current will always flow in a direction which will oppose the change that created it. Due to the conservation of energy Can be proved by working out the direction of the perceived current North pole of magnet repels, South attracts,

therefore electrons move in a certain direction and the current moves in the opposite direction so, we can use the magnetic field and current to find the force acting on the electrons

the opposite of this is the direction of the current

by using the right hand thumb rule, this current direction can be used to confirm the fact that the induced emf bites the hand that fed it

In terms of the conservation of energy, when the current is induced, the energy must come from somewhere If a north magnet is pushed into the end of an electromagnet, it cant be a south end, because the magnet would be attracted, and energy created from nothing

The end must be a north end to oppose the magnet and induce the current through this application of force to change the magnetic flux 2.6: Explain that, in electric motors, back emf opposes the supply emf

In an electric motor, when the coil is rotated, by the current flowing through the wire The movement of the wire in the magnetic field creates a back electromotive force The electromotive force created by the current flowing through the wire is called the supply emf The emf created by the movement of the coiled wire through the magnetic field is called the back emf the current induced when an electric motor spins When a motor is switched on, there is a large supply emf, but as the coils begin to rotate, the changing flux within the coils creates the back emf By Lenzs law, it must oppose its creation and thus flows in the opposite direction to the supply The back emf increases until it is equal to the supply emf This is the top speed, by Newtons first law, there is no longer a force increasing or decreasing the torque except resistances and external forces

Thus when starting an appliance, there is a large supply emf and a small back emf, so to keep the current manageable, a starting resistance is put on the circuit After this starting resistance is passed, the motor will be spinning enough to have a back emf that will limit the current 2.7: Explain the production of eddy currents in terms of Lenzs Law

Eddy currents are created when the magnetic flux within a conductor is changed When the magnetic field is going through the disk out of the page into the page and the disk spun The electrons move towards the field, so the perceived current flows in the opposite direction This means that the force of electrons is down the page, and the current flow of electrons out of the page This causes a circular current to be formed In accordance with Lenzs law, the electrons flow in such a way that creates an opposing magnetic field 2.8: Explain how electric cooktops and electromagnetic braking work Electromagnetic braking A metal disk, ie connected to a wheel an electromagnet is used to create a magnetic field through it this allows eddy currents to form the flow of electrons within the magnetic field, using the right hand slap rule create a force on the wheel, thus slowing down the circular movement

Induction heating Eddy currents create an increase in temperature in the metal Collisions between moving charges and the atoms of the metal Agitation of the atoms by the magnetic field changing direction at high frequency in an AC supply Eddy currents induced within the cooking pot material Undesirable in electrical equipment such as motors, generators and transformers Hinders the efficiency by slowing down the speed of rotation Advantages over other types of cooking Less heat loss to environment, like in gas cooking Heat induced is used to cook the food Induction cookers have an 80% efficiency, while gas has about 43% Electric cookers have a induction coil that produces a quickly changing electric field that creates eddy currents in the saucepan, thus heating it and cooking the food A ceramic plate is used to separate the saucepan from the coil ceramic because ceramic is highly heat tolerant

Induction furnace uses the heating effect of eddy currents to melt metal A non-metal container surrounded by the coil contains the metal The coil is supplied with an alternating current with a high range of frequencies Provides a changing magnetic field that Eddy currents in the metal raise its temperature until it melts

Also create a stirring effect, which allows better creation of alloys Take less time than flame furnaces Cleaner and more efficient 3.1: Describe the main components of a generator

A generator is a device used for producing electrical energy from mechanical energy Prime mover mechanical device used to drive the generator (steam turbine, water turbine etc) Uses induction to convert kinetic energy into electrical energy

Stator stationary parts (field structure) from a permanent or electromagnet Rotor moving parts Armature: the frame onto which the coil of wire is wound

Slip ring commutator and brushes to take the induced current away Split ring Commutator if its a DC generator

In a modern AC generator, the electromagnet is the rotor, the coils the stator 3.2: Compare the structure and function of a generator to an electric motor

The structure of a generator and electric motor is essentially the same In a generator, the rotor is moved by mechanical energy to induce a current and create electricity

In a motor, electrical energy is fed into the rotor to induce a rotational movement 3.3: Describe the differences between AC and DC generators DC generator

A DC current is produced where the flow of charge is in one direction only provided by a dry cell steady value

provided by a DC generator vary with time, but still in the same direction consists of a coil that rotates in a magnetic field

a commutator changes the direction of the electric current every half turn so as to have a continuous output direction

the output of a DC generator can be made smoother by including more coils at regular angles to the armature

note: in a real DC generator, often the armature is the rotor and the field structure is the stator

AC generator An AC current is produced when the direction of the current is constantly changing direction Provided by using a slip ring commutator allows an external circuit to be connected to a rotating coil

consists of a coil in a magnetic field that is rotated inducing a changing current

the output of an AC generator can be made smoother by including more coils at regular angles to the armature

note: in a real AC generator, often the field structure is an electromagnet ie the rotor, and the armature is the stator 3.4: Discuss the energy losses that occur as energy is fed through transmission lines from the generator to the consumer

Energy loss occurs often due to heat caused by: Friction in the bearings of the rotor

Heat generation in the conductors due to current Energy losses in the iron core due to magnetic properties (hysteresis)

Resistance is proportional to length of the conductor Thus: the longer the transmission wires, the higher the resistance and therefore loss of energy through heat R = l/A (resistance = resistivity * length / cross sectional area) Current needs to be kept low to reduce energy loss Energy is transmitted at high voltages (because I = P/V) thereby minimising current and energy lossAC generatordiagramsDC generator

diagrams3.5: Assess the effects of the development of AC generators on society and the environment

Before Faradays discovery of electromagnetic induction burning of wood was the major source of domestic power Then with the industrial revolution, coal was used in steam engines

Faradays discovery of induction changed the world Energy could be generated away from where it would be used and transmitted through wires over long distance

Allowed a clean modern city to be built and households to have convenient sources of energy: used for heating, lighting, food storage etc Power stations could be located away from cities reducing pollution Effects on society Reduction in unskilled jobs (machines take over) thus greater unemployment The middle class moved out into the outer suburbs in bigger houses with bigger blocks of land Rural communities have electricity

Effects on environment Fossil fuel power stations cause thermal pollution, acid rain, air pollution and global warming

Due to the release of particles and oxides o nitrogen and sulphur and carbon dioxide Effects on humans

Possible link with cancer and miscarriages: esp acute lymphoblastic leukaemia in children

However, nothing conclusive yet4.1: Describe the purpose of transformers in electrical circuits

Transformers are devices for transferring electrical energy from one circuit to another while changing the size of an alternating current A magnetic circuit with two multi-turn coils wound onto a common core Transformers allow generated voltage to be either increased or decreased before use Egs: television sets/ computer monitors to provide the higher voltage for the cathode ray tube Radios, for lower voltages in amplifier circuits Also: answering machines, cordless phones, digital cameras, battery chargers, digital clocks, computers, phones, printers, keyboards, etc 4.2: Compare step-up and step-down transformers

Transformers consist of two coils of wire, the primary and secondary coils Wound together onto the same soft iron core or linked by a soft iron core

A step-up transformer provides an output voltage that is greater than the input voltage A step-down transformer provides an output voltage that is less than the input voltage Primary coil provides a changing magnetic field that is confined by the iron core

Magnetic field induces an AC voltage on the secondary coil depending on the number of coils

Step-down transformer

Step-up transformer 4.3: Identify the relationship between the ratio of the number of turns in the primary and secondary coils and the ratio of primary to secondary voltage

Transformer equation Voltage in primary/voltage in secondary = number of coils in primary/number of turns in secondary

4.4: Explain why voltage transformations are related to conservation of energy

The principle of conservation of energy states that energy cannot be created or destroyed In a transformer, when the voltage is changed, in a step up or down, there is a trade off in current P = IV, so when V is increased, current is reduced, and when V is decreased, current is increased 4.5: Explain the role of transformers in electricity sub-stations

Power stations are usually located large distances from major cities (where the consumers are) Power loss over the transmission lines is a problem (transmission lines are basically long metallic conductors with significant resistance) resistance = resistivity * length / cross sectional area

ie: R = l/A We know that P = I2R Therefore power loss = I2R So, by decreasing the current, the power loss can be minimised

And to do this increase the voltage

4.6: Discuss why some electrical appliances in the home that are connected to the mains domestic power supply use a transformer

Some home appliances dont require, or require more than the full 240V supplied from the domestic mains Thus they use a transformer to adjust the voltage to the required level 4.7: Discuss the impact of the development of transformers on society

Transformers have allowed society to efficiently and conveniently use electricity Consequently, power stations can be placed further away from cities, allowing better living conditions Also, transformers have allowed rural areas to have access to electricity

For more detail, see question about effect of AC generators 5.1: Describe the main features of an AC electric motor AC motors are similar to DC motors except they do not have a commutator Stator stationary part of the motor and normally connected to the frame of the machine In an AC motor, it provides the external magnetic field Rotor most have a cylindrical rotor that rotates at high speed one revolution to each cycle of the AC power supply The parts experiencing magnetic flux are made up of thin steel laminations separated by insulation to reduce eddy currents Synchronous AC electric motor Uses a split ring commutator to allow the rotations to synchronise with the cycles of the AC power source These are useful in applications requiring a fixed motor speed Induction motor Based on the principle where when a magnet is spun around a disk, the disk will spin A squirrel cage is often used: when the rotor, current carrying coils are spun in the centre, the surrounding conducting squirrel cage will spinGather secondary information to discuss advantages/disadvantages of AC and DC generators and relate these to their use Most generators today produce AC electricity AC is more readily transformed into different voltages

Thus more versatile

AC can be rectified to produce DC for some applications

AC electricity can be generated in several ways, the most simple being a rotating coil in a magnetic field and a slip ring commutator

DC generators require a split ring commutator that can wear out

Thus require more maintenance

DC electric generator uses a rotating coil in a magnetic field and a split ring commutator DC generators can produce DC current near the generator

However, DC cant be transmitted over large distances without significant power loss Due to resistance of transmission lines Also require regular maintenance due to the split ring commutators

AC generators produce a voltage that can be efficiently changed using transformers, thus allowing transmission over long distances High voltages, and low currents thereby minimising line lossAnalyse secondary information on the competition between Westinghouse and Edison to supply electricity to cities Thomas Edison invented many things including the light bulb and photograph First person to establish a business supplying electricity for lighting houses and streets in cities Edison General Electric Company opened in New York City in 1882 Edison used a DC current system generators (dynamos) used a split ring commutator These wore out very quickly with the high speed steam driven generators Could only supply areas a few kilometres away due to power losses Relied on thick copper cables The AC transformer was invented by Joseph Henry, and it was first demonstrated in Paris in 1883 By Nikola Tesla, was working for the Edison Electric Company in France George Westinghouse bought the patent rights for Teslas generators and motors

Edison saw the threat and tried to discredit the AC system publishing a book warning about the horrible deaths caused by contact with AC cables

The Edison research facility hired Harold Brown to develop an electric chair using AC electricity using a Westinghouse generator Electrocution became the method of execution in the state of New York in 1888

The Westinghouse AC electricity was suggested as the best method of electrocution

In 1887 a group of businessmen in Buffalo USA set up a competition for the design of a system that would allow hydroelectricity to be generated from Niagara Falls to provide the electricity to a city 30km away Westinghouse won, and AC generators thus seen to be superior to DC generatorsGather and analyse information to identify how transmission lines are:

insulated from supporting structures

protected from lightning strikes Transmission lines are insulted from the earth and the supporting structures b being suspended high in the air on ceramic or glass insulators In dry air, sparks can jump a distance of 1cm for every 10 000 V of emf To prevent this jump, large insulators separate transmission lines and supporting towers The disk shape of the insulators increases the leakage path, so any contaminants or moisture will have a harder time conducting the current away from the transmission line Transmission lines are protected from lightning strikes by having a top earth wire that connects to the ground on top of each transmission tower This also serves to protect against sudden voltage surges or system faultsGather, analyse and use available evidence to discuss how difficulties of heating caused by eddy currents in transformers may be overcome Eddy currents are produced in conductors when the presence of a changing state of flux causes circular movements in the electrons In transformers, such fields are required, and thus eddy currents form in the iron core This causes a creation of heat and consequently a loss of energy The losses due to eddy currents in transformers are reduced by constructing an iron core of many layers of an insulated iron core This is known as a laminated iron core Thus the effect of eddy currents is reduced by allowing a smaller area for the eddy currents to operate in

Another method to reduce eddy current losses is to use ferrites complex oxides of iron and other metals These are good transmitters of magnetic flux but poor conductors of electricityGather and analyse secondary information to discuss the need for transformers in the transfer of electrical energy from a power station to its point of use

Power stations are often located further away from cities to reduce pollution and closer to fossil fuel sites to decrease cost of transport Thus, transformers are needed to allow electricity to be transmitted over long distances

Due to resistance in the transmission wires, there will be a loss of power when transmitting electricity over distance However, if a higher voltage is used, and a lower current, the amount of electric power lost can be significantly decreased (P=I2R, and P=IV) Thus transformers play a very important role in the transfer of electrical energy from power station to use, over long distanceGather, process and analyse information to identify some of the energy transfers and transformations involving the conversion of electrical energy into more useful forms in the home and industryEnergy can neither be created nor destroyed, only transformed into different forms Energy can be neither created nor destroyed, only transformed into different forms

In electrical appliances, electrical energy is harnessed to various causes Eg: hair dryer = the electric motor converts electrical energy into mechanical energy spinning a rotor Also, some electrical energy is transformed into heat due to the eddy currents in the iron core

The mechanical energy in turn in transformed into sound and kinetic energy of air particles by a fan

The air particles pass through a heating element where electrical energy is transformed into heat energy and light energy, thus heat energy is transferred out of the dryer by direct conduction and convection curentsPerform a first-hand investigation to demonstrate the motor effect

Aim: To observe the direction of the force on a current carrying conductor in an external magnetic fieldApparatus: variable DC power supply, variable resistor, connecting wires, retort stand, clamp, horseshoe magnet, switch, aluminium foil, two pieces of cardMethod: The foil strip was suspended between two pieces of card, and connected thus to the circuit

The horseshoe magnet was positioned with one pole on either side of the strip

The power pack was turned on and the results observedResults:

According to the right-hand palm rule, the strip experienced a forcePerform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet

Plan, choose equipment or resources for, and perform a first-hand investigation to predict and verify the effect on a generated electric current when:

the distance between the coil and magnet is varied

the strength of the magnet is varied

the relative motion between the coil and the magnet is varied

Aim: to study ways of inducing a current in a coiled conductor and to study factors affecting the size of the induced current

Apparatus: galvanometer, a coil of wire, bar magnets of varying strengths, electromagnetMethod: The coil was connected to the galvanometerThe bar magnets were held in various positions and speedsnear the coil, and through the coil and the effect on the galvanometer observedThe electromagnet was turned on and off in the presence of the coil

Results:

When the magnet is held stationary, no current is observed

When the magnet is moved in the vicinity of the coil, a current is observed

The faster the movement, the greater the current

The coil can be moved in relation to the magnet, instead, to the same effect

The turning on and off of the electromagnet near the coil creates a current

The stronger the magnetic field, the stronger the current producedPlan, choose equipment or resources for, and perform a first-hand investigation to demonstrate the production of an alternating current

Aim: To observe the output voltage of an AC generator using a cathode ray oscilloscope, and to observe the production of an AC currentApparatus: AC motor, cathode ray oscilloscope, hang-cranked model AC generatorMethod: The AC generator was connected to the CROThe resulting visual representation was observed

The hand-crank AC generator was observed, then connected to the CRO and the results observed

Results:

The CRO produced the following wave

The hand crank produced the same wave

The hand crank created an alternating current by means of a slip ring commutator that allowed the current to continuously change directions every half turnPerform an investigation to model the structure of a transformer to demonstrate how secondary voltage is produced

Aim: To set up a simple transformer, and to observe how both a DC and AC current can produce an output currentApparatus: galvanometer, two different number of turns coils, DC power supply, AC power supply, variable resistor, connecting wires, switchMethod:

The smaller coil (primary) was placed inside the larger coil (secondary)

The primary coil was connected with the switch, variable resistor and power supply (DC then AC)

The effects on the galvanometer was observedResults

A DC current does not induce a current in the output coil except when turned on and off

An AC current induces a current in the output coil

When the primary coil has less coils, there is an increase in the strength of the output current

When the primary coil has more coils, there is a decrease in the strength of the output current

Perform an investigation to demonstrate the principle of an AC induction motor

Aim: To investigate the principles behind an AC induction motorApparatus: copper or aluminium rod, two bar magnets, a galvanometerMethod: The bar magnets were set up with North facing South a distance apart

The galvanometer was connected to the conductorThe conductor was moved in various ways, slow then fast down through the magnets, slow then fast up through the magnets

Results

Down through the magnets produced a current in one direction, and up through the magnets one in the other directionThe faster the movement through the field, the greater the currentThe change of the angle to the field changes the current produced in accordance with F = nBILsinThe relative movement of the magnets had the same effect as the movement of the conductorF

B

I

x

.

.

.

B1

B2

I1

I2

F

F

I1

I2

B1

B2

F

F

d

F

Pivot

Pivot

F

d

F sin

Cone of stiff paper or plastic vibrates in and out producing sound waves

Soon Lau Class of 07

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