This WeekMagnetism: Are you attracted or repulsed?Where does magnetism come from?What use is magnetism?

Post pictures and notes on refrigeratorsElectrical motors turn electricity into workGenerators turn heat energy into electricity

Transformers for power transmission and Ipod.Earths Magnetic field. Northern lights.

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MagnetismElectric charge is also responsible for the force that we call magnetism.Moving charge, that is a current, produces a force field which we term the magnetic field B. Since atoms contain “moving charge” most atoms and substances have magnetic behavior. In the case of iron this effect is very strong.

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Magnetic fieldThere are differences between the electric field and the magnetic field. A magnet has two poles and a magnetic monopole has never been observed.The field lines are continuous loops Like poles repel and unlike poles attractA magnetic field only acts on moving charge The force is perpendicular to the velocity so the moving charge is accelerated but does not gain or lose energy

By definition the field lines enter a south pole and leave a north pole

http://www.physics.purdue.edu/class/applets/phe/mfbar.htm

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Earth’s magnetic field

The earth has a dipole field inclined at 11 degrees to the axis of rotation.The North Pole (Arctic) is actually a magnetic south pole.It is thought that the field is produced by circulating electric currents in the molten iron core.

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Form of the forceThe force a charged particle moving with velocity v in a magnetic field B is given by

F = qvperpendicularBor F = qvBperpendicular

This means the maximum force is when v is at right angles to B and that the force is zero if v is parallel to B or v = 0.For a current in a wire qv = qL/t = IL so the force on a current carrying wire of length L is

F = ILBperpUnits of B are tesla (N x sec/coulombs x meters)(N/amps.meters)

http://www.physics.purdue.edu/class/applets/phe/lorentzforce.htm

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Fields from currentsA current carrying wire produces circular field lines. Looking along the direction of the current the field lines are clockwise

A current loop produces a dipole field

A solenoid can produce a strong uniform field in a volume with small leakage. If it is placed in an iron cylinder the field is stronger and more contained

http://www.physics.purdue.edu/class/applets/phe/mfwire.htm

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Force between two infinite wires

If the two wires are very long then each wire sits in a B field which is at right angles to the wire.F/L = 2k’ I1 I2 /r

k’ = 1 x 10-7N/amp2

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Force on a coil: Meters and Motors

http://www.physics.purdue.edu/class/applets/phe/electricmotor.htm

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Moving conductor Suppose a wire is moving with velocity v in a magnetic field so that v is into the screen.Positive charge will feel a force to the right.If the wire is isolated then an electromotive force will exist between the ends of the wire and if the wire is part of a circuit this electromotive force will cause a current to flow.The electrical energy is produced by the force that is moving the wire and the wire requires a force to keep it moving at constant velocity

B

ε

F

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InductionIf a conductor is in a changing magnetic field an electromotive force is produced.If the conductor is part of a circuit then a current will flow.The induced current produces it’s own magnetic field and the direction of the induced current produces a magnetic field that opposes the change.Self induction occurs when the current changes in a circuit for example when it is switched on or disconnected. The induced EMF slows down the change of current.

anim0018.mov

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Magnetic fluxIn order to determine the induced EMF we have to define how the magnetic fieldchanges as we move a conductor through a magnetic field. The important quantity is called magnetic flux and it is a product of the magnetic field perpendicular to the loop times the area

Ф = BperpendicularAIf we have a loop of N turns

ε = NΔФ/t So if we turn 50 loops in 1/20 second

ε = ΔФ/t = 1000BAso if B was 1/10 tesla and A = 1/100 m2

ε = 1 volt

B

Ф= BA 0 -BARotating a coil

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Transformers and generators

ΔV2/ΔV1 = N2/N1 can be step up or step downNaturally generates AC

http://www.physics.purdue.edu/class/applets/phe/generator_e.htm

ФФ

AC AC

The changing current in the primary produces changing magnetic flux in the secondary and an induced voltage.

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Summary of Chapter 14Current produces a magnetic force field

F = qvperpB moving charge F = ILBperp currentTorque on a current loop - meters and motors

F/L = 2k’ I1 I2 /rk’ = 1 x 10-7N/amp2

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InductionФ = BperpendicularA ε = NΔФ/t

Transformer ΔV2/ΔV1 = N2/N1

Generator

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Magnetic field of the earthLiquid metal moving through a magnetic field generates a current, similar to that induced in the moving coil of an electric generator. That current in turn generates the magnetic field. This "self-generation" mechanism can dramatically amplify the small, random fields that always exist in magnetic materials. To do this, though, the flow must be both complex, mixing up the longitudinal and latitudinal directions, and rapid, "tangling up" magnetic field lines faster than they can untangle.

When filled with molten sodium and stirred at up to 26 revolutions per second, this tank generates a magnetic field--similar to the way the Earth's core creates a field. Previous experiments controlled the flow more carefully and avoided turbulence, so they were less like the Earth's core.

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Earth’s magnetic fieldOn Earth, the record of the reversal of the magnetic field is preserved in magnetic rocks which lie along the ocean floor.The magnetism preserved in these rocks points first in one direction, then in another direction.These rocks are lava flows or layers of microscopic sea creatures. The average time between reversals is ~ 250,000 years.The field traps charged particles in areas called the Van Allen belts. The field protects us from charged particles except at the poles

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6A-02 Weighing a Suspended Magnet

THE SECOND MAGNET’S WEIGHT IS SENSED BY THE BALANCE EVEN THOUGH IT ISN’T ACTUALLY “TOUCHING” THE APPARATUS.

Will the scale still balance

when the second magnet floats ?

?

Fgravity

Fmagnetic

Fmagnetic

Fgravity

The scale will read the sum of forces acting on bottom magnet: Fmagnetic + FgravityThe top magnet is floating so: Fmagnetic = Fgravity The scale reads: Fmagnetic + Fgravity = 2 Fgravity = 2mg

Using equal and opposite forces between magnets to weigh magnet

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Which orientation of the magnet causes

the beam to move upward ?

Downward ?

6B-02 Force on a Moving Charge

MAGNETIC FIELD CAUSES THE CHARGED PARTICLES TO DEFLECT. WE FIND THE DIRECTION OF FORCE WITH THE RIGHT-HAND RULE. THIS IS THE FORCE ON POSITIVE CHARGE!

Investigating the behavior of moving charge in magnetic field

Forc

e

F = q (v┴ B)

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Based on the direction of the

Magnetic Field and the direction that current flows, can

you predict in which direction the Force

points ?

6B-06 Magnetic Force on a Current-Carrying Conductor

CURRENT FLOWING ALONG THE AXLE IS PERPENDICULAR TO THE MAGNETIC FIELD. THERE IS A FORCE ON THE AXLE, CAUSING IT TO ROLL. IF THE CURRENT IS REVERSED, THE AXLE ROLLS IN THE OPPOSITE DIRECTION.

Finding the direction of Force on Current due to B-field

I┴

B F

F/L = I┴ B Use right-hand rule to find direction of F

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What differences occur in the

interacting fields if one of the wires is

replaced by a solenoid ?

What occurs when the current is sent

through? How about reversing the

current ?

6B-11 Force Between Coil and Wire

WHEN THE SOLENOID IS ACTIVATED AND A CURRENT IS SENT THROUGH THE WIRE, THE WIRE WRAPS ITSELF AROUND THE SOLENOID. WHEN THE CURRENT IN THE WIRE IS REVERSED, IT WRAPS AROUND THE SOLENOID IN THE OPPOSITE DIRECTION.

Forces between two conductors

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INDUCED CURRENT IN THE RING, CAUSED BY THE GROWING MAGNETIC FIELD WHEN THE SWITCH IS ACTIVATED, IS RESPONSIBLE FOR THE REPULSIVE FORCE BETWEEN THE COIL AND THE RING. IF A SPLIT RING IS PLACED OVER THE ELECTROMAGNET, THE COIL WILL NOT JUMP BECAUSE OF THE BROKEN “CIRCUIT” IN THE RING, PREVENTING THE CURRENT FLOW.

Is there any differences in

the two rings ?

Why one can jump up, the other can’t ?

6D-11 Jumping Ring

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Questions Chapter 14

Q1 The north pole of a hand-held bar magnet is brought near the north pole of a second bar magnet lying on a table. How will the second magnet tend to move?

Q4 Is it possible for bar magnet to have just one pole?

It will be repelled

The magnetic fields produced by currents require both a north and south poles. These poles do not exist as physical entities like an electron with one unit of charge. Physical laws do not prohibit the existence of monopoles, that is particles with “magnetic charge”, these have been searched for but never observed.

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Q6 If we regard the earth as magnet, does its magnetic north pole coincide with its geographical north pole? What defines the position of the geographical north pole?

Q7 We visualized the magnetic field of the earth by imagining that there is a bar magnet inside the earth (fig. 14.7). Why did we draw this magnet with its south pole pointing north?

The geographical north pole is defined by the axis of rotation. The magnetic north pole is determined by the currents and fields in the iron core of the earth. About every 250,000 years the field of the earth reverese.

The definition of the North pole is the point at which the North pole of a magnet would point. This means the North pole is a physical magnetic south pole.

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Q9 A horizontal wire is oriented along an east-west line, and a compass is placed above it. Will the needle of the compass deflect when a current flows through the wire from east to west, and if so, in what direction?

Q11 A uniform magnetic field is directed horizontally toward the north, and a positive charge is moving west through this field. Is there a magnetic force on this charge, and if so, in what direction?

The current will produce a field that appears clockwise looking west. This means the compass will point north/south

Point index finger along the velocity, the middle finger in the direction of B and then the thumb points in the direction of the force. The force points up.

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Q12 A positively charged particle is momentarily at rest in a uniform magnetic field. Is there a magnetic force acting on this particle?

Q13 If a uniform magnetic field is directed horizontally toward the east, and a negative charge is moving east through this field, is there a magnetic force on this charge, and if so, in what direction?

No. The particle must have a velocity.

No. There must be an angle between the velocity and the direction of B

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Q15 If we look down at the top of a circular loop of wire whose plane is horizontal and that carries a current in the clockwise direction, what is the direction of the magnetic field at the center of the circle?

Q17 A current-carrying rectangular loop of wire is placed in an external magnetic field with the directions of the current and field as shown in the diagram. In what direction will this loop tend to rotate as a result of the magnetic torque exerted on it?

The field is perpendicular to the plane in the direction that if you look in that direction the current is clockwise. So the answer is down.

B F

F

B

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Q24 A horizontal loop of wire has a magnetic field passing upward through the plane of the loop. If this magnetic field increases with time, is the direction of the induced current clockwise or counterclockwise (viewed from above) as predicted by Lenz’s law?

The current induced produces a magnetic field that opposes the increase so the induced magnetic field points down so the current must be clockwise viewed from above.

Q25 Two coils of wire are identical except that coil A has twice as many turns of wire as coil B. If a magnetic field increases with time at the same rate through both coils, which coil (if either) has the larger induced voltage?

The flux in A is twice that in B so the induced voltage is twice as large.

Q28 Does a simple generator produce a steady direct current? No. As the coil turns at constant angular velocity the rate of change of flux depends on the angle of the coil to the field so the current is AC

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Q30 Can a transformer be used, as shown in the diagram below, to step up voltage of a battery? Explain.

Q31 By stepping up the voltage of an alternating current source using a transformer, can we increase the amount of electrical energy drawn from the source?

V2/V1 = N2/N1So if N2 > N1 the voltage is stepped up.

No. For an ideal transformer the input power = output power. In a real transformer energy is lost due to heat. Feel the transformer for your laptop.

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Ch 14 E 4Two parallel lines, each carrying I = 2amps, exert a force per unit length of 1.6 x 10-5 N/m on each other. What is distance between the lines?

F/ℓ = (2k’ I1I2)/rr = (2k’ I1I2)/(F/ℓ) = (2(1 x 10-7)(2)(2))/(1.6 x 10-5) = 0.05 m r

I = 2A

II

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Ch 14 E 8Magnetic force on 40 cm straight wire segment carrying I = 5A is 2.5N. What is magnitude of magnetic field perpendicular to wire?

F = IℓBB = F/Iℓ = (2.5)/(5)(0.40) = 1.25 T

I = 5A 0.40mB

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Ch 14 E 10Loop of wire enclosing Area, A = 0.03m2, has magnetic field passing thru its plane at an angle. Component of magnetic field perpendicular to plane = 0.4T, while component parallel to plane = 0.6T. What is magnetic flux thru coil?

I = B1A = 0.4(0.03)

= 0.012Tm2 A

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Ch 14 E 12Coil of wire with 60 turns and cross-sectional area, A = 0.02m2, lies with it’s plane perpendicular to B = 1.5T magnetic field. Coil is rapidly removed B-field in time t=0.2s.a) What is initial magnetic flux thru coil?b) What is average voltage induced in coil?

a) Φ = NB1A = (60)(1.5)(0.02) = 1.8Tm2

b) ε = ΔΦ/t = (1.8 Tm2 – 0)/0.2s = 9V

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Ch 14 CP 2Small metal ball has charge q = +0.05C and mass,m = 0.025kg. Ball enters a region of magnetic fieldB = 0.5 T that is perpendicular to its velocityv = 200m/s.a) What is magnitude of magnetic force on ball?b) What is direction of magnetic force on ball?c) Will this force change magnitude of ball’s velocity?d) Use Newton’s 2nd Law, what is magnitude of

acceleration of the ball?e) Centripetal acceleration = v2/r. What is radius of the

curve ball will move thru in magnetic field?

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Ch 14 CP 2 (cont)

a) F = qv1B = (0.05)(200)(0.5) = 5N

b) (see diagram) Force in –z direction

c) To change magnitude of velocity is to change kinetic energy. If magnetic field changes kinetic energy then it must do work on charged ball. The right-hand rule shows us that velocity and force are always perpendicular. Therefore, the magnetic field can do no work!

d) F = ma = qv1B = 5N

a = 5N/0.025kg = 200 m/s2

....

....

ˆv vy=

ˆB Bx=z

xy

e) v2/r = 200m/s2 , r = v2/(200m/s2) = (200m/s)2/200m/s2 = 200m

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Ch 14 CP 4Transformer is designed to step down line voltage of110V to 22V. Primary coil has 400 turns of wire.a) How many turns of wire on secondary coil?b) Current in primary I1 = 5A. What is max current in

second coil?c) If transformer gets warm during operation, will current

in secondary coil equal that computed in previous question (b)?

a) ΔV2/ ΔV1 = N2/N1 , N2 = N1(ΔV2/ ΔV1) = 400(22/110) = 80 turns

b) ΔV2I2 ≤ ΔV1I1 I1 = 110/22 (5) = 25AMax current in second coil = 25A.

c) No, heat that warms up transformer is power dissipated in the formP = I2R. Power is lost to heat.

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WavesIn our everyday life there are many examples of waves for example, Sound, ocean waves, strings of musical instruments, organ pipes…These are examples of waves which need a medium to travel through and the general definition of such waves is

A disturbance which propagates through a medium but the medium itself only moves locally as the wave passes.A special case of a wave is an electromagnetic wave which can propagate through vacuum, e.g. radio, light, x rays ….Waves transport energy and momentum and energy is required to generate wavesThe medium must have elastic properties

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Wave properties

There are two types of wavesLongitudinal – consists of the propagation of a series of compressions and rarefactions and the local movement of the medium is an oscillation back and forward along the direction of the waveSound is one example

Transverse – where the movement of the medium is at right angles to the velocity of the wave. The strings of musical instruments is an example.

anim0019.mov

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Periodic wavesOne can propagate waves which are a single complicated pulse e.g. an explosion or a complicated continuous wave e.g. the wind. We will focus on regular repetitive waves

These waves have a pattern which repeats and the length of one pattern is called the wavelength λThe number of patterns which pass a point/second is called the frequency f and if the time for one pattern to pass is T then f = 1/T

v = λ/T = fλ

λ

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Waves on a stringIf we shake the end of a rope we can send a wave along the rope. The rope must be under tension in order for the wave to propagate

v = √(F/μ)F = TENSIONμ = MASS/UNIT LENGTH

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Standing wavesIf two identical waves exist on the same string but traveling in opposite directions the result can be standing waves in which some points never have a deflection.These are called nodes and some points oscillate between plus and minus the maximum amplitude, these are called antinodes.Standing waves provide the notes on musical instruments. When a string is secured at both ends and plucked or hit the generated waves will travel along the string and be reflected and set up standing waves.