1 Magnetism Magnetism: Permanent and Temporary 1.

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MagnetismMagnetism

Magnetism: Magnetism:

Permanent and TemporaryPermanent and Temporary

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AssignmentsAssignments

24/1-9,16-18,21-23, and 669/1-924/1-9,16-18,21-23, and 669/1-9 25/1-8,16,17,2125/1-8,16,17,21

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General Properties of MagnetsGeneral Properties of Magnets

Like magnetic poles repel; unlike Like magnetic poles repel; unlike magnetic poles attractmagnetic poles attract

Magnetic field lines are directed from Magnetic field lines are directed from north to southnorth to south

Magnetic field lines always form Magnetic field lines always form close loopsclose loops

A magnetic field exists around any A magnetic field exists around any wire that carries currentwire that carries current

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Bar MagnetsBar Magnets

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Gen’l Properties cont.Gen’l Properties cont.

A coil of wire (SOLENOID) that carries A coil of wire (SOLENOID) that carries a current has a magnetic field about a current has a magnetic field about a permanent magneta permanent magnet

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Forces Caused by Magnetic Forces Caused by Magnetic FieldsFields

When a current-carrying wire is When a current-carrying wire is placed in a magnetic field, a force placed in a magnetic field, a force acts on the wire that is perpendicular acts on the wire that is perpendicular to both the field and the wire. to both the field and the wire. Meters operate on this principle.Meters operate on this principle.

Magnetic field strength is measured Magnetic field strength is measured in tesla, T (one newton per ampere in tesla, T (one newton per ampere per meter).per meter).

B is the symbol for magnetic fieldB is the symbol for magnetic field

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Forces cont.Forces cont.

An electric motor consists of a coil of An electric motor consists of a coil of wire (armature) placed in a magnetic wire (armature) placed in a magnetic field. When current flows in the coil, field. When current flows in the coil, the coil rotates as a result of the force the coil rotates as a result of the force on the wire in the magnetic field.on the wire in the magnetic field.

The force a magnetic field exerts on a The force a magnetic field exerts on a charged particle depends on the charged particle depends on the velocity and charge of the particle velocity and charge of the particle and the strengthand the strength

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Forces cont.Forces cont.

of the magnetic field. The direction of the magnetic field. The direction of the force is perpendicular to both of the force is perpendicular to both the field and particle’s velocity.the field and particle’s velocity.

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Key EquationsKey Equations

F = BIL F = BIL Force on a current carrying Force on a current carrying wire in a magnetic field. Force = wire in a magnetic field. Force = magnetic field strength x current x magnetic field strength x current x length of wire. Newton = tesla x amp x length of wire. Newton = tesla x amp x metermeter

F = BqV F = BqV Force of a magnetic field on a Force of a magnetic field on a single charged particle. Force = single charged particle. Force = magnetic field strength x charge x magnetic field strength x charge x velocity of the charge. Newton = tesla x velocity of the charge. Newton = tesla x coulomb x m/scoulomb x m/s

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Hand Rule #1- B field direction Hand Rule #1- B field direction around a current carrying wirearound a current carrying wire

Point thumb in direction of current in Point thumb in direction of current in the wirethe wire

Fingers of your hand circle the wire Fingers of your hand circle the wire and show the direction of the and show the direction of the magnetic fieldmagnetic field– Knuckles, NKnuckles, N– Finger tips, SFinger tips, S

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Hand Rule #2 – Determine the Hand Rule #2 – Determine the polarity of an electromagnetpolarity of an electromagnet

Wrap the fingers of your right hand around Wrap the fingers of your right hand around the loops in the direction of the currentthe loops in the direction of the current

Extended thumb points toward the N pole Extended thumb points toward the N pole of the electromagnetof the electromagnet

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Sample ProblemsSample Problems

A straight wire that carries a 5.0 amp A straight wire that carries a 5.0 amp current is in a uniform magnetic field current is in a uniform magnetic field oriented at right angles to the wire. oriented at right angles to the wire. When 0.10 m of the wire is in the When 0.10 m of the wire is in the field, the force on the wire is 0.20 n. field, the force on the wire is 0.20 n. What is the strength of the magnetic What is the strength of the magnetic field, B?field, B?

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SolutionSolution

Known:Known: Unknown: Unknown:

I = 5.0 ampI = 5.0 amp B =?B =?

L = 0.10mL = 0.10m

F = 0.20 NF = 0.20 N

F=BIL F=BIL B = F/IL B = F/IL

= 0.20N/5.0 amp(0.10m)= 0.20N/5.0 amp(0.10m)

= 0.40 T= 0.40 T

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Sample ProblemSample Problem

A beam of electrons travels at 3.0 x A beam of electrons travels at 3.0 x 101066 m/s through a uniform magnetic m/s through a uniform magnetic field of 4.0 x 10field of 4.0 x 10–1–1 T at right angles T at right angles to the field. How strong is the force to the field. How strong is the force that acts on each electron?that acts on each electron?

KnownKnown UnknownUnknownV = 3.0 x 10V = 3.0 x 106 6 m/sm/s F =?F =?B = 4.0 x 10B = 4.0 x 10–1–1 T TQ = - 1.6 x 10Q = - 1.6 x 10–19–19 c c

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SolutionSolution

F = BqVF = BqV

= 4.0 x 10= 4.0 x 10–1–1 T (-1.6 x 10 T (-1.6 x 10–19–19c)(3.0 x 10c)(3.0 x 106 6

m/s)m/s)

= -1.9 x 10= -1.9 x 10–13–13 Tcm/s Tcm/s

= -1.9 x 10 = -1.9 x 10 -13-13 n n

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The small picture – how The small picture – how magnetism occursmagnetism occurs

Domain theory – when enough atoms Domain theory – when enough atoms of a substance line up in the same of a substance line up in the same directiondirection

Strong magnets – iron and steelStrong magnets – iron and steel

Very strong – Alnico alloyVery strong – Alnico alloy

Weak – aluminum, platinumWeak – aluminum, platinum

Natural – magnetite or lodestodes Natural – magnetite or lodestodes formed when rock was moltenformed when rock was molten

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Magnetic field linesMagnetic field lines

Magnetic flux, (Magnetic flux, () – number of field ) – number of field lines passing through a surfacelines passing through a surfaceUnit: weber = 1 nm/ampUnit: weber = 1 nm/amp

Magnetic flux density, B =Magnetic flux density, B =/A/A

Unit: wb/mUnit: wb/m2 2 = nm/a m= nm/a m2 2 = n/am= n/am1 wb/m1 wb/m2 2 = 1 Tesla= 1 Tesla

Earth, 10Earth, 10–4–4 T T Humans, 10Humans, 10–11–11 T T

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Electromagnetism-flowing Electromagnetism-flowing electrical current electrical current magnetism magnetism

Ampere’s Rule for parallel, straight Ampere’s Rule for parallel, straight conductors: F = 2k L Iconductors: F = 2k L I11 I I2 2 / d/ d

K = 10 K = 10 –7–7 n/a n/a2 2 = 10 = 10 –7–7 Tm/a Tm/a

L, length, mL, length, m

I, current, aI, current, a

d, distance between wiresd, distance between wires

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Solenoid – conducting linear coil Solenoid – conducting linear coil which acts like a bar magnetwhich acts like a bar magnet

Increase B, magnetic flux density byIncrease B, magnetic flux density byIncreasing the currentIncreasing the current

Adding loops of wireAdding loops of wire

Inserting an iron core into solenoid – now Inserting an iron core into solenoid – now it is an electromagnetit is an electromagnet

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Electromagnetic InductionElectromagnetic Induction

2121

Michael Faraday and Joseph Michael Faraday and Joseph Henry around the same time… Henry around the same time… Discovered that when there is Discovered that when there is

relative motion between a magnetic relative motion between a magnetic field and a complete circuit (and the field and a complete circuit (and the conductor cuts across the magnetic conductor cuts across the magnetic field), that electricity will flow!!!field), that electricity will flow!!!

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Hand rule #3 – shows force Hand rule #3 – shows force acting on wire in B fieldacting on wire in B field

Lay right hand flat, palm upLay right hand flat, palm up Extend thumb 90 degrees to rest of Extend thumb 90 degrees to rest of

fingersfingers Fingers point in direction of B fieldFingers point in direction of B field Thumb points in direction of current, IThumb points in direction of current, I Imaginary vector coming up Imaginary vector coming up

perpendicular out of the palm points in perpendicular out of the palm points in the direction of force acting on current the direction of force acting on current carrying wire.carrying wire.

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If current flows, there must be If current flows, there must be an EMF – this is EM inductionan EMF – this is EM induction

Faraday’s Law of Induction:Faraday’s Law of Induction:E = - N E = - N / / t t

E, emf, voltsE, emf, volts

-N, # of turns of wire (- means the current -N, # of turns of wire (- means the current opposes the change that induced it)opposes the change that induced it)

, change in flux in weber, wb, change in flux in weber, wb

t, change in time, sect, change in time, sec

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Sample ProblemSample Problem

If a coil of 200 turns is moved If a coil of 200 turns is moved perpendicularly in a magntic field at perpendicularly in a magntic field at a constant rate, find the induced a constant rate, find the induced emf. The flux linkage change ( emf. The flux linkage change ( / / t) is 4.00 x 10t) is 4.00 x 10-6-6 wb in 0.0100 sec. wb in 0.0100 sec.

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Problem solutionProblem solution

E = - N E = - N / / t t

E = (-200)(4.00 x 10 E = (-200)(4.00 x 10 –6–6 wb) wb)

1.00 x 10 1.00 x 10 –2–2 s s

E = -8.00 x 10 E = -8.00 x 10 –2–2 v v

Imagine what thousands of turns Imagine what thousands of turns would produce!would produce!

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Generators at Hoover Dam

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Electric GeneratorsElectric Generators

Convert mechanical energy into Convert mechanical energy into electrical energy by rotating a looped electrical energy by rotating a looped conductor (armature) in a magnetic conductor (armature) in a magnetic fieldfield

Alternating-Current electricity Alternating-Current electricity produced is conducted by slip rings produced is conducted by slip rings and brushes to be usedand brushes to be used

** Direct current can be produced by Direct current can be produced by

using split ringsusing split rings **

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A coil with a wire is wound around a A coil with a wire is wound around a 2.0 m2.0 m22 hollow tube 35 times. A hollow tube 35 times. A

uniform magnetic field is applied uniform magnetic field is applied perpendicular to the plane of the coil. perpendicular to the plane of the coil.

If the field changes uniformly from If the field changes uniformly from 0.00 T to 0.55 T in 0.85 s, what is the 0.00 T to 0.55 T in 0.85 s, what is the

induced emf in the coil? induced emf in the coil?

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A = 2.0 m2

N = 35

B = .55 T

T = 0.85 s

E = -N t = - NBA / t

E = 35 (0.55 T) (2 m 2)

0.85s

E = 45.3 v

http://www.phys.ufl.edu/~phy3054/extras/contents/Welcome.html

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AC Generator OutputAC Generator Output

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Four sides of a loop depicted Four sides of a loop depicted in a magnetic fieldin a magnetic field

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Cross-section of a rotating wire Cross-section of a rotating wire loop and output currentloop and output current

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3535

Lenz’s Law - Lenz’s Law -

The direction of an induced current is The direction of an induced current is such that the magnetic field resulting such that the magnetic field resulting from the induced current opposes the from the induced current opposes the change in the field that caused the change in the field that caused the induced current.induced current.

When the N pole of a magnet is moved When the N pole of a magnet is moved toward the left end of a coil, that end toward the left end of a coil, that end of the coil must become a N, causing of the coil must become a N, causing induced current flow in opposition. induced current flow in opposition.

3636

Lenz's law: The induced emf Lenz's law: The induced emf generates a current that sets up a generates a current that sets up a magnetic field which acts to oppose magnetic field which acts to oppose the change in magnetic flux. the change in magnetic flux.

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3838

Another way of stating Lenz's law is to say Another way of stating Lenz's law is to say that coils and loops like to maintain the that coils and loops like to maintain the status quo (i.e., they don't like change). If status quo (i.e., they don't like change). If a coil has zero magnetic flux, when a a coil has zero magnetic flux, when a magnet is brought close then, while the magnet is brought close then, while the flux is changing, the coil will set up its flux is changing, the coil will set up its own magnetic field that points opposite own magnetic field that points opposite to the field from the magnet. to the field from the magnet.

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On the other hand, a coil with a On the other hand, a coil with a particular flux from an external particular flux from an external magnetic field will set up its own magnetic field will set up its own magnetic field in an attempt to magnetic field in an attempt to maintain the flux at a constant maintain the flux at a constant level if the external field (and level if the external field (and therefore flux) is changed. therefore flux) is changed.

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InductanceInductance

The property of an electric circuit by The property of an electric circuit by which a varying current induces a which a varying current induces a back emf in that circuit or a back emf in that circuit or a neighboring circuit.neighboring circuit.

Mutual Inductance, M Mutual Inductance, M Self Inductance, LSelf Inductance, L

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Mutual InductanceMutual Inductance

Effect that occurs in a transformer Effect that occurs in a transformer when a varying magnetic field when a varying magnetic field created in the primary coil is carried created in the primary coil is carried through the iron core to the through the iron core to the secondary coil, where the varying secondary coil, where the varying field induces a varying emf.field induces a varying emf.

4242

M = -Es / M = -Es / Ip/ Ip/ t t

Shows the ratio of induced emf in one Shows the ratio of induced emf in one circuit to the rate of change of circuit to the rate of change of current in the other circuit.current in the other circuit.

M, inductance, HenryM, inductance, HenryEs, average induced emf across Es, average induced emf across

secondarysecondary Ip/ Ip/ t, time rate of change in current t, time rate of change in current

in primary coilin primary coil- sign, induced v opposes - sign, induced v opposes I I

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ProblemProblem

Find the mutual inductance in an Find the mutual inductance in an electrical device in which the EMF in electrical device in which the EMF in the secondary is 200. V and the rate the secondary is 200. V and the rate of change of the current is 2.0 x 10of change of the current is 2.0 x 10-3-3 a/s.a/s.

M = -Es / M = -Es / Ip/ Ip/ t t M = -200v / 2.0x10M = -200v / 2.0x10-3-3a/s a/s M = -1x10M = -1x105 5 HH

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Self InductanceSelf Inductance

Ratio of induced emf across a coil to Ratio of induced emf across a coil to the rate of change of current in the the rate of change of current in the coilcoil

L = -E / L = -E / I / I / t t

L, henryL, henry

I, current, ampI, current, amp

T, time, secT, time, sec

4545

Effective ValueEffective Value

www.sfu.ca/.../Graphics/Root_Mean_Square.gifwww.sfu.ca/.../Graphics/Root_Mean_Square.gif

Ieff = 0.707 Imax

Veff = 0.707 Vmax

4646

TransformerTransformer

Two separate coils of wire placed near one Two separate coils of wire placed near one another that are used to increase or another that are used to increase or decrease AC voltages with little loss of decrease AC voltages with little loss of energy. energy.

It contains a Primary coil and a Secondary It contains a Primary coil and a Secondary coilcoil

When the primary is connected to AC When the primary is connected to AC voltage, the changing current creates a voltage, the changing current creates a varying magnetic field that is carried varying magnetic field that is carried through the core to the secondary coil.through the core to the secondary coil.

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Transformer, cont.Transformer, cont.

In the secondary coil, the varying field In the secondary coil, the varying field induces a varying emf. This is called induces a varying emf. This is called mutual inductancemutual inductance

Secondary voltageSecondary voltage = = secondary #turnssecondary #turns

Primary voltage primary # turns Primary voltage primary # turns

Power = Voltage x CurrentPower = Voltage x Current

4848

Transformers lose no powerTransformers lose no power

Pp = Ps Pp = Ps VpIp = VsIs VpIp = VsIs Transformer Equation:Transformer Equation: IsIs = = VpVp = = NpNp Ip Vs NsIp Vs Ns

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Transformer ProblemTransformer Problem

A step-up transformer has a primary A step-up transformer has a primary coil consisting of 200 turns and a coil consisting of 200 turns and a secondary coil that has 3000 turns. secondary coil that has 3000 turns. The primary coil is supplied with an The primary coil is supplied with an effective AC voltage of 90.0v. A)What effective AC voltage of 90.0v. A)What is the Vs? B)If Is = 2.00a, find Ip. C) is the Vs? B)If Is = 2.00a, find Ip. C) What is the power in the primary What is the power in the primary circuit?circuit?

5050

Solution to Transformer Solution to Transformer ProblemProblem

Vs = NsVp/Np = 3000(90.0V)/200 = Vs = NsVp/Np = 3000(90.0V)/200 = 1.35 kV1.35 kV

Pp = Ps, VpIp = VsIs Pp = Ps, VpIp = VsIs Ip = VsIs/Vp Ip = VsIs/Vp == Ip =1350v(2.00a)/90.0v = 30.0aIp =1350v(2.00a)/90.0v = 30.0a

Pp = VpIp = 90.0v(30.0a) = 2.70 kWPp = VpIp = 90.0v(30.0a) = 2.70 kW

5151

Assignment: 488p1,5,7Assignment: 488p1,5,7

1. Ns = 1. Ns = VsNp/Vp=(2400v)(75turns)/120v VsNp/Vp=(2400v)(75turns)/120v 1500 turns1500 turns

5. A. Vs = VpNs/Np = 120v/5 =24.0 v5. A. Vs = VpNs/Np = 120v/5 =24.0 v

5. B. Is = Vs/Rs = 24v/15 W = 1.60 a5. B. Is = Vs/Rs = 24v/15 W = 1.60 a

5. C. Ps=(Is)5. C. Ps=(Is)22 Rs = (1.60a) Rs = (1.60a)2 2 (15.0 (15.0 ) = ) =

38.4 w38.4 w

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Sources or for more informationSources or for more information

http://physics.bu.edu/~duffy/py106.htmlhttp://physics.bu.edu/~duffy/py106.html http://sol.sci.uop.edu/~jfalward/http://sol.sci.uop.edu/~jfalward/

magneticforcesfields/magneticforcesfields/magneticforcesfields.html magneticforcesfields.html

Most any high school or college physics Most any high school or college physics texttext

www.physics.sjsu.edu/.../physics51/www.physics.sjsu.edu/.../physics51/mag_field.htmmag_field.htm

hyperphysics.phy-astr.gsu.edu/.../hyperphysics.phy-astr.gsu.edu/.../elemag.htmlelemag.html 5252