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Magnetism and Electromotive Force

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Magnets

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General Properties of Magnets

1. have polarity, north and south poles

2. poles attract is they are different and repel if they are alike – like electric charges

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Magnetic Fields 1. Field lines are drawn to represent the magnetic

field.

a. Field lines come out of the North pole

of a magnet (field lines are away from

positive charges)

b. Field lines go into the South pole of a

magnet (field lines are toward negative

charges)

c. Field lines are greatest in number at

the poles

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Electric Field for dipole

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Field of a Permanent Magnet

N S

B

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This Works For All Magnets

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Field Lines with iron filings

The Earth’s Magnetic Field

The northern hemisphere of the Earth contains the south pole of the “Earth magnet”.The Earth's magnetic field is similar to that of a bar magnet tilted 11 degrees from the spin axis of the earth.The Earth's core is not magnetic. So how did the Earth get its magnetic field? Magnetic fields surround electric currents, so we surmise that circulating electric currents in the Earth's molten metallic core are the origin of the magnetic field. A current loop gives a field similar to that of the earth.

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More magnetic properties

3. Permanent magnets

  a. do not lose their polarity

  b. AlNiCo – aluminum, nickel, cobalt

4. Non-permanent magnets

a. can be magnetized by induction

b. iron, cobalt, nickel alone

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Domains

At the atomic level, we see that magnetism is produced due to the alignment of the domains of groups of atoms.

Before magnetism After magnetism

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. Superconductors repel magnets by expelling the field lines from their surfaces. There is no magnetic flux inside a superconductor.

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Electromagnetism

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Two Electromagnetism Laws

Ampere’s Law Electrical currents create magnetic fields Right Hand Rule

Faraday’s Law Changing magnetic fields in a conductor

generates electricity Currents are induced in conductors when the

conductors either…(a) move in a magnetic field or(b) are in the presence of a changing magnetic field.

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Electromagnetism

Oersted (Denmark, 1800’s) showed magnetic effects could be created by moving charges. (Current carrying wires are surrounded by magnetic fields.)

Using the first right hand rule, we can see why current carrying wires will attract if the current is traveling in the same direction in both wires and repel if the current is traveling in opposite directions.

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The First Right Hand Rule

The direction of the magnetic field can be established by using the first right hand rule.a. Place your right hand on the wire with your thumb extended in the direction of conventional current flow (positive charges move)b. Curl you hand around the wire. Your fingers now point in the direction of the magnetic field.

c. The magnetic field goes around the wire.

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First Right Hand Rule

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The right-hand rule gives the direction of the magnetic field (N to S).

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Magnetic Field Around a Coil

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The Second Right Hand Rule

The North pole around a coil can be determined by using the second right hand rule.

a. Curl the fingers around the coil pointing in direction of current flow.

b. The direction your thumb points is the direction of the North pole

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Second Right Hand Rule

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Magnetic Field Near a Coil

Electromagnets can be strengthened by adding a soft iron core which becomes magnetized when current is turned on.

A coil of current carrying wire has a magnetic field making it an electromagnet.

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Wires with Parallel Currents

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Forces Caused by Magnetic Fields

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Forces Caused by Magnetic Fields

Faraday discovered that the force on a current carrying wire in a magnetic field is at right angles to both the current and the magnetic field.

The direction of the force on the wire can be determined using the third right-hand rule.

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The Third Right Hand Rule

Using an open right hand, point the thumb in the direction of the current flow and the fingers in the direction of the magnetic field.

 

The force is visualized as coming out of the palm of the hand

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Third Right Hand Rule

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The magnitude of the force can be calculated using the equation:

 F = BILThe strength of the magnetic field (magnetic

induction) is calculated using the equation:

 

B = F/IL

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Sample Problem

If a wire bearing a current of 10 A lies perpendicular to a uniform magnetic field and a force of 0.2 N is found to exist on a section of that wire 80 cm long, what is the magnitude of the magnetic field? F = BILB = F/ILB = 0.2 N/ (10 A x 0.8 m)B = 0.025 T

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Magnetic Field Strength

Magnetic field strength (actually the density of the flux lines ) is measured in teslas (T), equivalent to 1 N/A·m (1 T is very large.)

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Strengths of various magnetic fields.

1. The strength of the earth’s magnetic field is about 5 x 10-4 T 2. A lab magnet is about 0.01 T 3. Only the most powerful of electromagnets have a field strength of 1 T 4. Surface of a neutron star 108 T 5. In interstellar space 10-10 T

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The Earth’s Magnetic Field

Earth’s magnetic field

(1) 5 x 10-4 T

(2) points into the earth in the northern

hemisphere

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Devices which incorporate the effect of magnetic fields on current carrying wiresLoudspeakers – a coil of current carrying wire is forced

into and out of a magnetic field which causes a paper cone to vibrate

 Galvanometers  a. measure very small amounts of current  b. may measure as little as 50 A

  c. can be converted to ammeters or voltmetersElectric Motors – use a loop which can rotate 360 as a

result of changing the direction of the current just as the loop reaches vertical

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Force on a Single Charged Particle

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Force on a Single Charged

Particle The force of the magnetic field on current

carrying wires is a result of the force exerted on individual charges.

 

Cathode ray tubes use this concept to direct electrons to the inside surface of the screen where they strike the phosphor producing a picture.

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This force can be calculated using the formula

F = Bqv The direction of the force on the particle can be

predicted using the third right hand rule by extending the thumb in the direction of the velocity of the positive charge.

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1. The force is perpendicular to the velocity of the particle and the magnetic field.

2. Charges moving parallel to the magnetic field experience no force.

3. Maximum force is experienced when the particle is moving perpendicular to the field

4. The magnitude of the force is directly proportional to q and to v

5. The direction of the force depends upon the sign of the charge.

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Sample Problem

A He2+ ion travels at right angles to a magnetic field of 0.80 T with a velocity of 105 m/s.

Find the magnitude of the magnetic force on the ion.

F = Bqv

F = (0.80 T)2(1.6 x 10-19 )(105 m/s)

F = 2.56 x 10-14 N

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Sample Problem

A proton moves perpendicularly to a magnetic field that has a magnitude of 4.2 x 10-2 T. What is the speed of the particle if the magnitude of the magnetic force on it is 2.4 x 10-14 N?

F = Bqv sov = F/BqV = (2.4 x 10-14 N)/[(4.2 x 10-2 T)(1.6 x 10-19 C)]V = 3.57 x 106 m/s

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Electromotive Force

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INDUCTION: Creating Electric Current from Changing Magnetic

Fields

1. Michael Faraday and Joseph Henry

showed that current could be produced by moving magnets.

 2. Electromagnetic induction is the

production of potential difference by

moving a wire through a magnetic field.

Faraday’s Law of Induction

A loop of wire is connected to a current meter…

If a magnet is moved toward or away from the loop, a current is measured.

• If the magnet is stationary, no current exists.• If the magnet is stationary and the wire loop is

moved, a current is measured.

A current is set up in the loop as long as there is relative motion between the magnet and the loop.

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Induction

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Electromotive Force

1. EMF is not a force but rather an increase in potential and is measured in volts.

 

2. EMF can be calculated using the equation

 

EMF = BLv

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Devices which incorporate the concept of magnetic fields producing current

1. Microphones – movement of a diaphragm causes a wire to move into and out of a magnetic field inducing current.

 2. Electric generators 

a. convert kinetic energy into electrical energy.

  b. mechanical movement of an armature inside a magnetic field causes current to flow within the wire.

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Transformers

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Transformers

Change the voltage of the current without changing the power that is provided with alternating current.

They allow us to carry high-voltage at low currents and then convert it to low-voltage, high current for use.

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How do transformers work? A changing current through a coil of wire can create a changing magnetic field.

Currents can be induced in other wires by these changing magnetic field.

Therefore, the primary coil current must have AC.

The iron core of the transformer is not required but it does increases the efficiency a great deal.

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Transformer Calculations

3. Voltage changes can be calculated using the relationship between the voltages and the number of coils of wire in the transformer.

secondary voltage primary voltage

turns on secondary = turns on primary

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For an Ideal Transformer...

p

s

s

p

s

p

I

I

E

E

N

Na

Number of Turns

CoilVoltages

Coil Currents

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If a<1, the Es>Ep and we have a step up transformer.

If a>1, the Es<Ep and we have a step down transformer.

Step-up or Step-down?

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Step up transformers

a. increase voltage

 

b. televisions – 120 V to 25 kV

 

c. car batteries – 12 V to 103 V

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Step down transformers

a. decrease voltage

 

b. high voltage lines carry from

4.8 x 105 V to 120 V

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Ratio of the Number of Windings Matters

Secondary Voltage is V2 = (N2/N1) V1

Secondary Current is I2 = (N1/N2) I1But Power in =Power out

Is = Vp = Np

Ip Vs Ns

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An Example

My laptop computer requires about 12 Volts AC, which comes from an adapter (transformer) that is plugged into the wall socket.

What is the approximate ratio of the number of turns on this transformer? Which coil has more turns, the primary or the secondary?

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The Field Concept

Michael Faraday (1791 - ) had the idea that forces between bodies were cause by Fields that fill all space and act on the bodiesElectric Field Edue to charge

Faraday discovered the important connection between Electric Fields & Magnetic Fields: A moving or changing electric field generates a magnetic field and a moving or

changing magnetic field generates an electric field.

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Maxwell - Electricity & MagnetismJames Clerk Maxwell: Treatise on Electricity &

Magnetism (1873) is the last word on classical E&MRanks with Newton’s work as one of the great

accomplishments of physics

Maxwell’s EquationsFour equations that completely describe all of electricity and magnetism

1. Coulomb’s law - relates electric field to charges2. Ampere’s law (Generalized)- moving charge or changing

electric field generates a magnetic field3. Faraday’s law: changing magnetic field generates an

electric field4. Absence of free magnetic “charges” (only pairs of north-

south poles)

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Maxwell - Electricity & MagnetismMaxwell’s equations show that electric and magnetic

forces travel at a definite predicted speed -- NOT instantaneous “action at a distance”

Travel as electromagnetic waves - recall that a changing electric field generates a magnetic field and vice versa

Travel in free space (vacuum) at a speed determined by the constants in Coulomb’s law and Faraday’s law

Using values for the constants measured in the laboratory, speed predicted to be equal to the speed of light!

c = 3.0 x 108 m/s

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Electromagnetic WaveElectromagnetic wave in vacuum (free space)

Changing electric field generates magnetic field and vice versa

Direction of motion

Magnetic Field

Electric Field

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Summary of Classical Physics

Physics as it stood near the end of the 19th CenturyFundamental concepts: Time flows the same everywhere for all observers Space is described by 3 dimensions (Euclidean Geometry) Mass is never created nor destroyed (conserved) Charge (plus and minus) total is conserved Energy changes form but is conserved Momentum is conserved

Fundamental Objects and Laws: Particles have mass and move according to Newton’s laws Force originates in interactions between particles of matter

baseballs, rockets, ….. Waves are moving patterns in a medium - e.g. light is described

by Maxwell’s laws Sound, Light, …..

Waves have interference -- Particles do not