ELEN236

1.Electricity and Magnetism

All About Circuits:

Chapter 14: MAGNETISM AND ELECTROMAGNETISM

  • Permanent magnets
  • Electromagnetism
  • Magnetic units of measurement
  • Permeability and saturation
  • Electromagnetic induction
  • Mutual inductance

New Question Set on Magnetism, Inductance and Capacitance

1.1.1Introduction

What is a permanent magnet?

  • A material which has the intrinsic property of creating a magnetic field
  • E.g. neodymium magnet
  • Field always has a north and a south

  • Like poles repel. Opposite poles attract
  • Different types of magnetic material:

1)Ferromagnets (strongly attracted by magnetic field): can become permanent magents or will interacte strongly with magnetic fields

At the atomic level, the spin and orbital angular momentum of each of the electrons creates a magnetic dipole moment(in other words a tiny magnet). If all of the magnetic dipole moments are oriented in the same direction, then ferromagnets become permanent magnets

Examples of Ferromagnets:

  • Iron, Cobalt, Nickel, neodymium

2)Paramagnets(weakly attracted by magnetic field): The magnetic dipole moments will align to an externally applied field, but if the field is removed, the alignment is lost

Examples of Paramagnets:

  • Tungsten, cesium, aluminum

3)Diamagnets(weakly repelled by magnetic field): The magnetic dipole moments align to oppose an external magnetic field

Water is a good diamagnet

e.g. Levitating frog in a 16 Tesla magnetic field:

For more info:

What is an electromagnet?

  • A magnet whose magnet field is created by passing strong current through a wire.
  • Usually the wire is coiled around a ferromagnet to increase the field strength
  • Electromagnetism = interface between electric world and mechanical world

Electricity ↔ Magnetism ↔ Physical World

How?

  • A changing electric field creates a magnetic field
  • Current = movement of electric charges and is therefore a changing electric field. Any time there is current, a magnetic field will be created.
  • A changing magnetic field creates an electric field
  • E.g. a spinning magnet = a changing magnetic field which will create an electric field. A generator works by spinning magnets to create a voltage (electric field.
  • Other examples of electromagnetism at work:

▪ DC and AC motors▪ Generators

▪ Rail guns (maglev trains, theoretical space vehicle launch, weapons)

▪ speakers and microphones▪ transformers

▪ magnetic switches (reed switches, relays)

▪ Magnetic storage system (harddrives, tapes)

▪ Magnetic resonance imaging

▪ Magnetoencephalography (MEG)

▪ SQUID (Superconducting Quantum Interference Device)(e.g. Strange Days movie)

Again, the basic Idea behind Electromagnetism:

Electricity ↔ Magnetism

Some demos:

  1. Drop magnet down the copper rod
  2. PhET Bar Magnet
  3. PhET Electromagnet simulation:
  4. Electromagnetic Acceleration Overview (Plasmaboy):
    (also see )

1.2Magnetic Fields

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  • Magnetic poles are designated by North (N) and South (S).
  • The end of a magnet that points to the Earth’s north pole is called the North pole of the magnet.
  • Opposite poles attract and like poles repel
  • If this is true, what is the magnetic polarity of the North pole of the earth

1.2.1Magnetic Field Quantities

  • Given a magnet (permanent or electric) the strength of the magnetic field at some point away from the magnet depends on two things

1)How strong the magnet is

2)What kind of material the magnetic field is in and passes through

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  • Putting an iron bar in the vicinity of the permanent magnet will actually increase the magnetic field strength in and around the iron. The strength of a magnetic field is usually indicated in a diagram by how close together the lines representing the magnetic field are drawn. The lines are called lines of flux and the closer together the lines are, the greater the flux density. Lines of flux strive to be as short as possible, therefore the lines of flux that pass from one magnet to another tend to pull the magnets together (i.e., pull opposite poles together)
  • In many ways, a magnetic circuit is like an electric circuit:
  • This electric circuit has a “force” that is pushing electric charges. This force is the voltage. The opposition to the force is the electrical resistance in the circuit and the result of the force is an electrical current

There’s a cause (voltage) an effect (current) and an opposition (resistance)

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  • This magnetic circuit also has a force/cause (the magnet) creating an effect (the magnetic flux) and is encountering an opposition (in a magnetic field, this opposition is called reluctance)

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Comparison of Electrical and Magnetic Properties

Electrical Quantity / Unit / Magnetic Quantity / Units
Voltage (V) / Volts / Magnetomotive Force (MMF) / Amp-turns
Current (I) / Amps / Magnetic Flux (Φ) / Webers
Resistance (R) / Ohms / Reluctance (R) / Amp-turns/Weber
R=(ρl/A) / R=(1/μ)(l/A)
Current Density / Amps/m^2 / Magnetic Flux Density (B) / Tesla (Weber/m^2)
Electric Field / V/m / Magnetic Field Intensity (H) / Amp-turns/m
  • Each of the rows shows an electrical quantity and the analogous magnetic property.
  • Why do you think the units for MMF are Amp-turns?[1]
  • The amount of flux created by the MMF depends on the distance from the wire as well as the material the flux is passing through

Note the last two rows in the table above, they talk about Flux per unit area and mmf per unit length:

  • MMF is amp-turns due to a wire, but a more useful measurement is field intensity which is MMF per unit length
  • Field Intensity is denoted with the letter H
  • Flux tells us how much magnetic field is created, but a more useful measurement is flux density which is Flux per using area
  • Flux density is denoted with the letter B
  • While the two electrical and the magnetic quantities are analogous, they are not identical:
  • For example:

We can express a linear relationship between voltage, current (the slope of this line is 1/resistance):

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But the relationship between MMF, Magnetic Flux and Reluctance is not linear (to create a graph like the one below, you would increase the mmf, by turning up the current in an electromagnet and measuring the flux)

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Like with the V-I graph, the inverse of the slope of this graph will give us reluctance, but you can see that reluctance will not be constant. When will reluctance be greatest and when will it be lowest?

The above graph doesn’t actually tell the whole picture of the relationship between flux and MMF. Not only is the relationship non-linear, but it also exhibits hysteresis…this means that the relationship changes depending on if MMF is increasing or decreasing:

  • Just as we have a relationship between MMF and Φ,
    we have a relationship between H and B
  • μ is called the permeability of a material.
  • Represents how magnetized a material (which can include air or a vacuum) becomes in the presence of an applied magnetic field.
  • Looking at a graph similar to the Flux as a function of MMF graph above, what can you say about the permeability of the material represented in the graph:

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Some more questions about the graph

  • This graph demonstrates the magnetic phenomena of saturation and hysteresis. Using your understanding of these phenomenon, describe what would happen if an electromagnet fully energized with DC is suddenly turned off.[2]
  • Do electric circuits have a saturation point?[3]

1.2.2A Changing Electric Field Creates a Magnetic Field

PHET Example:

A current is moving electrical charge. If an electrical charge is moving, then its electric field is moving. Therefore a current carrying wire will create a magnetic field. In fact, the definition of current comes from the fact that current creates a magnetic field.

  • 1 Amp is defined as the current required to produce an attractive magnetic force of 2 × 10–7newtons per meter of length between two straight, parallel, infinitely long conductors with negligible cross sectional area placed one meter apart in a vacuum.[4] It’s a strange definition and I don’t know why the Coulomb isn’t used as a base SI unit and then define 1 Amp based on the Coulom.

The orientation of the magnetic field generated by the current depends on the direction of current:

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XXX add something like figures 6.4 and 6.5 from Boylestads Intro to E&M

  • If you imagine wrapping the fingers of your right hand around the wire, while pointing your thumb in the direction of conventional current flow. Your fingers will curl around the wire in the direction of the magnetic field being generated.
  • If you coil up a wire as shown in the picture on the right hand side, then the magnetic field from each wire adds to the whole magnetic field and you end up with a magnetic field that is stronger than if you had just one wire. The strength of the field from the coiled wire is equal to the strength of a single wire multiplied by the number of coils (turns) you have in the wire.
  • For this picture, an electrical wire is wrapped around part of an steel torus. The torus keeps the magnetic field concentrated inside of it.
  • What direction does the magnetic field go? [5]
  • If the field intensity from the wire before it is wrapped is 1 Amp-turn/m, what is the flux density of the field in the torus assuming the μ of steel is 8.74x10^-4 H/m?[6]

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  • Visualizing the magnetic field generated by loops of wire can be somewhat tricky. Try to determine which direction the field is inside one loop of wire, then all of the other loops will generate the same field. The field on the outside of the loops will be in the opposite direction.
  • Let’s quantify some of these values in an example:

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  • total length of the iron core toroid is 0.2m, and cross-sectional area is
  • current through wires is 10A
  • The wire is wrapped around the toroid 20 times
  • μ for the toroid is
  • Find the field intensity (H) and the flux density (B) in this toroid.
  • Using the concepts of flux, mmf, flux density and field intensity, we can see how magnetic circuits are analogous to electrical circuits in another way:

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In this magnetic circuit, let’s actually quantify some of these values. This circuit is somewhat more realistic: something could be placed in the air gap to expose it to a magnetic field. In an MRI (magnetic resonance imaging machine) that something could be you[7].

  • In the above circuit, assume that the “cause” is an electromagnet that has 1000 loops around the core
  • The total length of the circuit is 1 meter and the air gap is 10 cm.
  • The cross sectional area of the core is 0.1m2
  • μ for the toroid is
  • μ for the gap is
  • Determine how much current will be necessary to create 1Tesla of flux density
  • Two points to keep in mind:
  • Flux and B are constant throughout circuit (magnetic equivalent to KCL)
  • The mmf from the electromagnet equals the mmf in the core plus the mmf in the air gap (magnetic equivalent to KVL)

It takes a lot of mmf to create flux in an air gap (high reluctance)

It takes a lot of voltage to create a current through something with high resistance.

In the above example, the actual amount of flux is:

Applications

Current Clamp: the current in a wire can be measured indirectly by measuring the magnetic field around the wire. A current clamp is a measuring instrument that does just that. If you cannot break a wire to insert an ammeter, you can use a current clamp to measure the magnetic field around the wire and convert that in to a current.

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Motor: AC and DC motors work when current flows in the motor creating a magnetic field. A pre-existing magnetic field (often from permanent magnets) attracts or repels the magnetic field created by the current and since one of the magnetic fields is stationary and the other is on a rotor that can spin, the motor turns. We will cover motors in much more detail later.

Speakers: Speakers consist of a stationary permanent magnet and an electromagnet connected to a diaphragm. When current moves through the electromagnet in one direction, it will be attracted to the permanent magnet and move the diaphragm towards the permanent magnet. When current moves through the electromagnet in the other direction it will pushed away from the permanent magnet. The current alternates direction many times per second causing the diaphragm to move in and out. The diaphragm movement is what causes sound

1.2.3A Changing Magnetic Field Creates and Electric Field

PHET. Faraday’s Electromagnetic Lab:

The strength of the electric field created is measured in volts (electric field strength is actually measured in V/m) and is proportionally to the rate of change of the flux times the number of turns of wire:

Where the amount of flux that is measured must be perpendicular to the direction that current would be produced. For example, look at these pictures and determine which one will produce the greatest ΔΦ (i.e., change in flux):

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Going back to Faraday’s Law which is the equation relating the voltage produced by a changing magnetic field:

If you substitute, into the equation, you get:

So you can have a change in the flux density, or a change in the area through which the lines of flux go to you will induce a voltage. If you go back to Faraday’s EM Lab (PHET), you have the option of changing the area of the loop of wire…if that is all that you change, you can also induce a current.

Numerical examples:

1)A coil of wire with 1000 loops surrounds a permanent magnet with a flux of 10mWb. If the magnet is quickly withdrawn from the loop, decreasing the flux to 4mWb in 0.1s, what is the induced voltage?

2)How many loops of wire would you need to induce a voltage of 50V when the flux through the loops is changing at a rate of 0.01Wb/s?

1.2.4Lenz’s Law

When a changing external magnetic field induces a current in a conductor, the direction of the current is such that the magnetic field created by it will oppose the change in the external magnetic field

There doesn’t even need to be a circuit like shown above. If the object is a conductor of any shape, current will be created that will create a magnetic field in opposition to the changing external magnetic field

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[1] One Amp-turn is the amount of MMF that 1 turn of a wire in a vacuum carrying 1 amp of current generates

[2] It will maintain a residual flux. In order to remove the flux (magnetization), the core would have to have an external H field applied and then slowly reduced.

[3] Not really. Wires do not saturate when they reach a maximum current. What might happen though is too much current could flow through a wire causing it to overheat and possibly even melt.

[4]

[5] Clockwise

[6] (1Amp-turn/m)*26 turns*8.74x10^-4 = 0.0227 Teslas

[7] Look up MRIs and investigate the three primary ways MRIs can be created: permanent magnet, electromagnet, superconducting electromagnet.