Chapter 9:Magnetism & Inductance

Presented by: James, VE3BUX

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Magnetism: History / Importance• Navigation

– Allowed routine exploration beyond the sight of land• Science

– Allows the structural determination of chemicals via nuclear magnetic resonant (NMR) spectrography

• Medicine– Non-invasive imaging of patients via magnetic resonant

imaging (MRI)• Functionally the same as NMR but applied differently and

the procedure was renamed due to public concern over “nuclear safety”

• Electronics– Fundamental component of many circuits relies on

magnetism

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Magnetism: The basics

• Invisible force (much like electricity)• Can not be directly sensed by us

– Migratory birds found to have magnetite-bearing sensory cells, thus they “see” magnetic fields to a degree

– Human brain can be disrupted by extremely strong magnetic fields

• Earth’s magnetic field– Result of iron rich magma– Protects us from space radiation– Field strength is only ≈5x10-5 Tesla

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Magnetism: Types• Ferromagnetism

– Fe, Co, Ni most well known– R•Fe2O3 (ferrite), R=ZnO, etc– Li

• In 2009, a team at MIT demonstrated that Li gas exhibited ferromagnetism when cooled to 1 Kelvin by infrared laser

• Paramagnetism– Liquid O2, Platinum, Aluminum

• Diamagnetism– An effect where a material creates an

opposing magnetic field

Fe CoNi

O2 (l)

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Magnetism: Forces

• Opposites attract, like repel– Analogous to E.M.F.

• By convention, force extends from N-to-S

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Magnetism: Field Lines

NS

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Induction: Exploiting magnetism

• Devices which create and make use of magnetic fields via induction– Inductors, relays, solenoids, ignition coil, electric

motors, electrical generation, stoves• Induction is the process by which a magnetic

field is formed (induced) as electrons flow in a conductor– Recall that we measure the flow of # electrons per

second as Amperes!

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Induction• By passing a current through a wire,

a magnetic field is induced– Chapter 9 (tonight)

• Conversely, moving a conductor through a magnetic field induces an electric current– Chapter 10 (Nov 1st)

Note: These diagrams apply conventional current theory (the old, and incorrect notion that current moves from positive to negative). The course uses (the modern, and technically correct) electron flow model, so the direction of current is simply opposite.

Electron flow

Elec

tron

flow

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Inductance: Key Concept

• Inductance is the characteristic of an electrical conductor that:

OPPOSES CHANGE in CURRENT

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Potential Energy: Magnetic

• As current begins to flow, a magnetic field forms around the conductor and the magnitude remains constant as long as the current remains constant

• Think of the magnetic field as a reservoir for energy– Analogous to a capacitor storing a potential– Magnetic field is converted to electrical potential as

the magnetic field collapses, usually to great effect!

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Inductors: An introduction

• Inductors are devices which exploit the properties of a magnetic field which is formed by induction

• Unit of measure: Henrys (H)• Schematic symbol: L

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Inductor Design: Four factors

• There are four factors which determine the inductance of a coil:

1. Diameter2. Number of turns3. Length4. Core material

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Coil Factors: 1. Diameter1. Diameter: diameter = inductance

Any guesses as to why increasing diameter results in an increased inductance?• Has to do with the density of the magnetic field in the center of the coil• Greater coil area presents less opposition to the formation of a magnetic

field

Note: If we double the diameter, the inductance increases four-fold, therefore we can say that the inductance is a factor of cross-sectional area

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Coil Factors: 2. Number of Turns2. Number of turns: # turns = inductance

– By increasing the number of turns in a coil, we are effectively providing greater conductor length which increases the number of magnetic lines of force• Recall inductors “store” energy in the magnetic field, thus

increasing the size of the potential magnetic field increases the ability to store the magnetic energy

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Coil Factors: 3. Length3. Length: length = inductance

– This may seem counter-intuitive considering when you increase the number of turns in a coil, it increases the inductance

– Consider that by increasing the length of a coil, we present a longer path for the magnetic field flux to take, resulting in more opposition to the formation of a magnetic field

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Coil Factors: 4. Core material

• The material in the center of a coil affects inductance by increasing the ability of a magnetic field to pass– Known as magnetic permeability

• Vacuum = 1• Air = 1.00000037• Steel = 100• Ferrite (MnO•Fe2O3) = 640+• µ-metal = 20000+

– (approximately 75% nickel, 15% iron, plus trace copper and molybdenum)

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Inductors: Schematic representation

• Variable inductors value changed by varying:– Amount of core material inside coil

• Most variable inductors– Changing the number of turns

• So-called “roller inductors”• 1 = Contact wheel, 2 = contact bar, 3 = coil drive mechanism

• Most often, you will see either fixed, or tapped inductors

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Inductors: Associated losses• Factors influencing losses in inductors:– Resistive characteristics– Magnetic field coupling

• Resistive (power) losses are a result of the dissipation of energy as heat– Recall that P = I2R– Consider the length of conductor in a coil

• Do you recall the concept of conductivity/resistivity?

• Field losses are due to magnetic coupling in nearby conductive components which causes parasitic induction in those coupled components

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Inductors: Current vs Time / ELI

• Voltage reaches its maximum right away

• Current takes time to build up as magnetic field is established

63% of expected current after 1 time constant

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Time Constant: Inductors

• Time constant for inductors is defined as:– The time it takes the circuit to achieve 63% of the

total expected current• The time constant is calculated as:

RT= L

Where does the time constant value 63% come from?

Values must be in base units (ie. H and Ω)

Where n=1

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00015H

• Given the following values, calculate the time constant of the circuit– Inductor whose value is 1.5 mH– Resistor which is 220Ω

00015mH1.5mH

Recall: We must use “base” units such as H and Ω m = milli = thousandth = move decimal 3 places left

Inductors: Practice example

T =

(L)(R)

LR

= .220Ω = 0.0000068s = 6.8x10-6s ≈7µs

As you can see, realistic time constant values are vanishingly small!

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Inductors: Series / Parallel

• Treat inductors in the same way you treat resistors

Series Parallel

Lt = L1 + L2 + .. Ln 1 = 1 + 1 + .. 1 . Lt L1 L2 Ln

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Inductors: Series Example

• You have three inductors in series and their values are:L1 = 25mHL2 = 15mHL3 = 100µH

What is the total inductance of this simple circuit?

Lt = L1 + L2 + .. Ln = L1 + L2 + L3 = 25mH + 15mH + 100µH = 40mH + 0.1mH = 40.1mH

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Inductors: Series Example• Now you have three inductors in parallel and

their values are:L1 = 40mHL2 = 80mHL3 = 40mH

1 = 1 + 1 + .. 1 . Lt L1 L2 Ln

= 1 + 1 + 1 . L1 L2 L3

= 1 + 1 + 1 . 40 80 40= 1 . 16mH

1 . Lt

Lt = 16mH 1 . Lt

Cross-multiply

A common pit-fall here is forgetting that the formula is based on 1/Lt

Be sure that you recall this fact when you do the calculations on your own!

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Chapter 9: Magnetism & Induction

• Questions?• Let’s try the chapter questions together…– B-005-09-01– B-005-09-02– B-005-09-05– B-005-09-08– B-005-11-05– B-005-11-06– B-005-11-09– B-005-11-10

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