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Mechanical Engineering laboratory - Magnetism

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Mechanical Engineering Laboratory

A short introduction to…

MAGNETISM

and its practical applications

Michele Togno – Technical University of Munich, 28

March 2014 – 4

April 2014

Mechanical Engineering laboratory - Magnetism

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Magnetism

A property of matter

Archimedes (287-212 BCE)

A magnet is a material or object that produces a magnetic

field. This magnetic field is invisible but it is responsible for the

most notable property of a magnet: a force that pulls

on ferromagnetic materials, such as iron, and attracts or repels

other magnets.

Magnetite Fe

(lodestone)

History of magnetism

Sushruta, VI cen. BCE

(Indian surgeon)

Shen Kuo, 1031-1095

(Chinese scientist)

William Gilbert, 1544-1603

(English physician)

H.C. Oersted, 1777-1851

A.M. Ampere, 1775-1836

C.F. Gauss, 1777-1855

M. Faraday, 1791-1867

J.C. Maxwell, 1831-1879

H. Lorentz, 1853-1928

F. Savart, 1791-1841

J.B. Biot, 1774-1862

Mechanical Engineering laboratory - Magnetism

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The Earth magnetic field

A sort of cosmic shield

Mechanical Engineering laboratory - Magnetism

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Magnetic domains

and types of magnetic materials

Ferromagnetic: a material that could exhibit spontaneous

magnetization, that is a net magnetic moment in the absence

of an external magnetic field (iron, nickel, cobalt…).

Paramagnetic: material slightly attracted by a magnetic field

and which doesn’t retain the magnetic properties when the

external field is removed (magnesium, molybdenum,

lithium…).

Diamagnetic: a material that creates a magnetic field in

opposition to an externally applied magnetic field

(superconductors…).

Mechanical Engineering laboratory - Magnetism

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Magnetic field and Magnetic flux

Every magnet is a magnetic dipole (magnetic monopole is

an hypothetic particle whose existence is not experimentally

proven right now).

The magnetic field [Wb/m

] or [T] is the area in which a force

is experienced.

The magnetic flux [Wb] or [T·m

] is a measure of the

magnetic field in a certain medium.

Mechanical Engineering laboratory - Magnetism

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B & H…

Relationship between B (magnetic flux density) and H (magnetic field intensity):

B = µ

·H with µ

= 4·π·10

-7

[(V·s)/(A·m)] in vacuum

B = µ

·(H + M) = µ

·(H + χH) = µ

·µ·H in a medium

µ = 1 + χ is the magnetic permeability constant

For materials which are NOT ferromagnetic or diamagnetic materials, 10

-6

< χ < 10

-4

µ ≈ 1 without ferromagnetic medium

µ ≈ 1500 with the iron yoke in our experiment

Mechanical Engineering laboratory - Magnetism

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B(H) (or M(H)) in a ferromagnetic material

The relationship between field strength H and magnetization M is not linear in ferromagnetic materials:

MAGNETIC HYSTERESIS

When an external magnetic field is applied to a ferromagnetic material such as iron, the atomic dipoles

align themselves with it. Even when the field is removed, part of the alignment will be retained: the

material has become magnetized. Once magnetized, the magnet will stay magnetized indefinitely. To

demagnetize it, heat or a magnetic field in the opposite direction are required.

saturation

coercive field

remanence

Mechanical Engineering laboratory - Magnetism

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Magnetic field and currents/1

Oersted, 1820: he discovered the

connection between electricity and

magnetism

When he turned on the electric current in a wire, a compass

needle that was on another experiment changed its position.

Mind the right-hand rule

The Biot–Savart law is used for computing the

resultant magnetic field B at position r generated by

a steady current I (for example due to a wire):

Mechanical Engineering laboratory - Magnetism

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Magnetic field and currents/2

▪ Infinite wire:

▪ Solenoid:

Mechanical Engineering laboratory - Magnetism

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Magnetic circuit

Hopkinson’s law is the magnetic analogy to Ohm’s law.

Magnetomotive ‘force’ or magnetic Spannung:

Magnetic flux:

Where the total magnetic reluctance R [H=Wb/A] is the sum of the reluctances of different materials in

the circuit.

and the energy per unit volume stored in the magnetic field:

is the magnetic force

Mechanical Engineering laboratory - Magnetism

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Faraday law and Lorentz force

Lorentz force is the force

experienced by a charged particle

in a magnetic field

Faraday law of induction:

Given a loop of wire in a magnetic field, Faraday’s law of induction states the induced

electromotive force ε in the wire.

From Faraday’s law of induction and the Maxwell equations, the Lorentz force can be deduced:

Mechanical Engineering laboratory - Magnetism

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Lenz law and eddy currents

Lenz's law states that the current induced in a circuit due to a change or a motion in a magnetic field is

so directed as to oppose the change in flux or to exert a mechanical force opposing the motion.

law of conservation of energy

and 3

Newton’s law

The total amount of electromagnetic energy cannot change!

Eddy currents (also called Foucault currents) are electric currents induced within conductors by a

changing magnetic field in the conductor. Eddy currents will be generated wherever a conducting object

experiences a change in the intensity or direction of the magnetic field.

Mechanical Engineering laboratory - Magnetism

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How to measure a magnetic field

Some more applications of the Hall

effect: automotive fuel level indicators,

ABS break system, old PC keyboards…

The magnetic field can be measured with a probe

based on the Hall effect.

The Hall effect is the production of a voltage difference

(the Hall voltage) across an electrical conductor,

transverse to an electric current in the conductor and a

magnetic field perpendicular to the current.

at equilibrium:

Mechanical Engineering laboratory - Magnetism

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Magnetic Resonance Imaging

(1.5T– 3T)

Further practical applications of magnetic fields

Bending and focusing magnets

in particle accelerators (LHC 8.4T!)

Mass spectrometer

Mechanical Engineering laboratory - Magnetism

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Thank you for your attention

and

Enjoy your experiments!

Are you interested in radiation applied science & research? Have a look at our website and my personal logbook:

http://ardent.web.cern.ch/ardent/ardent.php

http://ardent.web.cern.ch/ardent/ardent.php?link=esr11-logbook

Mechanical Engineering laboratory - Magnetism

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Eddy currents experiment explanation

Slab of non-ferromagnetic material dropping between

two permanent magnets:

For instance, at the ‘exit’ we can imagine this

situation:

Mechanical Engineering laboratory - Magnetism

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Material Magnetic

susceptibility

[Vs/Am]

Water -9.0E-06

Iron >1000

Aluminum 2.22E-05

Graphite -1.4E-05

Oxygen 3.73E-07

Diamond -2.2E-05

Helium -9.85E-10

Magnetic susceptibility of some materials