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The Compass

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1088 Dream Poe Essays – ShenKuo

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- - Permanent magnets are dipoles (magnetic monopoles do not exist!)
- - The north and the south pole of a bar magnet have equal strength
- - Two north poles or two south poles repel each other, a north pole and a south pole attract each other
- - Magnetic field lines are directed from the north pole to the south pole

H

p

F

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A magnet (dipole) does not move in an uniform magnetic field, it only rotates

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p

The magnetic pole strength is defined by considering the work done by the field in moving a pole once around the wire:

I

F

The magnetic pole strength isdefined as work done per unit current. Thus, [p] = J/A = weber = Wb

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5

Ampère’s law can be used for structures with high symmetry

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Last week:

dE

dH

+

+

+

+

+

+

+

+

+

+

+

Electric charges at rest produce an electric field, moving electric charges produce an electric field and a magnetic field

7

For an infinite long wire:

dH

Biot-Savart law

Compare:

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dl

f

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Magnetic flux:

- B is a field density (number of lines per area)

- M is an indication of total field through an area (number of field lines)

- The unit of B is Wb/m2 = Tesla (T)

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The magnetic flux through any closed surface in a magnetic field is equal to the algebraic sum of the magnetic poles within the surface:

Magnetic monopoles do not exist!

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Biot-Savart law

Current through element dl:

Single magnetic pole:

Relations can be used to calculate the force between permanent magnets and current carrying objects (moving electric charges):

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Force between two bar magnets:

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Force from current in element dl on magnetic pole p:

dl

Force from magnetic pole p on current in element dl:

dl

redefinition of r

r

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Force from magnetic field on current loop:

l

Torque:

F

Magnetic dipole moment of a planar loop

w

F

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16

Magnetic field due to current (Biot-Savart):

Magnetic field due to moving charge:

Force on a current carrying wire:

Force on an electric charge:

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How big should the magnetic field be to steer the particles in a circular accelerator?

Circumference of Large Hadron Collider (LHC): 27 km (R = 4.3 km)

ac is centripetal acceleration (= v2/R)

Actual dipole field at LHC: B = 8.4 T

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- An electric charge accelerates in an electric field (gains kinetic energy).

- An electric charge does not gain kinetic energy in a magnetic field. It is deflected in a direction perpendicular to v and B.

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Magnetic field due to moving charge:

Electric field due to an electric charge:

+q

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- - In ferroelectric materials the positive and negative ions are positioned in an off-centrosymmetric configuration
- - Ferroelectric materials exhibit a spontaneous ferroelectric polarization

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- - Dielectric materials are insulating materials
- - Dielectric materials do not exhibit a spontaneous polarization, but a polarization is induced in an applied electric field
- - The polarization results from a small displacement of the electronic charges with respect to the positive nucleus.

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- Ferromagnetism originates from electron spins and orbital moments

- Each atom in a ferromagnetic material possesses a magnetic moment

- Atomic moment interact with each other via direct exchange and dipolar interactions

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Ferromagnet

Paramagnet

Antiferromagnet

T < TC

T > TC

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- In diamagnetic materials, current loops are induced by an external magnetic field

- The field that they produce is opposite to the external magnetic field

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- Chapter 16
- sebastiaan.van.dijken@aalto.fi

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