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# The Compass PowerPoint PPT Presentation

The Compass. 1088 Dream Poe Essays – Shen Kuo. 1. Permanent magnets. - Permanent magnets are dipoles (magnetic monopoles do not exist!) - The north and the south pole of a bar magnet have equal strength

The Compass

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### The Compass

1088 Dream Poe Essays – ShenKuo

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### Permanent magnets

• - 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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### Torque on a magnet in a magnetic field

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

3

### Magnetic field from a current carrying wire

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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### Ampère’s law

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

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### Magnetic field due to current in small element

Last week:

dE

dH

+

+

+

+

+

+

+

+

+

+

+

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

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### Magnetic field due to current in small element

For an infinite long wire:

dH

Biot-Savart law

Compare:

8

dl

f

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### Magnetic flux and magnetic flux density

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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### Gauss’ law for magnetostatics

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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### Two sources of magnetic field

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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### Example 1

Force between two bar magnets:

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### Example 2

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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### Example 3

Force from magnetic field on current loop:

l

Torque:

F

Magnetic dipole moment of a planar loop

w

F

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### From current to charge

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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### CERN

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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### Force on a charge in E + B field

- 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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### B-field and E-field due to moving charges

Magnetic field due to moving charge:

Electric field due to an electric charge:

+q

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### Ferroelectric materials

• - 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

• - 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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### Ferromagnetic materials

- 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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### Diamagnetic materials

- 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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