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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

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The compass

The Compass

1088 Dream Poe Essays – ShenKuo

1


Permanent magnets

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

2


Torque on a magnet in a magnetic field

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

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

4


Amp re s law

Ampère’s law

5


Amp re s law1

Ampère’s law

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

6


Magnetic field due to current in small element

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

7


Magnetic field due to current in small element1

Magnetic field due to current in small element

For an infinite long wire:

dH

Biot-Savart law

Compare:

8


Biot savart law for a closed circuit

Biot-Savart law for a closed circuit

dl

f

9


Magnetic flux and magnetic flux density

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)

10


Gauss law for magnetostatics

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!

11


Two sources of magnetic field

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):

12


Example 1

Example 1

Force between two bar magnets:

13


Example 2

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

14


Example 3

Example 3

Force from magnetic field on current loop:

l

Torque:

F

Magnetic dipole moment of a planar loop

w

F

15


Electromotor

Electromotor

16


From current to charge

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:

17


The compass

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

18


Force on a charge in e b field

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.

19


B field and e field due to moving charges

B-field and E-field due to moving charges

Magnetic field due to moving charge:

Electric field due to an electric charge:

+q

20


Ferroelectric materials

Ferroelectric materials

  • - In ferroelectric materials the positive and negative ions are positioned in an off-centrosymmetric configuration

  • - Ferroelectric materials exhibit a spontaneous ferroelectric polarization

21


Dielectric materials

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.

22


Ferromagnetic materials

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

23


The compass

Ferromagnet

Paramagnet

Antiferromagnet

T < TC

T > TC

24


Ferromagnetic materials1

Ferromagnetic materials

25


Diamagnetic materials

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

26


Reading @home

Reading @home

  • Chapter 16

  • [email protected]

27


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