Physics 1220/1320Physics 1220/1320

ElectromagnetismElectromagnetism

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ThermodynamicsThermodynamics

Lecture Magnetostatics, chapter 27-29

Magnetism- Contrary to common opinion, magnetism is just as common as electricity.

-Magnetic fields are due to the motion of electric charges

-All moving charges create magnetic fields

-Electric and magnetic fields will turn out to be ‘coupled’ and theexpression of the more general phenomenon of ‘electromagnetism’

-This phenomenon will explain the whole range of radiation and itsways of spreading.

- Unlike electric charges, magnetism always comes in the form of twoopposing poles (usually called North and South pole)

-The magnetic force, magnetic field lines behave differently than theelectric counterparts

Unlike polesattract,

Like polesrepel

Unit ‘Tesla’ [T] = [N/(Am)] , 10 k[G] = 1[T]

Many metals can be‘magnetized’ when brought in contact with a magnet.

The molten materialinside the earth rotatesand creates a smallmagnetic field.

Earth field near surface varies, ~ 1/3- 1/2 Gauss

State of the art -Permanent magnets have field strength ~ 24[T]

-Electromagnets up to

Field strength which occur in nature:Sun 6[kG] pulsars 10^8 [T], magnetars [GT]b/w two atoms ~ up to 70 [T]… in technology: 50 ft from powerline 40[mG]6’’ hair dryer 300[mG], microwave oven 6’’ 200[mG]

100[T]

Magnetic field B and magnetic force FB

Unit ‘Tesla’ [T] = [N/(Am)] , 10 k[G] = 1[T]

Magnetic Field Lines

Magnetic flux B, Gauss’s Law

!

Mass Spectrometers:Magnetic fields can act as ‘velocity selectors’ for charged particles:

v = E/B ie only particles with the right speed can pass through(condition: Fy =0)

In the famous Thompsonexperiment, this effect was usedto determine the ratio e/m forelectrons.

In the mass spectrometer, the effectis used to determine the mass of unknownparticles with high precision.

http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=53

http://www.pk-applets.de/phy/thomson/thomson.html

Hall Effect

Force on charge carrier in B

Transverse E builds through charge accumulationDue to FB until FE equal+opposite to FB Hall voltage

qEz+qvdBy=0Jx= nqvd

nq= (-JxBy/Ez)

Force on Current-Carrying Conductor

Force and Torque on a LoopForce and Torque on a Loop

Net force is zero

Torque is zero if dA parallel B and maxif perpendicular to B

Magnetic dipole moment =IA

Loops are important because electrons often perform loops,so material properties can be understood if one understandsB for conductor loops.

A potential energy is associated with the dipole moment in B.

In B, coils will tend to turn towardtheir position of Umin.

A case of practical importance is the energy of a coil in B:

Consider a coil which rotates from an initial position into onewhere its is parallel to B.

Note:

= NIABsin

How magnets work:

Forces on current loops in non-uniform BdF = I dl x B

Magnets in non-uniform fields –If free to move, all magnets will orientsuch that their axis // B

Permanent magnets:

http://ist-socrates.berkeley.edu/~cywon/Curie.htmlhttp://ist-socrates.berkeley.edu/~cywon/Stripe.html

Random order

Aligned atomic’s

tends to align’s with B

Presence of B makes net

Non-uniform B attractive force

Magnetic Field of moving charge

Unit Tesla [T] = [(Ns)/(Cm)] = [N/(Am)]

[0] = [N/A2] = [Tm/A] ‘permeability’ of free spaceand c2 = 1/(00)

Forces between two moving electrons

Magnetic Field of a Current Element:

Biot-Savart

B of Current Carrying Straight Conductor

Magnetic field of two wires

28.24

Find IFind I44 to make B at center of square zero: to make B at center of square zero:

Magnetic Field of a Circular Loop(atoms & electrons!)

Ampere’s Law

A more general integration path gives thesame result, as long as the wire is includedand the surface of integration is closed:

Field Inside a Long Cylindrical Conductor

Magnetic Field of a Solenoid

http://webphysics.davidson.edu/applets/BField/Solenoid.html

http://www.falstad.com/vector3dm/index.html