Electromagnetism. Last Time Electromagnetic induction: The process by which current is generated by moving a conductor through a magnetic field or a magnetic.

Electromagnetism

Last Time Electromagnetic induction: The process by which current is

generated by moving a conductor through a magnetic field or a magnetic field through a conductor.

Electromotive Force: When a wire moves through a magnetic field, a force is exerted on these charges causing them to flow as current.

Magnetic Flux: The strength of a magnetic field is determined by the amount of magnetic field lines crossing perpendicular to a surface.

Electric Generators: Convert mechanical power into electrical power.

Lenz’s Law: The induced EMF resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux change.

Last Time Self-Inductance: When a current is induced in a coil, an

EMF will be induced which opposes the increase in current. Back EMF: The EMF developed to oppose the increasing

current in the windings of a solenoid. Transformers: Increase or decrease AC voltage very

efficiently with minimal loss of power.

What You Will Learn About

JJ Thompson – Determining the mass of an electron (CRT)

How Electric and Magnetic Fields Interact

Mass Spectrometer Electromagnetic Radiation

JJ Thompson’s Experiment Determine the mass of an electron

Cannot be done directly – too small Instead, measure the charge to mass ratio

How did he do it?

JJ Thompson’s Experiment

If magnetic and electric fields are oriented at 90o angles to one another, the deflection of the electrons can be controlled.

Crossed Fields in the CRT

How do we make a charged particle go straight if the magnetic field is going to make it go in circles? Use a velocity selector that incorporates the

use of electric and magnetic fields. Applications for a velocity selector:

Cathode ray tubes (TV, Computer monitor) Mass Spectrometer Velocity Selector

Crossed Fields

• • • •

• • • •

• • • •

E and B fields are balanced to control the trajectory of the charged particle.

FB = FE

qvB = qE

v = E/B

+ + + + +

- - - - -E

- v - v

Phosphor Coated Screen

B out of page

- v

FB

FE

Determining the Charge to Mass Ratio

• Magnetism:Lorentz Force: FB = qv x B

Newton’s Second Law:

F = ma

qvB = mv2/R

q/m = v/BR

• Experiment was repeated for other ions to calculate their charge to weight ratio, thus allowing an estimate of the mass of the particle.

x x x x x x

x x x x x x

x x x x x x

x x x x x x

v

+

Fc

R

Determining the Charge to Mass Ratio (cont.)

• Electricity:

– For 2 parallel plates:

FE = qE

V = Ed = W/q = ½mv2

q v = 2qV

m

• Substitute v in the equation for the radius of the circle traversed by a charged particle in a magnetic field.

mv m 2qV 1 2Vm q 2V qB qB m B q m

B2r2

• • • •

• • • •

• • • •

+ + + + +

- - - - -E

-

FE• • • •

• • • •

• • • •

+ + + + +

- - - - -E

-

FE

R = = = =

Mass Spectrometer

Thompson noticed that he sometimes had more than one dot on the screen. This was the first time that isotopes were seen experimentally.

Mass to charge ratio of positively charged ions can be used to identify molecules in the mass spectrometer.

Mass Spectrometer – How does it work?1. Sample is heated into a gaseous state.2. Sample is ionized into positive ions by knocking

off electrons with high energy electrons.3. Sample is accelerated between two charged

plates.4. Sample proceeds through a velocity selector

using crossed fields.5. Sample proceeds into a magnetic field.

a. The more massive the ion, the less it will be deflected in the magnetic field.

6. Sample passes through a detector where the signal is amplified and processed by a computer.

Mass Spectrometer

Mass Spectrometer - Applications

-Paleoceanography: Determine relative abundances of isotopes (they decay at different rates - geological age)

-Space exploration: Determine what’s on the moon, Mars, composition of the solar wind, etc. Check for spacecraft leaks.

-Detect chemical and biol. weapons (nerve gas, anthrax, etc.).

-Blood doping: steroid and drug use.Mass Spectrometer

Electromagnetic Waves Let’s assume that we have electric fields

without a charged body. Can it happen? 1860 – Years after Faraday and Oersted made

their discoveries – James Maxwell hypothesized that electric fields changing in time would create magnetic fields and vice-versa.

Maxwell further predicted that either accelerating charges (changing current) or changing magnetic fields would produce electric and magnetic fields that would move through space (Electromagnetic Wave).

Electromagnetic Waves (cont.)

www.hyperphysics.comElectromagnetic Wave

Characteristics of Electromagnetic Waves They are transverse waves. When the electric field is at a maximum, the magnetic field

is also at a maximum. Use RHR to determine the direction of B relative E.

The electric and magnetic fields are always perpendicular to one another.

They are sinusoidal. EM Radiation travels at the speed of light in a vacuum.

Normandale Community College

Transmitting Radio Waves Produced by alternating the potential back and forth on an

antenna. AM = Amplitude Modulation where information is

imbedded into the wave by changing its amplitude or power.

FM = Frequency Modulation where information is imbedded into the wave by changing its frequency.

Receiving Radio Waves Process of receiving a radio signal is reverse that

of transmitting. The electric field will cause electrons in the

antenna to oscillate back and forth in the conductor, which in this case is an antenna.

This changing current can be electronically manipulated to convert it into sound at your speakers.

Note: Antenna needs to be oriented in the same direction (parallel) to that producing the wave in order to optimally receive the signal, i.e. if one is vertical, then so should the other.

Electromagnetic Spectrum

www.Purdue.edu

Speed of Light Speed of Light: c = 3.00 x 108 m/s

The relationship between o and o support James Maxwell’s hypothesis that electromagnetic radiation is composed of changing E and B fields.

The relationship between the speed of a wave, its frequency and its wavelength is determined by:

v = f

Where: f = frequency = wavelength

oo

c

1

Energy of Electromagnetic Radiation Elect. Energy Density = Elect. Energy/Volume

Elect. Energy Density = ½oE2

Mag. Energy Density = Mag. Energy/Volume Mag. Energy Density = 1

2o

Total Energy Density = Elect. Energy Density + Mag. Energy Density

= 1 1 2 2o

B2

oE2 + B2

Energy of Electromagnetic Radiation Since the electric and magnetic fields contain the

same amount of energy:

= oE2

= B2

Therefore: 1

o o

E = cB

1o

B2E2 =

The Doppler Effect What you already know: Sound waves exhibit the Doppler

Effect – source of sound moving in relation to observer.

fo’ + fs

2fs

Where:

fo’ = Observed wave frequency

fs = Emitted wave frequency

vrel = relative speed of source and observer

Note: If the source and observer are moving closer together then the equation will have a plus sign (blue shifted). If they are moving apart, then then it will be a minus sign (red shifted).

vrel =

Light Polarization Light is generally emitted from its source

with the electric field oscillating in various directions.

Polarizers eliminate the oscillations in all directions but one.

Polarized light has only half the energy of the incident beam.

www.mic-d.com

Light Polarization Light is generally emitted from its source with

the electric field oscillating in various directions.

Polarizers eliminate the electric field oscillations in all directions but one.

Polarized light has only half the energy of the incident beam.

Note: polarizers canonly work on transverse waves such as light. They don’t work on longitudinal waves such as sound waves.

www.mic-d.com

Light Polarization in Nature Light incident upon the molecules

in the atmosphere will excite electrons in the atoms to oscillate in a direction 90o from the incident beam.

Oscillating electrons act as antennas that re-emit the light that is now polarized.

Over 50% of the light that reaches the surface of the earth is polarized!

www.mic-d.com

Key Ideas Electromagnetic waves consist of electric

and magnetic fields oscillating together. Electromagnetic waves are transverse

waves. The electromagnetic spectrum consists of

radio waves (long wavelength) to gamma waves (short wavelength).

Energy Density: energy of wave is equal to a sum of both the magnetic field and electric field intensity.

Key Ideas Doppler Effect: When two objects are

moving further apart they are called red-shifted while they are considered blue-shifted if moving closer together.

Polarization: The process by which the electric field component of EM radiation is limited to only one direction.