ISP209s7 Lecture 13 -1-

Today

• Announcements: – HW#6 is due by 8:00 am Wednesday February

28th.– The second extra credit problem is due Feb 28 at

8:00am

• Electric Fields• Electric Circuits• Light and the Electromagnetic Spectrum

ISP209s7 Lecture 13 -2-

The Strength of the Electric Field

• Electric potential – SI unit is the Volt (V)

• Electric field is rate of change of potential

• The minus sign means that electric fields point from + to – charge.

x

VE

ISP209s7 Lecture 13 -3-

Electric Field Example

Electric Potential Energy:

EPE = Q V = -0.5x10-6 C 60VEPE = -3.0x10-5 J

Electric Field

E = -V/x =-(50V-90V)/1m= 40 V/m+ means to the right in this case

Q = -0.5 C = -0.5x10-6 C

ISP209s7 Lecture 13 -4-

Sample Problem

0 1 2 3 4distancem0

20

40

60

80

100

laitnetoPV What is the magnitude

of the electric field at:• 0.5 m?• 1.5 m?• 3.0 m?

The field is 0 V/m at 0.5 m and 3.0 m since the slope is zero. m

V

mm

VVE 100

12

0100

x

V 1.5m)at (

(1m,0V)

(2m,100V)

ISP209s7 Lecture 13 -5-

Another Sample

Two (-) and two (+) of equal strength.

ISP209s7 Lecture 13 -6-

Maxwell’s Equations - 1864• These 4 equations describe the full relationship

between the electric and magnetic field.

• They also predict the existence of an electromagnetic wave that travels with speed c

• This was possible due to the math of Maxwell and the insight of Faraday

Charge makes an electric field.

Moving charge makes a magnetic field.

Changing magnetic field makes an electric field

Magnets always have a north and a south pole0

1

14

4

B

t

B

cE

t

E

cJ

cB

E

ISP209s7 Lecture 13 -7-

Electric fields and potential

• In equilibrium the electric field in a metal conductor (electrons to move) is zero.

• This means that inside a metal the electric potential is flat, like the flat top of a table.

• Sitting inside a metal cage is like sitting on top of a large, flat table. As long as you are in the center, there is no danger of falling off.

• This is why being in a car during a thunder storm is relatively safe.

ISP209s7 Lecture 13 -8-

Flow of Charge - Current

• Current is the rate of flow of charge. SI units is Ampere = 1 Coulomb/second

• Batteries are like pumps that lift charge to a higher potential. The charge flows down the hill to the other side of the battery.

A battery is like a pump.

Moving Charge does work on the way downV

ISP209s7 Lecture 13 -9-

Ohm’s Law

• The amount of current that flows is related to the drop in potential (V) and the resistance to the flow of current, R (SI unit Ohms)

• Ohm’s Law: V=IR• Analogy: The amount of water flowing in a

river is related to the drop in elevation (volts) and the size of the river (resistance).

ISP209s7 Lecture 13 -10-

Types of materials

• Conductor – electrons in the conduction band; electrons relatively free to flow (copper, aluminum, gold, silver)

• Insulator – no electrons is the conduction band; electrons can not flow (wood, most rubber, most glass, most plastic)

• Semiconductor – at finite temperature, some electrons are in the conduction band (used in most electronics; silicon, germanium)

• Superconductor – at very low temperature electrons pair and can move freely without resistance (Niobium, Titanium, Lead)

ISP209s7 Lecture 13 -11-

Conductor

electrons

energy

Conductionband

V

Electrons hit bumps, but are free to roll.

ISP209s7 Lecture 13 -12-

Insulator

electrons

energy

Conductionband

V

Electrons are not free to roll.

ISP209s7 Lecture 13 -13-

Semiconductor

Velectrons

energy

Conductionband

light LED – light emitting diode

ISP209s7 Lecture 13 -14-

Superconductor

electrons

energy

Conductionband

V

No resistance to flow (also no use of energy)

ISP209s7 Lecture 13 -15-

Energy and Power

• Energy is the ability to do work: Work = force x distance • Energy comes in two forms

– Kinetic – energy of motion – Potential – energy of position

o Electric EPE = Q (V); Q is the charge, V is the volts

• Examples:• A charge of 0.5 C is pumped by a battery “up” 1.5 V. How much energy did this take? EPE = QV = 0.5 C x 1.5 V = 0.75 J

ISP209s7 Lecture 13 -16-

Where are we?

• We have talked about two forces in nature• Gravity – General Relativity (Space and time are tied into a 4 dimensional space-time. Gravity is the result of the curvature of space.)• Electromagnetism – Electric and magnetic forces are the result of charge and the motion of charge.• Are the gravity and electricity related? Are all the forces in nature related?

• The modern picture of electromagnetism is that the electric force is carried by the photon.• A photon is a small bundle of energy. We see photons in the range of 1.8 eV (red) to 3.1 eV (violet) [1 eV = 1.6E-19 J]

ISP209s7 Lecture 13 -17-

Inverse square law

2d4

L[Watts]intensity

This explains why the electric force has the form it does:

2

29

212

2121 1099.8;

C

Nmk

r

kqqEqF

Inverse square law

L is the luminosity(measured in watts), d is the distance to the source

+

21

ISP209s7 Lecture 13 -18-

Gravity and Electric Forces

Newton’s Universal Law of Gravity:

Coulomb’s Law (Electric Force)

2

2

221 11673.6;

kgNmEG

r

mGmF

2

2

221 999.8;

CNmEk

r

qkqF

ISP209s7 Lecture 13 -19-

Wavelength and Frequency

m

Wavelength Frequency = 1/period

Distance over which the wave repeats

Number of cycles (repeats) per second.

period = 2.0 s

ISP209s7 Lecture 13 -20-

The Electromagnetic Spectrum

Prentice-Hall 2005

Speed = f – wavelengthf – Frequency, Hz (1/period)(1/s)

For lightSpeed c = 3.0E+8m/s

Energy = h fh = 6.625E-34 Js = 4.136E-15 eVs

ISP209s7 Lecture 13 -21-

Around Visible Electromagnetic Spectrum