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