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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 -1- The Strength of the Electric Field • Electric potential – SI unit is the Volt (V) • Electric field is rate of change of potential V E x • The minus sign means that electric fields point from + to – charge. ISP209s7 Lecture 13 -2- Electric Field Example Q = -0.5 mC = -0.5x10-6 C Electric Potential Energy: EPE = Q V = -0.5x10-6 C 60V EPE = -3.0x10-5 J Electric Field E = -V/x =-(50V-90V)/1m= 40 V/m + means to the right in this case ISP209s7 Lecture 13 -3- Sample Problem V 80 Potential 100 60 (2m,100V) What is the magnitude of the electric field at: • 0.5 m? • 1.5 m? • 3.0 m? 40 20 0 (1m,0V) 0 1 2 3 distance m 4 The field is 0 V/m at 0.5 m and 3.0 m since the slope is zero. V 100V 0V V E (at 1.5m) 100 2m 1m x m ISP209s7 Lecture 13 -4- Another Sample Two (-) and two (+) of equal strength. ISP209s7 Lecture 13 -5- Maxwell’s Equations - 1864 • These 4 equations describe the full relationship between the electric and magnetic field. E 4 4 1 E B J c c t 1 B E c t B 0 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 pole • 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 ISP209s7 Lecture 13 -6- 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 -7- 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 down V ISP209s7 Lecture 13 -8- 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 -9- 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 -10- Conductor Conduction band electrons V Electrons hit bumps, but are free to roll. ISP209s7 Lecture 13 energy -11- Insulator Conduction band electrons V Electrons are not free to roll. ISP209s7 Lecture 13 energy -12- Semiconductor Conduction band electrons V energy light LED – light emitting diode ISP209s7 Lecture 13 -13- Superconductor Conduction band electrons V energy No resistance to flow (also no use of energy) ISP209s7 Lecture 13 -14- 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 -15- 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 -16- Inverse square law Inverse square law L[Watts] intensity 4 d 2 L is the luminosity(measured in watts), d is the distance to the source This explains why the electric force has the form it does: + 1 2 2 kq2 Nm F q1 E2 q1 2 ; k 8.99 109 2 r12 C ISP209s7 Lecture 13 -17- Gravity and Electric Forces Newton’s Universal Law of Gravity: 2 Gm1m2 Nm F ; G 6 . 673 E 11 2 2 kg r Coulomb’s Law (Electric Force) 2 kq1q2 Nm F 2 ; k 8.99 E 9 2 C r ISP209s7 Lecture 13 -18- Wavelength and Frequency l 1.0 m period = 2.0 s Wavelength Distance over which the wave repeats Frequency = 1/period Number of cycles (repeats) per second. ISP209s7 Lecture 13 -19- The Electromagnetic Spectrum Speed = l f l – wavelength f – Frequency, Hz (1/period)(1/s) For light Speed c = 3.0E+8m/s Energy = h f h = 6.625E-34 Js = 4.136E-15 eVs Prentice-Hall 2005 ISP209s7 Lecture 13 -20- Around Visible Electromagnetic Spectrum ISP209s7 Lecture 13 -21-