Chapter 18: Electric Charges, Forces, and Fields Brent Royuk Phys-112 Concordia University
Electric Charge Electrostatics vs. Electricity Historical Development Elektron and Magnesia 2
Electric Charge Basics Like repels, opposites attract Charge can move Two kinds of charge How do you know it s only two? Two materials: insulators and conductors Neutral means balanced charge So a water stream is always attracted: polarization Charge by contact or induction Charging by induction: which charge does it get? What is an electrical ground? 3
Electric Charge Basics Charge by contact or induction Charging by induction: which charge does it get? Simulation 4
Charging by Induction 5
Electric Charge Franklin s single fluid model, 1747 surplus (glass) or deficiency (rubber/amber) Unfortunate coin toss Actually, we know it s electrons that move: surplus =, deficiency = +. And electron is negative, proton is positive. Bummer. Triboelectric Charging (charging by rubbing) Metric unit of charge: the Coulomb (a lot of charge) 1 Coulomb = 6.25 x 10 18 electrons Usually more useful: charge of electron e = 1.6 x 10-19 C Notice inverse relationship Classical electromagnetism does not require the use of electrons Charge symbol, q, and q = ne (charge is quantized) Van de Graaf & Wimshurst Franklin s Kite 6
Big Sparks 7
Coulomb s Law The inverse square relationship Just like gravity The Law F = kq 1q 2 r 2 k = 9.0 x 10 9 Nm 2 /C 2 More fundamental: k = 1 ε o = 8.85 x 10-12 C 2 /N m 2 4πε o 9
Coulomb s Law Examples What is the Coulomb force between two 1C charges one meter apart? From here to Lincoln? What is the Coulomb force between two protons separated by r = 1 x 10-15 m? F E Example 18.1: = 2.27 x 10 39 F G If two +1.0 µ charges experience a force of 0.23 N, how far apart must they be? 10
The Electric Field To circumvent the idea of instantaneously propagating forces we posit the existence of a force field We call this the electric field, E E is a vector. Handwritten notation: A field is a quantity that has a value at every point in space. For example, a temperature map is a scalar field and a windspeed map is a vector field! E And guess what: Fields are real! 11
Definition: The Electric Field! E =! F q o Direction is defined by how a positive test charge q o would move For a point charge, E = F q o = kqq o r 2 q o = kq r 2 Note the difference between q and q o +q What is here? 12
Electric Vector Fields Vectors can be found for any point near the charge configuration This defines the electric field 13
The Electric Field Examples What is the electric field vector 12 cm away from a point charge of -42 µc? An isolated electron is acted on by an electric force of 3.2 x 10-14 N. What is the magnitude of the electric field at the electron s location? A 3.2 ng dust particle contains an excess of a billion electrons. What is the direction and magnitude of an E-field that would keep the particle from falling? Two charges of +4.0 µc and +9.0 µc are 30 cm apart. Where on the line joining the charges is the electric field zero? 14
Electric Field Lines Replace vector arrows with continuous lines. The field is always in the direction of the lines. Direction defined by positive test charge. Note that more lines/area means a stronger field Can field lines cross? Examples Single point Charge Like and unlike point charge pairs Dipoles See next page 15
Electric Field Lines 16
The Parallel-Plate Capacitor A Capacitor stores charge Between parallel plates the E-field is quite uniform. 17
Charges on a Conductor 1. The electric field is zero everywhere inside a charged conductor If it were not, the charges would re-arrange themselves until it is 2. Any excess charge on an isolated conductor resides entirely on the surface of the conductor Since charges repel each other and are free to move in a conductor 3. The electric field at the outer surface of a charged conductor is perpendicular to the surface. 18
Charges on a Conductor 4. The excess charge on a conductor in electrostatic equilibrium is more concentrated at regions of greater curvature. Again, tangential components would move charges Therefore the E-field is concentrated at tips of conductors The lightning rod 19
The Faraday Cage Movie What is the safest place to hide during a lightning storm? 20