1 Chapter 21

2 Hydrodynamics and Electromagnetism Much of the terminology is the same Some concepts can be applied between the two fields

3 Amber

4 Charging By Induction

5 Two Things You Already Knew 1. Opposite charges attract 2. “Like” charges repel

6 Remembering Gravitation Newton’s Law of Gravitation

7 What is Mass? “resistance to acceleration” More fundamentally, a physical property of matter In large quantity, groups of matter seem to be always attracted to one another Personally, I’d say “mass” is a lot weirder than “charge”

8 What is charge? Physical property of matter Two flavors: “plus” and “minus”

9 What is the smallest charge possible? Millikan Oil Drop Experiment In 1910, Millikan was able to measure the charge of the electron Recall: Atom made up of nucleus and clouds of electrons outside nucleus Recall: nucleus: made up of protons and neutrons. Protons have charge equivalent to electrons. Neutrons are neutral Smallest charge possible is x Coulombs (C) aka e

10 Definition of Coulomb Abbreviation: C Amount of charge through a cross- section of wire in 1 second when there is 1 Ampere (A) of current. (We’ll cover the amp later)

11 Okay, Mr. Smartguy, what about these quark-things? Quarks– particles which make up the proton and neutron The “up” quark has charge of +2/3 e The “down” quark has charge of -1/3 e They don’t count because there are no “free” quarks. They always are confined in a particle Proton- uud Neutron-udd

12 Fundamental Particles ParticleSymbolCharge in units of e Electron e, e -,  - Protonp+1 Neutronn0 Anti-electron (positron) -- +1 Anti-proton Anti-neutron0 Alpha particle  or 4 He Up quarku+2/3 Down quarkd-1/3 Any element of atomic number, z ZNXZNXz

13 How Charges Behave in materials Conductors– charges move freely Insulators—charges cannot move easily Semiconductors—charges only move freely when certain conditions are met (heat, sufficient voltage, etc) Superconductors-charges move effortlessly and cannot be stopped once they are moving

14 Just like mass, charge is conserved What is X?

15 Coulomb’s Law Charles Augustin de Coulomb used a torsion pendulum to establish “Coulomb’s Law”

16 k k is equal to 1 for electrostatic units We use SI so in this case k is equal to 8.98 x 10 9 N·m 2 /C 2 k is actually formed from two other constants  = ….  0 = x C 2 /(N·m 2 ) Called the permittivity of free space

17 The product of q 1 and q 2 If the product, q 1 q 2,is negative then the force is attractive If the product, q 1 q 2,is positive then the force is repulsive Your book uses the absolute value in the case of determining magnitude of force.

18 Where is r-hat? The force is directed along the shortest distance between two points, just like gravitation. In the case to the right, the force is directed along lines from the center of the spheres.

19 1+1=2: The principle of superposition Sometimes difficult problems can be made simple by using the principle of superposition. Problem: Find the electric field of sphere with a hole in it. = - The E-field of the whole sphere The E-field of a sphere with a hole in it The E-field of a small sphere The principle of superposition is one of the most powerful problem solving tools that you have

20 At this point, You should be able to work any of these force problems Make a force diagram Show charges and locations Use Coulomb’s law This is all Physics 250 stuff NOW LET’S DO SOME PHYSICS 260!

21 Electric Field Why do I need this concept? Assume that you have a charge in space: we need a general expression for when we add another charge, q. What force will be exerted on q? Have I seen this before? Remember F=mg Our new expression: F=qE E is the electric field that is present in the space wherein q was placed. E is usually the result of other charges which previously have been located in the same space. Since E=F/q then the units are newtons per coulomb (N/C). Another set of units is volts per meter (V/m).

22 A representation of earth’s gravitational field

23 Electric Field Lines Rules for Field Lines 1. Electric field lines point to negative charges 2. Electric field lines extend away from positive charges 3. Equipotential (same voltage) lines are perpendicular to a line tangent of the electric field lines

24 Your Task For the rest of this chapter and chapter 22, we will investigate how to calculate the electric field This quantity represents an infinite set of vector quantities, in other words, a vector field.

25 The Problem In order to calculate this quantity, we need to know how the charge creating the electric field is distributed in space The geometrical distribution of the charge will have the biggest effect on the magnitude and direction of the electric field

26 4 Geometrical Situations-Point Charge Point charge: All charge resides at a geometric point so there is no geometrical distribution r-hat points out from the geometric point

27 4 Geometrical Situations-Line Charge Line charge: All charge resides along a line A charge density must be created: a mathematical description of the geometrical distribution of the charge For a line charge, this is called the linear charge density,  (units C/m)

28 4 Geometrical Situations-Surface (or area) Charge Surface charge: All charge resides on top or under a surface (or area) surface charge density,  (units C/m 2 )

29 4 Geometrical Situations-Volume Charge Volume charge: All charge resides in a particular volume volume charge density,  (units C/m 3 )

30 Electric Dipoles A pair of charges, one “+” and the other “-” which are separated by a short distance Electric dipole is represents the electrical distribution of many molecules Positive and negative are relative concepts: “positive” means less negative charges than “negative”

31 Force and Torque on the Electric Dipole Why is this important? Principle of microwave oven, amongst other applications Recall:  =r x F If F=qE, then  =qE r sin  ( where  is the angle between E and r) Let d=distance between two charges Electric Dipole Moment Necessary because the charge and distance between charges are easy to characterize p=qd Note: p is a vector in the direction pointing from 1 charge to the other  =pE sin  or  =p x E

32 Potential Energy Recall that  W=-  U  W=F·r=Fr cos  =qEd cos   U=-qd E cos  U = - p·E which is the potential energy of a dipole in an electric field