Learning Outcomes from Last Time Class 3 Electrostatic Forces Physics 106 Winter 2018 Press CTRL-L to view as a slide show. You should be able to answer these questions: What is science? What is physics? What is meant by physical "law"? How does physics make use of models? What do equations tell us? What don t they tell us? What math will I need for this course? What are the four fundamental interactions of nature? What two kinds of models do we use to describe forces at a fundamental level? What is meant by a "field"? Learning Outcomes What Causes Forces -Two Experiments Today we will discuss: The nature of forces Charging by conduction and induction Coulomb s law - the force between point charges Using Coulomb s law Virtual Particles (QED):You and a friend are standing on an ice sheet. You throw a softball to your friend. What happens? What Causes Forces -Two Experiments Static Electricity Virtual Particles (QED):You and a friend are standing on an ice sheet. You throw a softball to your friend. What happens? Geometric Models (General Relativity): steel balls on a cloth frame. Why are the balls attracted? What do you know about "static electricity"?
Static Electricity How Will We Treat Electric and Magnetic Forces? What do you know about "static electricity"? What will happen when a charged rod is brought near to a stream of water? Why? Field Lines The Foundations of Electric and Magnetic Theory We ll use electric and magnetic field lines. From Michael Faraday, c. 1820s Model based on experimental results. Field lines don t really exist, but reality behaves the way field lines would behave if they existed! First Observations -Greeks Benjamin Franklin Observed electric and magnetic phenomena as early as 700 BC Found that amber, when rubbed, became electrified and attracted pieces of straw or feathers Also discovered magnetic forces by observing magnetite attracting iron 1706-1790 Systematic work on electricity in the 1740s led to the "one fluid" model of electricity. Positive charge was a surplus of fluid, negative charge a deficit.
Properties of Electric Charges Properties of Charge Two types of charges: + and Likes repel and unlikes attract Positive charges are protons Protons are held firmly in the nucleus Negative charges are electrons Objects become charged by gaining or losing electrons Electric charge is always conserved Charge is usually exchanged rather than created Positive and negative charges are always created and annihilated in pairs Properties of Charge Insulators Charge is quantized Most charge is a multiple of a fundamental unit of charge, symbolized by e Electrons have a charge of e Protons have a charge of +e Quarks are believed to have charges of ±1/3e or ±2/3e. The SI unit of charge is the coulomb (C) e =+1.60 10 19 C Insulators are materials in which electric charges do not move freely Glass and rubber are examples of insulators When insulators are charged by rubbing, only the rubbed area becomes charged Conductors Semiconductors Conductors are materials in which the electric charges can move freely Most metals are good conductors When charge is placed on a conductor, it spreads over the surface of the material The characteristics of semiconductors are between those of insulators and conductors Silicon and germanium are examples of semiconductors
Demonstrations Charging by Conduction and Induction Stream of Water Electrophorus Charging by Conduction A charged rod touches a conducting sphere Some electrons on the rod move to the sphere When the rod is removed, the sphere is left with a charge The sphere has the same charge as the rod What s wrong with these pictures? Charging by Induction Start with an uncharged conducting sphere. Charging by Induction Bring a negatively charged rubber rod near the sphere. Electrons are repelled to the opposite side of the sphere. Charging by Induction Connect a ground wire to the far side of the sphere. Electrons flow to ground.
Charging by Induction Remove the ground wire. Charging by Induction Positive charge remains on the sphere. Note that a negatively charged rod gave positive charge to the sphere. Polarization Examples of Polarization In most neutral atoms or molecules, the center of positive charge coincides with the center of negative charge In the presence of a charged object, these centers may separate or rotate slightly This results in more positive charge on one side of the molecule than on the other side This realignment of charge on the surface of an insulator is known as polarization The charged object (on the left) induces charge on the surface of the insulator A charged comb attracts bits of paper due to polarization of the paper The force between the objects is attractive because the force is stronger between closer charges. Coulomb s Law Charles Augustin de Coulomb 1736-1806 Studied electrostatics and magnetism Investigated strengths of materials
Coulomb s Experiment Coulomb s Law Try doing the "Virtual Lab" What were Coulomb s conclusions? Coulomb found that an electrical force has the following properties: It is along the line joining the two particles and inversely proportional to the square of the separation distance, r, between them It is proportional to the product of the charges It is attractive if the charges are of opposite signs and repulsive if the charges have the same signs Coulomb s Law Using Coulomb s Law Mathematically, q 1 q 2 F = k e r 2 k e is called the Coulomb Constant k e = 8.99 10 9 Nm 2 /C 2 Typical static charges can be in the μc range Applies only to point charges or charged spheres. In the equation q 1 q 2 F = k e r 2 a positive force is repulsive and a negative force is attractive, but we need signs to tell us directions, so... We usually ignore the sign and write the magnitude of the force as a positive quantity: q 1 q 2 F = k e r 2 Vector Nature of Electric Forces Vector Nature of Electric Forces The direction of electrostatic forces is either repulsive......or attractive
Electrostatics and Gravity The Superposition Principle Gravitational and electrical forces have much in common. q 1 q 2 F E = k e r 2, F G = G m 1m 2 r 2 Forces of multiple charges add as vectors You should know this if you need to take the MCAT Superposition Principle Example Superposition Principle Example Just add the vector forces on charge 3 from each of the other charges. Even if the forces are in one dimension, you should draw a free body diagram with arrows! The force exerted by q 1 on q 3 is F 13 The force exerted by q 2 on q 3 is F 23 The total force exerted on q 3 is the vector sum of F 13 and F 23 Superposition Principle Superposition Principle In principle, the force between two arbitrary charges can be determined by breaking the charge into small charges, and adding all the Coulomb s law forces between pairs of charges. In our problems, all the charges will be in a straight line.
Superposition Principle Using Coulomb s Law What is the direction of the force on each charge? The magnitude of which force is the largest? Problem Solving Strategy Example 1 Draw a diagram of the charges in the problem Identify the charge of interest Units - Use SI Units Apply Coulomb s law For each charge, find the force on the charge of interest Determine the direction of the force Sum all forces Three charges are along the x axis: The force on the charge at the origin is zero. Find the charge on the left. Example 1 Example 1 The middle charge is the "free body." The middle charge is the "free body." Draw the force vectors on it. Draw the force vectors on it.
Example 1 Example 1 Apply Coulomb s law: The middle charge is the "free body." The two forces are equal and opposite. q 3 q 1 k e (0.60m) 2 = k q 2 q 1 e (0.20m) 2 q 3 (0.60m) 2 = q 2 (0.20m) 2 q 3 = 9q 2 = 108μC Example 2 Find the force on the right charge. Example 2 Find the force on the right charge. F 12 = k e q 1 q 2 (0.20m) 2 F 32 =+k e q 3 q 2 (0.80m) 2 q 1 q 2 F = k e (0.60m) 2 + k q 3 q 2 e (0.80m) 2 q 1 q 2 F = k e (0.60m) 2 + k q 3 q 2 e (0.80m) 2 F = 8.99 10 9 4 10 6 12 10 6 0.60 2 8.99 10 9 108 10 6 12 10 6 0.80 2