# 21.1 Coulomb s Law - Electric Charge - Conductors and Insulators - Coulomb s law 21.2 Charge is quantized 21.3* Charge is conserved

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1 INTRODUCTION We will understand how electric and magnetic fields affect charged particles Lorentz Force Law: we will learn to describe how electric and magnetic fields are produced by charged particles Four fundamental equations of electromagnetism Maxwell Equations 1 Chapter 21 Coulomb s Law - Electric Charge - Conductors and Insulators - Coulomb s law 21.2 Charge is quantized 21.3* Charge is conserved 2 1

2 Classified by electrical sign: positive charge and negative charge An object with equal amounts of the two kinds of charge is electrically neutral (no net charge), whereas one with an imbalance is electrically charged. Ways of charging: friction, conduction, induction Charging object by friction: charge a glass rod by rubbing one end with silk - charge a plastic rod by rubbing one end with wool - + Charges with the same electrical sign repel each other. Charges with the opposite electrical sign attract each other. 3 Classify materials according to the ability of charge to move: - Conductors: materials in which a significant number of charged particles are free to move - Insulators: materials in which charged particles are not free to move - Semiconductors: materials (like Si, Ge) whose conductivity can be (usefully) controlled - Superconductors: materials which offer no resistance at all to the movement of charged particles The properties of conductors & Insulators are due to the structure and electrical nature of atoms Matter consists of. - electrons : - protons: - neutrons: -e +e 0 elementary charge, e = C Electrons and protons are the basic charges in nature. Net charge for an object: 4 2

3 An object said positive charged: doesn t mean that it gains proton, but just loses electrons! An atom is missing (gaining) an electron is called a positive (negative) ion Explanation for an insulating rod charged by rubbing: - Ionization: The process of removing an electron from the electron cloud of an atom - Force of friction can break molecular bonds - Molecular ions can be created, when one of bonds in large molecule is broken - Tiny amount of charge are transferred from one to the other. 5 Metals are conductors. It can be charged by conduction or induction Charging by Conduction: Conduction just means that the two objects will come into actual physical contact with each other (this is why it is sometimes called charging by contact ). - In an isolated conductor, any excess charge is located on the surface of the conductor (so that net force on any of it is zero)! Charge induced by Induction: induced charges in a conductor without physical contact with an charged object - Copper rod is still neutral - Evidence of mobility of charge in conductor: Induced charge How conduction can eliminate excess charge on an objector? - also called: Ground the object, discharge the object - by setting up a pathway of conductors between an objector and the Earth s surface - Earth s surface is a huge conductor 6 3

4 Coulomb s Law: Electrostatic force: SI Unit of charge: C (Chapter 26) Permittivity constant: Constant: ( Comparison with: Newton s equation for gravitational force: ) Shell theorems: A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell s charge were concentrated at its center. If a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell. Electrostatic force: Vector ( including direction and magnitude) - Charges with the same (opposite) electrical sign repel (attract) each other. 7 Electrostatic force: Vector (direction and magnitude) - Charges with the same (opposite) electrical sign repel (attract) each other. A couple of questions: How do we express a vector? magnitude and direction How do we find net electrostatic force if there are several point charges? How do we express a vector? Unit vector: i, j, k ; corresponding to positive x, y, z directions Direction Unit Vector Force + x direction - x direction + y direction - y direction + z direction - z direction 8 4

5 What about arbitrary vector? Electrostatic force can be expressed as (method1: magnitude-angle notation): F: magnitude y Fsinθ θ F Fcosθ x θ : Angle relative to positive x axis (along counter-clockwise direction) For example: if the force is along negative y axis, then θ = 270, or -90. Electrostatic force can be written as (method 2: unit-vector notation): 9 Net force (Principle of superposition) on particle1 from n charged particles (2, 3, 4,.n) is given by: (Eq. 21-7) We can express the net force in unit notation: We can find the magnitude and angle of the net force: Magnitude Angle 10 5

6 -- sample problems Sample Problem (p616): (a) Fig. 21-7a show two positively charged particles fixed in place on an x axis. The charges are q 1 = Candq 2 = C, and the particle separation is R = m. What are the magnitude and direction of the electrostatic force F 12 on particle 1 from particle 2? (b) Fig. 21-7c is identical to Fig.21-7a except that particle 3 now lies on the x axis between particles 1 and 2. Particle 3 has charge q 3 = C and is at a distance 3R 4from particle 1. What is the net electrostatic force F 1, net on particle 1 due to particles 2 and 3? (c) Fig. 21-7e is identical to Fig.21-8a except that particle 4 is now included. It has charge q 4 = C, is at a distance 3R 4 from particle 1, and lies on a line that makes an angle θ = 60 with the x axis. What is the net electrostatic force F 1, net on particle 1 due to particles 2 and 4? sample problems Given: q 1 = C, q 2 = C, q 3 = q 4 = C, θ = 60 (a) (b) (c) 12 6

7 -- sample problems Sample Problems (p618): Fig. 21-9a show two particles fixed in place: a particle of charge q 1 =+8q at the origin and a particle of q 2 =-2q at x = L. At what point (other than infinitely far away) can a proton be placed so that it is in equilibrium (the net force on it is zero)? Is that equilibrium stable or unstable? sample problems Sample Problem (p619): In Fig.21-9a, two identical,electrically isolated conducting spheres A and B are separated by a (center-to-center) distance a that is large compared to the spheres. Sphere A has a positive charge of +Q, and sphere B is electrically neutral. Initially, there is no electrostatic force between the spheres (assume that there is no induced charge on the spheres because of their large separation.) (a) Suppose the spheres are connected for a moment by a conducting wire. The wire is thin enough so that any net charge on it is negligible. What is the electrostatic force between the spheres after the wire is removed? (b) Next, suppose sphere A is grounded momentarily, and then the ground connection is removed. What now is the electrostatic force between the spheres? 14 7

8 21.2 Charge is Quantized Any positive or negative charge q can be written as: Elementary charge: e Particle: electrons protons neutrons Symbol: e or e- p n Charge: -e +e 0 15 Problems: 21-38: Fig shows four identical conducting spheres that are actually well separated from one another. Sphere W (with an initial charge of zero) is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B (with an initial charge of 32 e) and then they are separated. Finally, sphere W is touched to sphere C (with an initial charge of +48e), and then they are separated. The final charge on sphere W is +18e. What was the initial charge on sphere A? 16 8

9 Problems: 21-12: Two particles are fixed on an x axis. Particle 1 of charge 40 μc is located at x = -2.0 cm; particle 2 of charge Q is located at x = 3.0 cm. Particle 3 of charge magnitude 20 μc is released from rest on the y axis at y = 2.0 cm. What is the value of Q if the initial acceleration of particle 3 is in the positive direction of (a) the x axis and (b) the y axis? 17 9

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