* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture Notes: Y F Chapter 21
Survey
Document related concepts
Introduction to gauge theory wikipedia , lookup
Elementary particle wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Magnetic monopole wikipedia , lookup
Fundamental interaction wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Speed of gravity wikipedia , lookup
Electromagnetism wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Maxwell's equations wikipedia , lookup
Field (physics) wikipedia , lookup
Lorentz force wikipedia , lookup
Transcript
Electric Charge, Electric Forces, and Electric Fields (Y&F chapter 21) 1. “Ordinary” Matter is made up of elementary particles called: electrons, protons, and neutrons. 2. These particles have mass and a property called “Electric Charge” 3. Electric Charge, or “charge” is a scalar quantity. 4. The electric charge of the electron is negative, the electric charge of the proton is positive, and the neutron – zero. 5. The magnitude of the electric charge of electron is equal to that of the proton. Important Principle Number One: Charge is Conserved - The algebraic sum of all the electric charges in any closed system is constant Important Principle Number Two: The magnitude of the electron (and proton) charge is the natural unit” of charge. Fractional charges are not observed in ordinary matter. Important Observation About Charge There are a huge number of of electrons, and protons in a “human-sized” piece of matter (~1028 electrons in your body). Your body is (approximately) electrically neutral because there are an approximately equal number of protons and electrons in your body. When we speak of a body as having a non-zero charge we usually mean that it has an imbalance in the number of + and – charges. Because the number of individual charges in a “macroscopic” object is so large, we will often consider charge to be a continuous variable (i.e. a real number) as opposed to being a discrete variable (i.e. integer) This is similar to the situation where we identify the MASS of an object in terms of a continuous variable (kilograms) when, in fact, it is actually given by the number of atoms in in the object times the mass of an individual atom. Coulomb’s Law -There is a force between any two charges -The force is directed along the line between the charges -The force is attractive if the charges are of different sign, repulsive if they are the same. -The magnitude of the force is proportional to the product of the two charges (q1 x q2) -The force is inversely proportional to the square of the distance between the charges. r q1q2 F = k 2 r̂ r Important - Force is a Vector F (Force) is in q (Charge) is in r (Distance) is in Newtons Colombs Meters k must have units of Newtons(meters)2(coulomb)2 Coulomb’s Law F (Force) is in Newtons q (Charge) is in Colombs r (Distance) is in Meters r̂ (Unit Vector- points AWAY from other charge) r q1q2 F = k 2 r̂ r k must have units of Newtons(meters)2/(coulomb)2 For reason that will become clearer soon, we choose to define the constant “k” in terms of another number: 2 N ⋅ m k= = 8.988 x10 9 (4πε 0 ) C2 1 r F= 1 q1q2 r̂ 2 4πε 0 r r̂ r F= 1 q1q2 r̂ 2 4πε 0 r Principle of “Superposition” tells us the force on a charge from a single other charge. The principle of superposition states that the force on a charge from a collection of other charges is just the vector sum of the individual forces from each of the charges. To Determine the force on charge q from a number of charges q1, q1, q1 … r F= qq1 1 qq2 1 qq3 r̂ + r̂ + r̂ + ... 2 1 2 2 2 3 4πε 0 r1 4πε 0 r2 4πε 0 r3 1 r 1 qqi F =∑ r̂ 2 i 4πε 0 ri The Electric Field If I place a charge q in the vicinity of a collection of charges q1, q1, q1…then the force on q will be given by : r 1 qqi F =∑ r̂ 2 i i 4πε 0 ri Note that the Total Force is proportional to q: r 1 qi F = q∑ r̂ 2 i i 4πε 0 ri or r r F = qE The Electric Field Minor Problem…What if putting charge q in the vicinity of the other charges causes them to move? Definition of the Electric Field: r E = lim it q →0 r F q We can calculate the Electric filed from a collection of charges from: r 1 qi r̂ F = q∑ 2 i i 4πε 0 ri Which Gives v 1 qi r̂ E=∑ 2 i i 4πε 0 ri Y&F Example 21.10 Example: Electric Field from a ring of charge Step 1 – Consider a tiny portion of the ring (call it dQ) and treat it as a point charge r Step 2 – Calculate the contribution to the total field (call it dE ) that results from dQ. Step 3 – “Add up” these tiny bits of electric by evaluating an integral: r r E = ∫ dE Note: Below is the sort of level of detail I would expect for a problem on an Exam Question What does the field from the ring of charge look like if we are very far away? 1 xQ Ex = 4πε 0 ( x 2 + a 2 ) 3 / 2 If x2>>a2 then x2 + a2 → x2 Ex = Ex = 1 xQ 4πε 0 ( x 2 ) 3 / 2 1 xQ 4πε 0 x 3 1 Q Ex = 4πε 0 x 2 This looks just like the field from a point charge Question What does the field from the ring of charge look like if we are very far away? 1 xQ Ex = 4πε 0 ( x 2 + a 2 ) 3 / 2 If x2>>a2 then x2 + a2 → x2 Ex = Ex = 1 xQ 4πε 0 ( x 2 ) 3 / 2 1 xQ 4πε 0 x 3 Three Important Concepts: 1. Breaking a continuous distribution into infinitesimal pieces and integrating. 2. Using symmetry to simplify the set-up of the problem. 3. Checking the result by looking at the “limiting” behavior. 1 Q Ex = 4πε 0 x 2 This looks just like the field from a point charge v 1 qi r̂ E=∑ 2 i i 4πε 0 ri For a discrete set of point charges: What happens if the charges are not points but are distributed continuously? r We can replace the charge qi by the “infinitesimal charge dq (r ) and write: r v 1 dq(r ) E=∫ r̂ 2 4πε 0 r all r If we say the charge is distributed by a charge density given by ρ (r ) we have: r r dq (r ) = ρ (r )dv This gives: v E= dv is an “infinitesimal” volume element r ρ (r ) 1 ∫ 4πε all 0 r 2 r̂dv Don’t Panic – There won’t be any hard problems that use this! The Electric Field Minor Problem…What if putting charge q in the vicinity of the other charges causes them to move? Definition of the Electric Field: r E = lim it q →0 r F q We can calculate the Electric filed from a collection of charges from: r 1 qi F = q∑ r̂ 2 i i 4πε 0 ri Which Gives or for continuous charge distribution v 1 qi E=∑ r̂ 2 i i 4πε 0 ri v E= r ρ (r ) 1 ∫ 4πε all 0 r 2 r̂dv ELECTRIC FIELD “LINES” An Electric Field assigns VECTOR to each point in space: r r E (r3 ) r r E (r1 ) r r1 r r2 r r E (r2 ) r r3 A convenient way to visualize the Electric Field is with “ELECTRIC FIELD LINES” The local direction of the Field Lines is the direction of the electric field at that point The “density” of electric field lines is proportional to the magnitude of the electric field at that point The direction of the electric field line give the direction of the force on a charge particle at that point. It does not necessarily represent the direction of motion of a charged particle at that point! Electric Field Lines The electric field line is everywhere tangent to the local electric field Electric Field Lines are CONTINUOUS Lines That Begin and End on Charges The Sense of the Field Lines is Away from the + charge The Local Direction of the Electric Field is along the Field Line The Local Strength of the Electric Field is Proportional to the Density of Lines A Note About Conductors and Insulators A CONDUCTOR is a material in which electric charges are free to “move around” An INSULATOR is a material in which the electric charges are immobile Conductors can be CHARGED or UNCHARGED Insulators can be CHARGED or UNCHARGED (refers to net charge) Electric Field Inside a Conductor 1. Charges can move freely inside a conductor (actually it is only the electrons that move) 2. Assume that there is an Electric Field Inside Conductor: 3. Since the Charges are free to move, they we be pushed towards the surface of the Conductor: 4. The field of these charges will tend to cancel the original Field. 5. They will continue to move until the field is zero The Electric Field inside a Conductor is EXACTLY ZERO End of Chapter 21 You are responsible for the material covered in T&F Sections 21.1-21.6 You are expected to: • Know what the following are: • Understand Coulomb’s Law including the notion of a unit vector and to be able to express the direction of the electric field. • Calculate the force on a point charge due to another point charge. • Calculate the electric field from a point charge and, using superposition, calculate the electric field from a simple collection of point charges. • Understand the notion of Electric Field Lines and be able to roughly sketch the field lines for simple collections of charges. charge, electrons, protons, atomic number, conductors, insulators, electrostatic force, superposition, and electric field. Recommended F&Y Exercises chapter 21: 3,13,14,15,16,24,44,49