1 1 Physics 8.02T http://web.mit.edu/8.02t/www For now, please sit anywhere, 9 to a table 2 8.02 Course Notes Revised Introduction to Electricity and Magnetism Dourmashkin, Belcher, and Liao Online at http://web.mit.edu/8.02t/www/coursedocs/current/guide.htm 3 W01D2: Outline Introductions Course Overview Vector and Scalar Fields Charge Electric Force Electric Field2 4 Course Details We will not go over all the course details in class, you can click the link 8.02 Introduction on http://web.mit.edu/8.02t/www/ Or go directly to http://web.mit.edu/8.02t/www/materials/Presentations/8.02_Introduction.pdf Online Registration If you are in a M/W/F class for 8.02, you will need to register for the course “8.02r-MW Electricity and Magnetism (Monday and Wednesday)”. If you are in a Tuesday/Thursday/Friday class for 8.02, register for “8.02r-TTh: Electricity and Magnetism (Tuesday and Thursday)”. The following link will get you to either course and the web site will require certificates: https://lms.mitx.mit.edu/ Reading Questions Answer Reading Questions online in the appropriate course for your section. Reading Questions due at 8:30 am the day of class. The following link will get you to either course and the web site will require certificates: https://lms.mitx.mit.edu/3 Problem Sets For each week’s problem set: 1) you will submit your answers to two problems online in the appropriate course for your section. 2) You will hand in your answers to six written problems in your section slot in the boxes outside the door of 32-082 or 26-152 depending on which is your classroom. Make sure you clearly write your name and section on your problem set. 3) Both online and handwritten are due Tues 9 pm Announcements Math Review Week Two Tuesday from 9-11 pm in 26-152 PS 1 due Week Two Tuesday at 9 pm. Submit two problems on online and hand in six problems in the appropriate section boxes outside 32-082 or 26-152 Bring Clickers to Monday/Tuesday Class 8 9 8.02: Electricity and Magnetism Also new way of thinking… How do objects interact at a distance? Fields We will learn about electric & magnetic fields: how they are created & what they affect Maxwell’s Equations Lorentz Force Law E ⋅ dAS∫∫=Qinε0E ⋅ dsC∫= −ddtB ⋅ dAS∫∫B ⋅ dAS∫∫= 0B ⋅ dsC∫=µ0Ienc+µ0ε0ddtE ⋅ dAS∫∫ F = q(E +v ×B)4 10 Scalar and Vector Fields Review Vector Analysis in Online Course Notes http://web.mit.edu/8.02t/www/coursedocs/current/guide.htm 11 Scalar Fields Temperature Scalar Field: every location has an associated value (number with units) 12 Scalar Fields - Contours Colors represent surface temperature Contour lines show constant temperatures5 13 Vector Fields Vector (magnitude, direction) at every point in space Example: Velocity vector field - jet stream 14 Coulomb’s Law, Electric Fields and Discrete Charge Distributions 15 Electric Charge Two types of electric charge: positive and negative Unit of charge is the coulomb [C] Charge of electron (negative) or proton (positive) is Charge is quantized Charge is conserved ±e, e = 1.602 × 10−19C Q = ± Ne6 16 Electric Force The electric force between charges q1 and q2 is (a) repulsive if charges have same signs (b) attractive if charges have opposite signs Like charges repel and opposites attract !! 17 Charging 18 How Do You Get Charged? • Friction • Transfer (touching) • Induction +q Neutral - - - - + + + +7 19 Demonstrations: Instruments for Charging 20 Demonstration: Bouncing Balloon Van de Graaf Generator D17 Why is the balloon attracted to the metal sphere? 21 Coulomb's Law Coulomb’s Law: Force on q2 due to interaction between q1 and q2 ke=14πε0= 8.9875 × 109 N m2/C2 F12= keq1q2r122ˆr12 ˆr12:unit vector from q1 to q2 ˆr12=r12r12 ⇒F12= keq1q2r123r12 r12:vector from q1 to q28 22 In Class Problem: Coulomb's Law Vector Analysis Find a vector expression for the unit vectors in terms of 22 ˆr32=?ˆr12=?ˆr31=? ˆi andˆj.23 Coulomb's Law: Example r32= (12ˆi −32ˆj) mr32= 1ma = 1 m q1 = 6 C q3 = 3 C q2 = 3 C F32= ? F32= keq3q2r32r323 r32 =(81× 109)2(ˆi − 3ˆj) N = (9 × 109N ⋅ m2C2)(3C)(3C)12(ˆi − 3ˆj)m(1m)324 The Superposition Principle F3=F13+F23 Fj=Fiji=1N∑Many Charges Present: Net force on any charge is vector sum of forces from other individual charges Example: In general:9 25 In Class Problem: Force on a Charged Object Three charged objects are located at the positions shown in the figure. Find a vector expression for the force on the negatively charged object located at the point P. 26 Electric Field 27 Electric Field The electric field at a point P due to a charged object (source) with charge qs is the force acting on a test point-like charged object with charge qt at that point P, divided by the charge qt : Es(P) ≡Fst(P)qt Es(P) = keqsrst2ˆrs(P)Units: N/C10 28 Superposition Principle The electric field due to a collection of N point charges is the vector sum of the individual electric fields due to each charge E =E1+E2+ ..... =Eii=1N∑29 Concept Question: 5 Equal Charges Six equal positive charges q sit at the vertices of a regular hexagon with sides of length R. We remove the bottom charge. The electric field at the center of the hexagon (point P) is: 1.E =2kqR2ˆj 2.E = −2kqR2ˆj 5.E = 0 4.E = −kqR2ˆj 3.E =kqR2ˆj30 Group Problem: Electric Field on Axis (Symmetry) dsq−q+PConsider two point charges of equal magnitude but opposite signs, separated by a distance d. Point P lies along the perpendicular bisector of the line joining the charges, a distance s above that line. What is the E field at P? iˆjˆ11 31 Electric Field Lines 1. Direction of field at any point is tangent to field line at that point 2. Field lines point away from positive charges and terminate on negative charges 3. Field lines never cross each other 32 Concept Question: Field Lines Electric field lines show: 1. Directions of forces that exist in space at all times. 2. Directions in which positive charges on those lines will accelerate. 3. Paths that charges will follow. 4. More than one of the above. 5. I don’t know. 33
View Full Document
Unlocking...