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Physics: Electricity and Magnetism Week 1 Notes

by: Tori Colthurst

Physics: Electricity and Magnetism Week 1 Notes PHYS 212

Marketplace > University of Illinois at Urbana-Champaign > Physics > PHYS 212 > Physics Electricity and Magnetism Week 1 Notes
Tori Colthurst
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About this Document

These notes cover both the prelectures and the lectures. Covering topics such as Coulomb's Law, Superposition, Electric Fields, Continuous Charge Distributions, etc.
University Physics: Electricity and Magnetism
Matthias Grosse Perdekamp
Class Notes
coulomb's, Law, Coulomb, electric, Charge, proton, electron, Superposition, components, electricfields, Fields, Field, line, Of, Discrete, distribution, Continuous, Vector, sum




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This 6 page Class Notes was uploaded by Tori Colthurst on Monday August 29, 2016. The Class Notes belongs to PHYS 212 at University of Illinois at Urbana-Champaign taught by Matthias Grosse Perdekamp in Fall 2016. Since its upload, it has received 26 views. For similar materials see University Physics: Electricity and Magnetism in Physics at University of Illinois at Urbana-Champaign.

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Date Created: 08/29/16
Physics Electricity and Magnetism (Professor Perdekamp) : ​Week 1 Notes    ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  Prelecture: Coulomb’s Law  ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  Electric Charge       Gravity  Electric Charge      What is charge?  Electric charge is responsible for   electric forces.   Two kinds of electric charge: positive and negative  Two kinds of electric force: attractive and repulsive  Note: this is in contrast to gravitational force where mass only attracts    Building Blocks of Matter            Conductors:  Insulators:  Electrons free to move Electrons don’t/cannot move  (metals) (plastics)    Coulomb’s Law​ (1785)  ex)        r^ determines direction F1,2​nd F​  2,1​Newton’s 3rd Law pairs!  If the resultant number is: ​positive → force is repulsive            negative → force is attractive        Units and Constants    SI Units   Charge  Coulombs (C)  Distance  Meters (m)  Force  Newtons (N)    Constants  ­19​ e (electric charge)  +/­ 1.6 x 10​  ​C  k (Coulomb’s law constant)  1/4εpi  or  9 x 10​ 9Nm​ /C​   2 G (gravitational constant)  6.67 x 10​   ­11N m​ /kg   ­31​ M​e​(mass of electron)  9.1 x 10​  kg  M​p​(mass of proton)  1.6 x 10​  kg     Which is the stronger force between a proton and an electron?      The coulomb’s force is much stronger than the  gravitational force between an electron and a proton!                 Superposition Principle     Note: this is a vector sum!              ex)  q​ 1​uC and q​ =­1u2​and q​ =4uC, all3​re 1 m apart, what is the net force on q​ ?  3​ F​3​net = F​ 1​ F​ 2​ 0.018 + (­0.036) = ­0.018 N  ­6 ​ Note: u = 10​  and the forces from F​  and F​  a1​ in oppo2​te directions     ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  Lecture: Coulomb’s Law  ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  Coulomb’s Law:​ force on a charge due to another charge is proportional to the product  of the charges and inversely proportional to the separation squared.   Force is always parallel to a line connecting charges (direction depends on charges)    Notation:​  F​   1,2​e by 1 on 2 r^​1,2​nit vector that points from 1 to 2    Superposition:​ (more than 2 charges present)  total force on any given charge is vector   sum of forces  If you change the charge of the particle you are analyzing for the net force    then the direction of the vector changes by 180 degrees and the   magnitude is the same    ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  Prelecture: Electric Fields  ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­                       point charge infinite line of charge    Electric Field:​ force per unit charge at   a designated point in space  Since F is directly proportional to q, if we  double q, F will double as well (the ratio   of F/q is constant)          As you move farther from the charge q, the strength of the  electric field decreases as E (proportional to) 1/r​    2   (as seen by the graph to the left)  Note: a spherical charge has a spherically symmetric field!        ex)     electric dipole (two equal magnitude oppositely charged particles)    The E​  Q​ larger here because the point is closer to Q than ­Q.      Note: the electric field is not spherically symmetric!        The E​  ­Q​larger here because the point is closer to ­Q than Q.         E field of continuous charge distribution  Take the vector sum of individual charge’s fields to get the  total Electric field   The sum of a finite # of charges then becomes an integral  over a continuous charge distribution    ex)  find the E­field at point p above an infinite line of  charge (aka continuous charge distribution)    Red vectors represent the individual electric field  components from the charges within the line    Notice: the ​contributions in the x direction from each  segment will exactly cancel out​ because the line is  infinite      They ​y contributions, however, do not cancel out, ​   in fact they all contribute to a net Electric field in the  same direction. (all positive)              Designate ​tiny segment      to have charge dq and      length dx​, then  integrate across these  small segments to find the  entire electric field    Rewrite the equation from above  with all necessary substitutions   and the final equation will be ←       Point Charge(​Discrete Distribution​)  2 Has spherical symmetry and is inversely proportional to r​        Infinite Line of Charge(​Continuous Distribution) ​  Has cylindrical symmetry and is inversely proportional to r (as shown above)              ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  Lecture: Electric Fields  ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­  If more than 2 charges are present, the total force / electric field is the vector sum of the  forces / electric fields     The electric field at a point in space is simply the force per unit charge at that point  E = F/q  The electric field due to a point charged particle   E = Kq/r​ 2  The electric field ​points towards negative ​and ​points away from positive    Superposition for Electric Fields    The summation above becomes an integral → integrate over all charges (dq)     r^​ is a vector from dq to the point at which E   is defined         Helpful Equations for Rewriting dq   Linear   λ= Q/L  (Coulombs/meter)  2​ Surface  σ= Q/A  (Coulombs/meter​ )  3​ Volume  ρ= Q/V  (Coulombs/meter​ )  Surface Area of a sphere = 4(pi)r​   2 Volume of a sphere = 4/3(pi)r​   3 Surface Area of a cylinder = 2(pi)rL  Volume of a cylinder = (pi)r​ L  2​   *Almost always use dq = λdx as the substitution*   


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