1 / 22

Physics 2102 Lecture: 03 TUE 26 JAN

Physics 2102 Jonathan Dowling. Physics 2102 Lecture: 03 TUE 26 JAN. Electric Fields II. Michael Faraday (1791-1867). What Are We Going to Learn? A Road Map. Electric charge - Electric force on other electric charges - Electric field , and electric potential

lindsey
Download Presentation

Physics 2102 Lecture: 03 TUE 26 JAN

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Physics 2102 Jonathan Dowling Physics 2102 Lecture: 03 TUE 26 JAN Electric Fields II Michael Faraday (1791-1867)

  2. What Are We Going to Learn?A Road Map • Electric charge- Electric force on other electric charges- Electric field, and electric potential • Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors • Electric currents-Magnetic field - Magnetic force on moving charges • Time-varying magnetic field  Electric Field • More circuit components: inductors. • Electromagneticwaves-light waves • Geometrical Optics (light rays). • Physical optics (light waves)

  3. k = Coulomb’s Law For Charges in a Vacuum Often, we write k as:

  4. Definition of Electric Field: +q1 –q2 P1 P2 –q2 P1 P2 E-Field is E-Force Divided by E-Charge E-Force on Charge E-Field at Point Units: F = [N] = [Newton] ; E = [N/C] = [Newton/Coulomb]

  5. Definition of Electric Field: Force on Charge Due to Electric Field: Force on a Charge in Electric Field

  6. Force on a Charge in Electric Field + + + + + + + + +  Positive Charge Force in SameDirection as E-Field (Follows) E – – – – – – – – – –  + + + + + + + + +  Negative Charge Force in OppositeDirection as E-Field (Opposes) E – – – – – – – – – – 

  7. Electric Dipole in a Uniform Field Distance Between Charges = d • Net force on dipole = 0; center of mass stays where it is. • Net TORQUE : INTO page. Dipole rotates to line up in direction of E. • |  | = 2(qE)(d/2)(sin ) = (qd)(E)sin = |p| E sin = |p x E| • The dipole tends to “align” itself with the field lines. • What happens if the field is NOT UNIFORM??

  8. First: Given Electric Charges, We Calculate the Electric Field Using E=kqr/r3. Example: the Electric Field Produced By a Single Charge, or by a Dipole: Charge Produces E-Field Second: Given an Electric Field, We Calculate the Forces on Other Charges Using F=qE Examples: Forces on a Single Charge When Immersed in the Field of a Dipole, Torque on a Dipole When Immersed in an Uniform Electric Field. E-Field Then Produces Force on Another Charge Electric Charges and Fields

  9. Continuous Charge Distribution • Thus Far, We Have Only Dealt With Discrete, Point Charges. • Imagine Instead That a Charge q Is Smeared Out Over A: • LINE • AREA • VOLUME • How to Compute the Electric Field E? Calculus!!! q q q q

  10.  = q/L  = q/A  = q/V Charge Density • Useful idea: charge density • Line of charge: charge per unit length =  • Sheet of charge: charge per unit area =  • Volume of charge: charge per unit volume = 

  11. Computing Electric Field of Continuous Charge Distribution dq • Approach: Divide the Continuous Charge Distribution Into Infinitesimally Small Differential Elements • Treat Each Element As a POINT Charge & Compute Its Electric Field • Sum (Integrate) Over All Elements • Always Look for Symmetry to Simplify Calculation! dq =  dL dq =  dS dq =  dV

  12. Differential Form of Coulomb’s Law E-Field at Point q2 P1 P2 Differential dE-Field at Point dq2 P1

  13. dx dx Field on Bisector of Charged Rod • Uniform line of charge +q spread over length L • What is the direction of the electric field at a point P on the perpendicular bisector? (a) Field is 0. (b) Along +y (c) Along +x P y x a • Choose symmetrically located elements of length dq = dx • x components of E cancel q o L

  14. y x Line of Charge: Quantitative P • Uniform line of charge, length L, total charge q • Compute explicitly the magnitude of E at point P on perpendicular bisector • Showed earlier that the net field at P is in the y direction — let’s now compute this! a q o L

  15. dE Line Of Charge: Field on bisector Distance hypotenuse: [C/m] Charge per unit length: P a r dx q o x Adjacent Over Hypotenuse L

  16. Units Check! Coulomb’s Law! Line Of Charge: Field on bisector Integrate: Trig Substitution! Line Charge Limit: L >> a Point Charge Limit: L << a

  17. Binomial Approximation from Taylor Series: x<<1

  18. y Example — Arc of Charge: Quantitative –Q E • Figure shows a uniformly charged rod of charge -Q bent into a circular arc of radius R, centered at (0,0). • Compute the direction & magnitude of E at the origin. 450 x y dQ = lRdq dq q x l = 2Q/(pR)

  19. z y x Example : Field on Axis of Charged Disk • A uniformly charged circular disk (with positive charge) • What is the direction of E at point P on the axis? (a) Field is 0 (b) Along +z (c) Somewhere in the x-y plane P

  20. y x • Choose symmetric elements • x components cancel Example : Arc of Charge • Figure shows a uniformly charged rod of charge –Q bent into a circular arc of radius R, centered at (0,0). • What is the direction of the electric field at the origin? (a) Field is 0. (b) Along +y (c) Along -y

  21. Summary • The electric field produced by a system of charges at any point in space is the force per unit charge they produce at that point. • We can draw field lines to visualize the electric field produced by electric charges. • Electric field of a point charge: E=kq/r2 • Electric field of a dipole: E~kp/r3 • An electric dipole in an electric field rotates to align itself with the field. • Use CALCULUS to find E-field from a continuous charge distribution.

More Related