1 / 64

Lecture Set 3 Gauss’s Law

Lecture Set 3 Gauss’s Law. Spring 2007. Calendar for the Week. Today (Wednesday) One or two problems on E Introduction to the concept of FLUX Friday 7:30 session if wanted Quiz – Chapter 23 – Electric Field Gauss’s Law & some problems EXAM APPROACHING. Note.

davismarvin
Download Presentation

Lecture Set 3 Gauss’s Law

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. Lecture Set 3Gauss’s Law Spring 2007

  2. Calendar for the Week • Today (Wednesday) • One or two problems on E • Introduction to the concept of FLUX • Friday • 7:30 session if wanted • Quiz – Chapter 23 – Electric Field • Gauss’s Law & some problems • EXAM APPROACHING

  3. Note • Pleas read the material on Electric Dipoles • We will NOT cover it in class but it is part of the course. • We will use it later in the semester. • It could show up on the exam.

  4. Approximate Schedule

  5. The figure shows two concentric rings, of radii R and R ' = 2.95R, that lie on the same plane. Point P lies on the central z axis, at distance D = 2.20R from the center of the rings. The smaller ring has uniformly distributed charge +Q. What must be the uniformly distributed charge on the larger ring if the net electric field at point P due to the two rings is to be zero?[-3.53] Q

  6. Definition – Sort of - Electric Field Lines

  7. Field Lines  Electric Field

  8. Last time we showed that

  9. Ignore the Dashed Line … Remember last time .. the big plane? s/2e0 s/2e0 s/2e0 s/2e0 s/2e0 s/2e0 E=0 E=s/e0 E=0 We will use this a lot!

  10. NEW RULES (Bill Maher) • Imagine a region of space where the ELECTRIC FIELD LINES HAVE BEEN DRAWN. • The electric field at a point in this region is TANGENT to the Electric Field lines that have been drawn. • If you construct a small rectangle normal to the field lines, the Electric Field is proportional to the number of field lines that cross the small area. • The DENSITY of the lines. • We won’t use this much

  11. What would you guess is inside the cube?

  12. What about now?

  13. How about this?? • Positive point charge • Negative point charge • Large Sheet of charge • No charge • You can’t tell from this

  14. Which box do you think contains more charge?

  15. All of the E vectors in the bottom box are twice as large as those coming from the top box. The top box contains a charge Q. How much charge do you think is in the bottom box? • Q • 2Q • You can’t tell • Leave me alone.

  16. So far … • The electric field exiting a closed surface seems to be related to the charge inside. • But … what does “exiting a closed surface mean”? • How do we really talk about “the electric field exiting” a surface? • How do we define such a concept? • CAN we define such a concept?

  17. Mr. Gauss answered the question with.. Yup .. Gauss's Law

  18. Another QUESTION: Not Quite Solid Surface Given the electric field at EVERY point on a closed surface, can we determine the charges that caused it??

  19. A Question: • Given the magnitude and direction of the Electric Field at a point, can we determine the charge distribution that created the field? • Is it Unique? • Question … given the Electric Field at a number of points, can we determine the charge distribution that caused it? • How many points must we know??

  20. Still another question Given a small area, how can you describe both the area itself and its orientation with a single stroke!

  21. The “Area Vector” • Consider a small area. • It’s orientation can be described by a vector NORMAL to the surface. • We usually define the unit normal vector n. • If the area is FLAT, the area vector is given by An, where A is the area. • A is usually a differential area of a small part of a general surface that is small enough to be considered flat.

  22. E n En The “normal component” of the ELECTRIC FIELD

  23. E n En DEFINITION FLUX

  24. q We will be considering CLOSED surfaces The normal vector to a closed surface is DEFINED as positive if it points OUT of the surface. Remember this definition!

  25. “Element” of Flux of a vector E leaving a surface For a CLOSED surface: n is a unit OUTWARD pointing vector.

  26. q This flux is LEAVING the closed surface.

  27. Definition of TOTAL FLUX through a surface

  28. Flux is • A vector • A scaler • A triangle

  29. VisualizingFlux n is the OUTWARD pointing unit normal.

  30. Definition: A Gaussian Surface Any closed surface that is near some distribution of charge

  31. Remember Component of E perpendicular to surface. This is the flux passing through the surface and n is the OUTWARD pointing unit normal vector! n E q q A

  32. Flux is -EL2 ExampleCube in a UNIFORM Electric Field Flux is EL2 E area L Note sign E is parallel to four of the surfaces of the cube so the flux is zero across these because E is perpendicular to A and the dot product is zero. Total Flux leaving the cube is zero

  33. Simple Example r q

  34. Gauss’ Law Flux is total EXITING the Surface. n is the OUTWARD pointing unit normal. q is the total charge ENCLOSED by the Gaussian Surface.

  35. Simple ExampleUNIFORM FIELD LIKE BEFORE E No Enclosed Charge A A E E

  36. Q L Line of Charge

  37. Line of Charge From SYMMETRY E is Radial and Outward

  38. What is a Cylindrical Surface?? Ponder

  39. Drunk Looking at A Cylinder from its END Circular Rectangular

  40. Infinite Sheet of Charge +s h E cylinder We got this same result from that ugly integration!

  41. Materials • Conductors • Electrons are free to move. • In equilibrium, all charges are a rest. • If they are at rest, they aren’t moving! • If they aren’t moving, there is no net force on them. • If there is no net force on them, the electric field must be zero. • THE ELECTRIC FIELD INSIDE A CONDUCTOR IS ZERO!

  42. More on Conductors • Charge cannot reside in the volume of a conductor because it would repel other charges in the volume which would move and constitute a current. This is not allowed. • Charge can’t “fall out” of a conductor.

  43. Isolated Conductor Electric Field is ZERO in the interior of a conductor. Gauss’ law on surface shown Also says that the enclosed Charge must be ZERO. Again, all charge on a Conductor must reside on The SURFACE.

  44. Charged Conductors Charge Must reside on the SURFACE - - E=0 - - E - s Very SMALL Gaussian Surface

  45. Charged Isolated Conductor • The ELECTRIC FIELD is normal to the surface outside of the conductor. • The field is given by: • Inside of the isolated conductor, the Electric field is ZERO. • If the electric field had a component parallel to the surface, there would be a current flow!

  46. Isolated (Charged) Conductor with a HOLE in it. Because E=0 everywhere inside the conductor. So Q (total) =0 inside the hole Including the surface.

  47. A Spherical Conducting Shell withA Charge Inside. A Thinker!

  48. Insulators • In an insulator all of the charge is bound. • None of the charge can move. • We can therefore have charge anywhere in the volume and it can’t “flow” anywhere so it stays there. • You can therefore have a charge density inside an insulator. • You can also have an ELECTRIC FIELD in an insulator as well.

  49. E O r Example – A Spatial Distribution of charge. Uniform charge density = r = charge per unit volume (Vectors) A Solid SPHERE

More Related