1 / 11

Continuous Charge Distributions

Continuous Charge Distributions. Electric Potential. Potential for Line of Charge. The potential of a line of charge can be found by superposing the point charge potentials of infinitesimal charge elements. so: over entire charge distribution Express all variables in terms of x

lana
Télécharger la présentation

Continuous Charge Distributions

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. Continuous Charge Distributions Electric Potential

  2. Potential for Line of Charge • The potential of a line of charge can be found by superposing the point charge potentials of infinitesimal charge elements.so: over entire charge distribution • Express all variables in terms of x • dx = infinitesimal length containing dq of charge

  3. Potential for Line of Charge • dq = ldx and

  4. Potential for Line of Charge • If point is perpendicular to end of line of charge, a = 0 and b = L, the length of the line and equation becomes:

  5. Potential for Line of Charge • If point is at midpoint of line, a = b = L/2 and equation is

  6. Potential for Ring of Charge

  7. Potential for Ring of Charge • The potential of a ring of charge can be found by superposing the point charge potentials of infinitesimal charge elements. • Since the potential is a scalar quantity, and since each element of the ring is the same distance r from the point P, the potential is simply given by: Q = total charge l = linear charge density

  8. Potential for Disc of Charge • The potential of a disc of charge can be found by superposing the point charge potentials of infinitesimal charge elements. • The evaluation of the potential can be facilitated by summing the potentials of charged rings

  9. Potential for Disc of Charge

  10. Potential for Disc of Charge • Write potential dV at point P: • Integrate from a = 0 to a = R

  11. Potential for Disc of Charge • The integral is of the form ∫undu, with u = x2 + a2and n = -½ • The integral evaluates to:

More Related