1 / 18

The Electric Dipole

+q. d. The Electric Dipole. -q. An electric dipole consists of two equal and opposite charges ( q and -q ) separated a distance d. The Electric Dipole. +q. d. p. -q. We define the Dipole Moment p magnitude = qd , p

jaser
Download Presentation

The Electric Dipole

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. +q d The Electric Dipole -q An electric dipole consists of two equal and opposite charges (q and -q ) separated a distance d.

  2. The Electric Dipole +q d p -q We define the Dipole Moment p magnitude = qd, p direction = from -q to +q

  3. E +q d The Electric Dipole -q q Suppose the dipole is placed in a uniform electric field (i.e., E is the same everywhere in space). Will the dipole move ??

  4. E +q d The Electric Dipole -q q What is the total force acting on the dipole?

  5. F+ E +q d F- -q q The Electric Dipole What is the total force acting on the dipole?

  6. F+ E +q d F- -q q The Electric Dipole What is the total force acting on the dipole? Zero, because the force on the two charges cancel: both have magnitude qE. The center of mass does not accelerate.

  7. F+ E +q d F- -q q The Electric Dipole What is the total force acting on the dipole? Zero, because the force on the two charges cancel: both have magnitude qE. The center of mass does not accelerate. But the charges start to move. Why?

  8. F+ E +q d F- -q q What is the total force acting on the dipole? Zero, because the force on the two charges cancel: both have magnitude qE. The center of mass does not accelerate. But the charges start to move (rotate). Why? There’s a torque because the forces aren’t colinear and aren’t acting exactly at the center of mass.

  9. F+ +q d d sin q F- q -q The torque is: t = (magnitude of force) (moment arm) t=(2qE)(d sin q/2)=qEdsinq and the direction of t is (in this case) into the page

  10. q +q E d p -q q t= qEdsinq but we have defined : p = q d and the direction of p is from -q to +q Then the torque can be written as: t = pxEt = p E sin q

  11. Y Electric dipole moment p = qd +q l q d X x E+ E- -q E Field Due to an Electric Dipoleat a point x straight out from its midpoint Calculate E as a function of p, x,and d

  12. Y +q l q d X x E- E+ -q E You should be able to find E at different points around a dipole where symmetry simplifies the problem.

  13. Torque on a Dipole in an Electric Field(another version of the derivation)

  14. A Dipole in an Electric Field

  15. 4. In which configuration, the potential energy of the dipole is the greatest? a c b E d e

  16. Example: Electric Field of a Dipole Lets find the E field here at a distance Z from the dipole center z We can use the binomial expansion on these two terms

  17. The Binomial Expansion (a +x)n For any power of n, the binomial (a + x) can be expanded two ways or This first expression is particularly useful when x is very much less than a so that the first few terms provide a good approximation of the value of the expression. There will always be n+1 terms

  18. E ~ 1/z3 • E =>0 as d =>0 • Valid for “far field”

More Related