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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

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The Electric Dipole

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  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”

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