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

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

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

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

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

The Electric Dipole -q +q F- F+ E  d 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.

The Electric Dipole -q +q F- F+ E  d 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?

-q-q +q+q F- F+ E  d 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.

-q-q +q F- F+  d d sin  The torque is:   magnitude of force) (moment arm)   (2qE)(d sin  qE dsin  and the direction of  is (in this case) into the page

but we have defined : p = q d and the direction of p is from -q to +q Then the torque can be written as:   p x E  = p E sin  -q +q+q  d p E    qE dsin 

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

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

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

A Dipole in an Electric Field

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

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

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 The Binomial Expansion (a +x) n

E ~ 1/z 3 E =>0 as d =>0 Valid for “far field”