Download q - AdvancedPlacementPhysicsC

The Electric Dipole
+q
d
-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
direction = from -q to +q
The Electric Dipole
E
+q
d
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 ??
The Electric Dipole
E
+q
d
q
-q
What is the total force acting on the dipole?
The Electric Dipole
F+
E
+q
d
Fq
-q
What is the total force acting on the dipole?
The Electric Dipole
F+
E
+q
d
Fq
-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.
The Electric Dipole
F+
E
+q
d
Fq
-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. Why?
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.
F+
+q
d
d sin q
F-
q
q
The torque is:
t = (magnitude of force) (moment arm)
t = (2qE)(d sin q/2)= qE dsin q
and the direction of t is (in this case)
into the page
q
+
pq
d
q
E
-q
t = qE dsin q
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 = pxE
t = p E sin q
Field Due to an Electric Dipole
at a point x straight out from its midpoint
Y
Electric dipole moment
p = qd
+q
l
q
d
X
x
E+
E-q
E
Calculate E as a function of p, x,and d
Y
+q
d
l
q
X
x
E-
E+
-q
E
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)
t = Fx sin q  F (d  x) sin q = Fd sin q
F = qE
F = qEd sin q
p = qd
| t |= pE sin q
t = p E
A Dipole in an Electric Field
dW = tdq
qf
qf
qf
qi
qi
qi
U f  U i =  tdq =  pE sin qdq = pE  sin qdq
qf
qi
= pE[ cos q ] = pE (cosq i  cos q f )
U i = 0 q i = 90
U =  pE cos q
U = pE
4. In which configuration, the potential energy of the dipole
is the greatest?
a
c
b
E
d
e