Last lecture
The electric dipole
Electric field due to a dipole
Electric dipole moment
This lecture
Continuous charge distributions
Matter in electric fields
Continuous charge distributions
use calculus
So far we have only considered the
electric field that is produced by one, or
perhaps a few, point charges
Volume charge density
 = q/V
Surface charge density
 = q/A
Linear charge density
 = q/L
Continuous charge distributions
Here
dq =  dV and the integration is over a volume.
If the charge is distributed on a surface or a line, we use
dq =  dA
or dq =  dL
Volume charge density
 = dq/dV
Surface charge density
 =dq/dA
Linear charge density
 = dq/dL
Example 20.6 p 337
A ring shaped conductor
with radius a carries
charge Q uniformly
distributed around it.
Find the electric field at
point P that lies on the
axis of the ring.
Do on board
Example 20.7 p 337 Line Charge: a
power line’s field
A long, straight electric power line
coincides with the x axis and carries a
uniform line charge density λ (unit: C/m).
Find the electric field on the y axis using
the approximation that the wire is
infinitely long.
sinθ
Please read through this
example in the textbook.
We will do a similar one in
Wednesday’s workshop.
θ
20. 5 Matter in electric fields
To study the role of electric fields we need to separate two different tasks:
1)
calculating the electric field produced by a given distribution of charge
2)
calculating the force that a given field exerts on a charge placed in it.
We have so far considered 1) with the electric field (from Coulomb’s Law) due to
•
•
•
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a point charge (done last lecture)
Now we will consider
2) – what happens to
an electric dipole
charges placed in an
a line of charge
existing (external)
a charged disk (in Wed Workshop) field.
20.5 Matter in electric fields
What happens to a charged particle when it is in an electric field
produced by other stationary or slowly moving charges?
An electrostatic force acts on the particle
F=qE
in which q is the charge of the particle (including its sign) and E is
the electric field that the other particles have produced at the
position of the particle (an external field).
A positive charge that is free to move but is at
rest in an electric field E will
A. accelerate in the direction perpendicular to E
B. remain at rest
C. accelerate in the direction opposite to E
D. accelerate in the same direction as E
E. do none of the above
Answer: D
CHECKPOINT:
(a) What is the direction of the
electrostatic force on the electron
due to the electric field shown?
(b) In which direction will the electron
accelerate if it is moving parallel to
the y axis before it encounters the
electric field?
(c) If, instead, the electron is initially
moving rightward, will its speed
increase, decrease, or remain
constant?
Answers: (a) left
A increase
B decrease
C constant
(b) left
A
left
B
right
C
up
D down
(c) decrease
Millikan’s oil-drop apparatus for
measuring elementary charge
(1910-1913)
An ink-jet printer
Example 20.8 in Wolfson: electrostatic analyser with curved plates
The figure show the path of negatively charged particle 1 through a
rectangular region of uniform electric field; the particle is deflected
towards the top of the page.
Is the field directed
A. leftward
B. rightward
C. upward or
D. downward?
Three other charged particles are shown
approaching the region of electric field.
Which are deflected towards the top and which
towards the bottom?
Electric dipoles in
electric fields
An H2O molecule has a
permanent electric dipole
moment that points in the
direction from the centre
of negative charge to the
centre of positive charge
Polar molecules have permanent
electric dipole moments
A dipole in a uniform electric field experiences equal
and opposite forces that tend to rotate the dipole so
that its dipole moment is aligned with the electric
field (torque).
Field E causes a torque  on the
dipole. The direction of the
torque is into the page, which
we show by the symbol . This
defines the direction of
rotation.  = p x E
See more on torques in Wolfson 10.2, p158
Nonpolar molecules have no
permanent dipole moment. In an
external electric field, E, the
charges within the molecule
become separated in space……it
acquires an induced dipole
moment parallel to E. It is said
to be polarised.
Here, F1 > F2
In a non-uniform electric
field the dipole experiences
a net force. Here the point
charge polarises a nonpolar
molecule and attracts it
Dipoles in field of
another dipole
Dipole B aligns with
the field of dipole A,
then experiences a net
force towards A
Dielectrics
Molecular dipoles in a
dielectric align with
the external field and
reduce the net field
within the dielectric
Applications (see p340):
microwave cooking and
liquid crystals