Transcript 1/22 - SMU Physics

Chapter 23
1.
2.
3.
4.
5.
6.
A review on Coulomb’s Law
Define Electric Field
Define Electric Field Line
Examples on How to Calculate for the
Electric Field
Charge Particles Experience Force in an
Electric Field
Quiz 1/22
Coulomb’s Law, Review

The formula:
Fe  ke

r
2
or
q1q2
F12  ke 2 rˆ12
r
The units (SI):




q1 q2
Charge: coulomb (C)
Distance: meter
Force: Newton
The constants:

Ke, the Coulomb constant:
ke = 8.9876 x 109 N.m2/C2 = 1/(4π ε o)

εo the permittivity of free space:
ε o = 8.8542 x 10-12 C2 / N.m2
Electric Field: the definition of this
concept





The electric force acts through space, i.e., the effect is
produced even with no physical contact between objects.
One way to offer an explanation (we met this situation
before, what is that?), as Faraday initiated, is the
concept of a field in terms of electric fields.
An electric field is postulated to exist in the region of
space around a charge (of called the source charge).
The strength and direction of that electric field at a point
in space is then measured by the force of the electric
field exerts on another charge (often called the test
charge) at that point.
Mathematically:
E


F
qo
The electric field, E , is a vector. The test charge, qo, is
usually a very small charge compared with the source
charge, so that its existence does not distort the
electrical field generated by the source charge.
Unit: Newton/Coulomb or N/C.
Electric Field Lines, a way to
illustrate the field



Electric field is introduced to
explain the fact the electric forces
act through space.
We use a set of specially defined
lines to illustrate the field. The lines
do not exit in space, but they
should do in your mind, and you
must be able to “see” them with
your mind’s eyes.
Now let’s define these electric field
lines:



They start from positive charge, end
at negative charge.
Their density in space (number of
lines in unit volume) indicates the
field strength.
The tangent of an electric field line
at a given point points to the
direction of the field at that point.
Hence no lines can cross.
Field lines of one
point positive
source charge in
space
Field lines of one
point negative
source charge in
space
More cases on how to draw
electric field lines




Electric dipole: the charges
are equal and opposite.
The charges are equal and
positive.
Can you draw for the case
charges are equal but
negative?
A slightly more general case:
the charges are not equal,
not the same polarity.
An even more general case: Electric Field
Lines when the source charge is not seen

Electric field may not come
from static source charges. So
there is need to just draw
electric field lines to represent
the electric field. In the case in
the right side figure:
 The density of lines through
surface A is greater than
through surface B. So the
magnitude of the electric
field is greater on surface A
than B
 The electric field strength
(number of lines) times the
surface area (A or B) is
called the electric flux.
How to calculate the electric field
generated by a point source charge q


From the definition:
F
E
qo
Place the test charge q0. The force
on q0 is given by Coulomb’s law:
qqo
Fe  ke 2 rˆ
r

Then, the electric field will be
Fe
q
E
 ke 2 rˆ
qo
r

The electric field only depends on
the source charge, not the test
charge.
How to calculate electric field generated by many
charges? Superposition with electric field from
each charge.
When the charges are
still point charges:
from
to
Example
(23.5, page 653):
qi
Ei  ke 2 rˆi
ri
E   Ei  k e 
i
i
qi
rˆ
2 i
ri
If you do not feel comfortable about
the math here, raise your hand.
How to calculate electric field generated by many
charges? Superposition with electric field from
each charge.
When the charges are
distributed over volume V:
from
to
dE  k e
dq
rˆ
2
r
dq
rˆ
2
r
V
E  ke 
Again if you do not feel comfortable
about the math here, raise your hand.
Examples on how to calculate electric field
from a continuous charge distribution
Example 23.6 (page 656)
Examples on how to calculate electric field
from a continuous charge distribution
Example 23.7 (page 657)
Examples on how to calculate electric field
from a continuous charge distribution
Example 23.8 (page 658)
Charge Particles Experience
Force in an Electric Field

From the definition of electric field:
E
F
q
We know that charge particles experience force in
an electric field:
Fe  qE

This formula, although a simple transformation from
the definition, is a lot more useful.
Two examples
Example 23.9 (page 662)
Example 23.10 (page 663)
Preview sections and
homework 1/22, due 2/3

Preview sections:



Section 24.1
Section 24.2
Homework:


Problem 12, page 667.
Problem 36, page 669.