Lecture2:
1.ReviewofCoulomb’slaw
2.IntroductiontothenotionofElectricFields
3.ElectricFieldsforvariouscharge
configurations
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The concepts of coulomb's law, electric fields, and their relation to various charge configurations. It includes examples and exercises to help understand the concepts.
Typology: Slides
2012/2013
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Lecture
Review
of
Coulomb’s
law
Introduction
to
the
notion
of
Electric
Fields
Electric
Fields
for
various
charge
configurations
Recap
Coulomb’s
Law
12 2 2
1
2 1
12
particle
to
due
particle
on
Force
r
r
r
F
q
q
k
e
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Another
example:
23
2
2
13
2 1
3
(^33)
23
2
3
2
13
3 2
1
23
13
3
r
r
E
F
r
r
F
F
F
a
q
k
q a
k
q
a
q
q
k
q a
q
k
e
e
e
e
Electric
field:
An
electric
field
E
( r
)^
is
the
Coulomb’s
law
force
at
the
position
r
on
a
positive
charge
of
q
Coulomb
due
to
all
other
sources.
The
electric
force
on
a
point
charge
q
at
the
position
r
is
)
(
)
(
r
E
r
F
q
i‐
clicker
exercise
The
diagram
below
shows
equal
positive
charges
arranged
on
an
equilateral
triangle.
Choose
the
point
A,
B,
C,
D,
E
which
has
the
smallest
total
electric
field
strength.
A C
B
D
E
Electric
field
due
to
point
charges:
Example
consider
a
long
thin
uniformly
charged
rod:
‐L
L
y
E P x
L
E
R
E
Q
^
^
^
^
^
Ly
Q
k
y
L
L
Q Ly k
y
x
x
Qy Ly k
y
x
dx
Qy L k
y
x
ydq
k
E
dx L Q
dq
e
e
L L
e
L L
e e
y
(^2) / 1 2
2
(^2) / 1 2
2
2
(^2) / 3 2
2
(^2) / 3 2
2
i‐
clicker
exercise
Consider
a
large
flat
plate
of
area
A
made
of
a
material
which
has
a
uniformly
distributed
positive
charge
q=
A.
Which
vector
A,B,C,
or
D
represents
the
direction
of
the
electric
field
a
small
distance
above
the
center
of
the
plate?
A D
C
B
Electric
field
generated
by
a
ring
of
charge
d
a
a
Q
dq
2
2
2
2
a
x
x
a
x
dq
k
dE
e
x
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Electric
field
generated
by
a
ring
of
charge
d
a
a
Q
dq
2
2
2
2
a
x
x
a
x
dq
k
dE
e
x
(^2) / 3 2
2
(^2) / 3 2
2
a
x
Qx
k
dq
a
x
x
k
dE
E
e
e
x
x
i‐
clicker
question
E
What
is
the
magnitude
and
direction
up,
down)
of
the
electric
field
between
oppositely
charged
plates?
(^00) 0 0
/
E.
D.
C.
B.
A.
Summary
'
|'
|
)'
(
|
|
) (
2
2
r
r
r
r
r r r r r r E
dq
k
q
k
e
i
i^
i i
e
)
(
)
(
r
E
r
F
q
0
^
e
plate x^
k
E
F
1
F
2
2
2 1
2
2
1
1
L
q q k
qq L k
e
e^
F
F
q
1
q
2
2
1
o
o
2
2
o
o
1
1
ˆ
60
sin
ˆ
60
cos
ˆ
60
sin
ˆ
60
cos^ F
F
F
y
x
F
F
y
x
F
F
Some
of
your
questions:
How
to
understand
and
handle
continuous
charge
distributions
At
the
a
microscopic
(classical)
viewpoint
elementary
charges
are
discrete;
at
a
macroscopic
viewpoint
it
is
often
convenient
to
consider
a
distribution
of
charges.
dr
Q L
dq
r
d Q A
dq
r
d
Q V
dq
:
charges
Line
:
charges
Surface
:
charges
Volume
(^32)