Download Electrostatic Forces and Electric Fields

Electrostatic Forces
and Electric Fields
Your Guide to the Universe
Coulomb’s Law
We know that charges exert forces on other charges.
You are going to be given the means to calculate
these forces. The force (F) between two point
charges is...
•Proportional to the magnitude of each charge
•Inversely proportional to square of the separation
between their centers (r)
•Directed along the line connecting their centers
F  kC
q1 q2
r
2
kc = 8.99 x 109 N·m2/C2
Coulomb’s Law
So long as your units for charge (q) are in
coulombs, and your units for distance (r)
are in meters, your units for force will
nicely cancel out.
F  kC
q1 q2
 Nm
N
2
 C
r
2
2
 C  C 
 2 
 m 
Inverse Square Laws
m1 m2
Fg  G
2
r
F  kC
q1 q2
r
force
9F
r/3
4F
r/2
F
r
F/4
2r
3r
F/9
2
Field Forces
As mentioned previously, the electric
force is like the gravitational force in that
it is a field force. Unlike contact forces,
which require physical contact between
objects, field forces are capable of acting
through space.
Force
Field Strength 
Quantity Responsibl e for Force
Gravitational Fields
The space surrounding any mass M may
be considered to be a gravitational force
field, meaning that any other mass
located within this space will experience
a force of attraction due to the mass M.
Gravitational Fields
The strength of the gravitational field will
depend upon:
(a) How far the object is from the mass and,
(b) How big the mass is.
Relatively strong
gravitational field
close to earth:
Relatively weak
gravitational field, no
matter how close:
Graphical Representation
The gravitational force field surrounding any mass
may be represented graphically where:
(a) The arrows indicate the direction that a mass
placed in the field would experience a force.
(b) The spacing between adjacent field lines is an
indication of field strength.
Field Strength
Force
Field Strength 
Quantity Responding to Force
Gravitational Field Strength =
Fgrav
Fe
Electric Field Strength =
q
m
=g
The Electric Field
The space surrounding charged
particles is an electric field, and
can be represented graphically,
similar to that of the gravitation
field.
A field can be read as a map
indicating the direction and
relative strength of a force on a
positive charge placed in the
field.
Graphical Representation
For the electric field:
(a) Arrows are drawn to indicate the
direction of the force that would be
experienced by a positive test charge
placed in the field.
(b) The spacing between adjacent arrows
are an indication of the field strength.
A greater line density means a
stronger field strength.
Positive Test Charge
A positive test charge is a tool
used to help analyze an electric
field. By placing a positive test
charge in different locations, and
asking, “What forces act on the test
charge here?”, you can start to map
out the electric field.
WHAT IF I
moved over
here?
+
Electric Field Surrounding
Single Point Charges
(a) Arrows are drawn to indicate the
direction of the force that would be
experienced by a positive test charge
placed in the field.
(b) The spacing between adjacent arrows are
an indication of the field strength. A
greater line density means a stronger
field strength.
More Electric Fields
The direction of the
electric field at any
point is tangent to
electric field lines, if
they are curved.
More
Electric
Fields
Rules for Drawing
Electric Field Lines
Hmm…
1. Lines must begin on positive charges
or at infinity, and must terminate on
negative charges or at infinity.
2. The number of lines drawn leaving a
positive charge or terminating on a
negative charge must be proportional
to the size of the charge.
3. No two field lines from the same field
can cross each other.
Density of Lines
Where is the Electric Field
the Strongest?
Rank these locations in order of the
electric field strength - from largest to
smallest.
C, B, E, A, D
Which of These is Incorrect?
The diagrams below show electric field lines
surrounding point charges. Which of these
is incorrect, and why?
(a) A
(b) B
(c) C
(d) D
(e) E
(c) (d), and (e)
Arrows begin on
a positive charge.
Arrows should be
evenly distributed.
Arrows terminate
on negative charge.
What’s Wrong with
This Picture???
Hmm…
Electric field lines should never cross, because
the lines show the direction that a positive test
charge would experience a force if placed in the
field.
What Type of Charges
(+/-) are A and B??
A
B
A is positive, and B
is negative.
What
would I
do???
+
Which Charge is Bigger?
Positive or Negative?
The Graphical Representations
are Only Qualitative…
You can tell, relatively speaking,
how strong the field is by reading
electric field lines. However, you
can also quantify the field strength.
Electric Field Strength (E)
The electric field strength at some
location in an electric field indicates the
amount of force that would be exerted on
a charge placed there.
Force
Field Strength 
Quantity Responding to Force

E

Fon q
q0
0
q0 = test charge
Electric Field Strength (E)
Let’s look at point A, a location in the

electric field some distance r from
 Fon q
the +Q charge, as shown. The electric
field strength (E) at point A is defined
E
as the force per unit charge exerted
q0
on a charge placed there.
0
A

Fon q 0
EA 
q0
Q q0
kc 2
Q
r

 kc 2
q0
r
-Q
Electric Field Strength

E

Fon q 0
q0
Q q0
kc 2
Q
r

 kc 2
q0
r
The electric field strength at any
location in an electric field only depends
on the other charges creating the field,
and not the size of the charge placed at
that location.
Electric Field Strength
Due to a Point Charge
The magnitude of the electric field
strength at some location A some
distance r from a single point
charge Q is given by the equation:

Q
EA  k c 2
r
The direction of the electric
field at point A is the direction
a positive test charge would
experience a force.
Multiple Charges
If there are multiple point charges
contributing to the electric field at a
point A in space, the electric field is
the vector sum of the electric field
contributions of each individual
charge at A:

Q
EA   k c 2
r
So you add the
electric fields
due to each
point charge??
The Flip Side
If you know the electric field strength at
some point, you can easily calculate the
force on a charge (q0) placed there:


q 0 EA  Fon q0 at A
Electric Field Strength
Let’s say that the electric field strength at
point A is 10 N/C, and is directed to the
left, as shown. There is no charge at A, but
IF we place a charge of +1 C , it will
experience a force of 10 N. If a charge of
+2 C is placed at A, it will experience a
force of 20 N.