Download The Electric Field

The Electric Field
Early scientists and philosophers
struggled with the idea of “action at a
distance”.
How was the electric force
propagated?
Michael Faraday proposed that a
“field” extended outwards from all
charged objects, and that these fields
interacted with one another.
Fields are a great mathematical
convenience.
Faraday 1791-1897
The Field can be visualized mentally,
graphically, and actually seen under
certain circumstances……
Before TV there was no Nova, or Discovery Channel….
Michael Faraday popularized public lectures about cutting edge science.
Here he is giving one of his famous Christmas Lectures at the Royal
Institution in London, 1856
Visualizing the Electric Field
These figures are from the book
“Conceptual Physics” by Paul Hewitt
• 
This is a photograph of a tank of oil
(an electrical insulator) with millions
of tiny cotton fibers (insulating and
non-magnetic) suspended in it.
• 
In the center is a metal object that is
electrically charged
• 
The cotton fibers mysteriously align
themselves pointing radially outward
from the charge.
• 
Nothing is touching them, and they
are not touching each other
• 
“Something” with Faraday decided to
call “The Electric Field” is reaching
out through space and moving the
fibers.
Visualizing Electric Fields: A Single Point-Charge
The number of field lines starting
on a positive charge (or ending on
a negative charge) is proportional
to the magnitude of the charge.
The electric field is stronger
where the field lines are closer
together.
Field lines trace the direction that
a tiny positive “test charge”
would move if placed at that
location.
Visualizing Electric Fields: Two Charges
The lines emanating from two equal charges, opposite in
sign will connect to form a Dipole (two poles).
While if the charges are the same, the lines will avoid each
other, and the charges repel
ConcepTest 16.12a Electric Field Lines I
1)
What are the signs of the
charges whose electric
fields are shown at right?
2)
3)
4)
5) no way to tell
ConcepTest 16.12a Electric Field Lines I
1)
What are the signs of the
charges whose electric
fields are shown at right?
2)
3)
4)
5) no way to tell
Electric field lines originate on
positive charges and terminate
on negative charges.
ConcepTest 16.12b Electric Field Lines II
Which of the charges has
the greater magnitude?
1)
2)
3) Both the same
ConcepTest 16.12b Electric Field Lines II
Which of the charges has
the greater magnitude?
1)
2)
3) Both the same
The field lines are denser around
the red charge, so the red one
has the greater magnitude.
Follow-up: What is the red/green ratio
of magnitudes for the two charges?
Math Definition of Electric Field
The electric field E is the vector
describing the force exerted by a
single charge or distribution of
charges, per unit charge.
F = Eq
The definition assumes that the
field can be calculated anywhere, by
computing the force exerted on a
tiny “test charge” so small that it
doesn’t add its own field to the mix
Calculating the Electric Field
For a point charge Q, we calculate its Electric Field
using an imaginary (minute) test charge “q”:
Since the force between 2 charges is given by
Coulomb's law, the force felt by our tiny test charge q
would be
F = k Qq/r2
F=Eq
E= F/Q
Where the Electric field is
(units of newton per coulomb)
= k Q/r2
This is similar to the way we
simplify the law of gravitation for
everyday situations, by finding ‘g’
and then simply using
F = mg
ConcepTest 16.8a Field and Force I
Between the red and the
blue charge, which of
them experiences the
greater electric field due
to the green charge?
+1
d
+2
1)
+1
2)
+2
3) the same for both
+1
d
+1
ConcepTest 16.8a Field and Force I
Between the red and the
blue charge, which of
them experiences the
greater electric field due
to the green charge?
+1
d
1)
+1
2)
+2
3) the same for both
+2
Both charges feel the same electric
field due to the green charge because
they are at the same point in space!
+1
d
+1
Q
E=k 2
r
Using Coulomb’s Law for Multiple Charges
Coulomb’s law strictly describes point charges.
Superposition: for multiple point charges, the forces
on each charge from every other charge can be
calculated and then added as vectors.
The net force on a charge is the vector
sum of all the forces acting on it.
Where would this sort of thing be important?
1
ConcepTest 16.6 Forces in 2D
2
3
Which of the arrows best
4
represents the direction
of the net force on charge
+2Q
d
+Q
+Q due to the other two
charges?
d
+4Q
5
1
ConcepTest 16.6 Forces in 2D
2
3
Which of the arrows best
4
represents the direction
of the net force on charge
+2Q
d
+Q
+Q due to the other two
d
charges?
+4Q
The charge +2Q repels +Q towards
the right. The charge +4Q repels +Q
upwards, but with a stronger force.
Therefore, the net force is up and to
+2Q
the right, but mostly up.
Follow-up: What happens if the
yellow charge would be +3Q?
+4Q
5
Vector Electric Field Calculation See Example 16.9 in the book
Find the Direction and Magnitude of the Electric Field
due to a a pair of unequal Charges.
(takes 10 min, a good recap on using vectors.)
We can go over this in recitation
ConcepTest 16.9c Superposition III
-Q
+Q
What is the direction of
the electric field at the
position of the X ?
2
3
1
4
+Q
5
ConcepTest 16.9c Superposition III
-Q
+Q
What is the direction of
the electric field at the
position of the X ?
2
3
1
4
+Q
5
The two +Q charges give a resultant E field
that is down and to the right. The –Q charge
has an E field up and to the left, but smaller
in magnitude. Therefore, the total electric
field is down and to the right.
Follow-up: What if all three charges reversed their signs?
More Complex Field Lines and Symmetry
•  The electric field between two closely spaced,
oppositely charged parallel plates is constant.
•  Where might this configuration occur?
Shielding of Electric Field by a Conducting
Enclosure - in this case a Metal Ring
Charged Rod
Metal Ring
Note the field lines
are due to induced
charge only
Look inside the ring:
there are no lines!
Figure taken from the book “Conceptual Physics” by Paul Hewitt
Proof that the Electric Field is Zero
Everywhere inside a Conductor
-
Think about how the electric
field depends on Charge and
Distance.
EA=kQA/r12 and
EB=kQB/r22
Step 1. Compare the distances,
for convenience:
r2 = 2r1
r2/r1 = 2
-
A
QB/QA = AreaB/AreaA
=4
-
r1
P
-
r2
-
B
-
(r2/r1)2 = 4
Step 2. Compare the
charges:
-
-
-
Step 3. Combine.
Result:
EB/EA = kQB/r22
kQA/r12
The test charge feels
equal opposite fields
from all directions -> No
net field
= 4/4 =1
Charge on the Earth according to Coulomb’s Law
Electric Field at the Earth’s Surface is about
E = 150 N/C, and points toward Earth’s center.
We can assume the Earth’s net charge resides
at the center and use coulomb’s law to find out
how big it is:
Definition of Electric Field: E=kQ/r2
Rearrange for Q:
Q=Er2/k
= 150 * (6373x103)2 / 9x109
= 680,000 C
Where does this charge come from?
The E-field surrounding a charged sphere is
indistinguishable from that of a point charge (Which is
also true of a gravitational field)
Electricity in Lightning, Thunderstorms
Raindrops and ice crystals charged by
friction as they travel up and down
inside the cloud segregate, causing an
electric field.
The ground below becomes charged by
induction
When the electric field gets strong enough,
the air “breaks down” and becomes
conductive, causing lightning to strike
Globally, ~2000 on-going thunderstorms cause about 100 lightning strikes to earth each second.
Electric Fields and Conductors
The static electric field inside a conductor is zero. The free charges
“instantly” align themselves to totally cancel the external field.
The net charge on a conductor is all on its surface. -Charges want to be
as far apart as possible. The is NO Electric field inside the car!
(has nothing to do with tire rubber)
This result is known as the Faraday Cage
Another Example - Lighting Rods
Rods focus the
induced electric field
that appears in the
ground beneath the
thunderstorm. With two
consequences:
1. Charge can leak
away through the air
2. If a breakdown
occurs, the stroke will
hit the rod and be
carried into the ground,
protecting nearby
areas.
Annually in the USA lightning causes more than 26,000 fires with damage to property in excess of $5-6 billion.
Summary of Chapter 16
•  Two kinds of electric charge – positive and negative
•  Charge is conserved
•  Charge on electron:
•  Conductors: electrons free to move
•  Insulators: nonconductors
•  Semiconductors - insulators that conduct in response to electric field
•  Objects can be charged by conduction or induction
•  Coulomb’s law: very strong compared to all other forces.
•  Electric field is force per unit charge:
•  Electric field can be represented by electric field lines
•  Static electric field inside conductor is zero; surface field is
perpendicular to surface
•  Gauss’s law:
The Electric Field Surrounding Two Charges
1.  A Negative, B Positive
2.  Both Negative
3.  Both Positive
4.  A Positive, B Negative
1.  A Negative, B Positive
A
B
2.  Both Negative
3.  Both Positive
4.  Cannot tell
Application of Electrostatics: Photocopy
Machines
What special property must the roller have?
And the toner particles? What about the paper?
Photocopy Machines and Computer
Printers Use Electrostatics
Laser printer is similar, except a computer
controls the laser intensity to form the image
on the drum