Transcript Lecture26

Reading Quiz
The voltage (or electric potential)
of a battery determines
• how much work the battery can
do on an electric charge.
• how much net electric charge is
in the battery.
• how much electric field is around
the battery.
(P.E.)  qV
Work  qV
Electrostatics:
•
Force - Coulomb’s Law
A Vector law
•
The electric field. E
The electric field is a vector field
•
Electric potential.
A scalar -like work
q1q2
F  k 2 rˆ
r
q1
E  k 2 rˆ
r
V  E  d
Two positive charges exert equal but
oppositely directed forces upon one
another, according to Coulomb’s law and
Newton’s third law of motion.
Coulomb’s Law:
The electrostatic force between two
charged objects is proportional to the
quantity of each of the charges and
inversely proportional to the square of the
distance between the charges.
q1q2
F k 2
r
Coulomb’s Law:
q1q2
F k 2
r
Note: looks a lot like Newton’s law of
Gravitation.
q1q2
F k 2
r
If both charges are negative, the force
is also repulsive.
If one is positive and the other
negative, the force is attractive.
If a system contains many charges, the net
force (vector) on any one of them is the
(vector) sum of the individual forces from
the individual charges (superposition).
Quiz 1
Two equal charges are 1 meter apart. If
the distance between them is
increased 4 times, what increase in
each charge is require to keep the
force between them the same.
1. 2 times
2. Square root 2
3. 4 times
4. 8 times
Electric Field:
The electric field at a given point in space
is the electric force per unit positive charge
that would be exerted on a charge if it were
placed at that point.
E = F/qo
It is a vector having the same direction as
the force on a positive charge.
The direction of the electric field lines
around a positive charge can be found
by imagining a positive test charge q0
placed at various points around the
source charge. The field has the same
direction as the force on a positive
test charge.
Note: Lines of E point away from
positive charges, toward negative
charges.
The electric field lines associated with a
negative charge are directed inward, as
indicated by the force on a positive test
charge, q0.
NOTE: We can also write F = qoE,
which tells us how much force F is
exerted by the field E for any charge qo.
The electric field lines associated with
two equal but opposite-sign charges (an
electric dipole).
The field can be determined by using the
field from one charge, and adding the
field from the other charge. This is called
“superposition.”
We created this new concept, the
electric field, because sometimes it is
more convenient to work with.
However, the electric field is real.
There actually is energy stored in the
field that can be detected by
experiment.
Quiz 2
Electric field lines
1. Start on a positive charge and
go to infinity
2. Start on a negitive charge and
go to infinity
3. Start on a positive charge and
end on a negitive charge
4. Can start and end on any charge
sign is not important
The Electric Potential
Moving an electric charge through
space where electric fields are present
can require work, since forces
associated with the fields act on the
charge.
This work can be described as a change
in potential energy. We introduce the
new concept of “electric potential” to
describe the amount of work needed to
move a charge through a region with
electric fields.
Two parallel metal plates containing
equal but opposite-sign charges
produce a uniform electric field in the
region between the plates.
“CAPACITOR”
(This is a convenient device that allows
us to talk about a region where the
electric field does not change. This
makes the calculations much easier.)
An external force F, equal in magnitude
to the electrostatic force qE, is used to
move the charge q a distance d in a
uniform field.
The increase in potential energy when a
charge q is moved against the
electrostatic force is analogous to what
happens when a mass m is lifted against
the gravitational force.
We call this the electrostatic potential
energy (instead of the gravitational
potential energy).
The change in electric potential is
equal to the change in electrostatic
potential energy per unit of positive
test charge:
PE
V 
q
This is the definition of potential.
It is measured in volts.
A positive charge is moved from the
bottom plate to the top plate by an
external force.
QUIZ 3
A +2 coulomb charge is lifted through
the plate how much work is done.
1.
2.
3.
4.
10000 N
20000N
600N
300N
The electric potential (represented by the
dashed lines of constant potential)
increases as we move closer to a
positive charge.
a
.
b
.
Quiz 4
What is the potential difference in moving
From a to b.
1. 15 V
2. -15V
3. 25 V
4. -25V
5. Can tell not in a straight line
Quiz 5
a
.
b
.
What is the work done in moving a +2
coulomb charge from a to b?
1. 50 N
2. 30 N
3. 25 N
4. 20 N
5. 15 N