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Ch.25 - Electric Potential.
LNK2LRN 2008/09 AP Physics C January 22 to 28.
Plans for the Week and Assignments:
1. THURSDAY(01/22): Intro. to Ch.25 - Electric Potential. HW: Read and
Study pages 763-68, then solve problems 1, 7, and 13 on pages 787-88.
2. FRIDAY(01/23): Potential Difference and Potential Energy Due to Point
Charges. HW: Read and Study pages 768-71, then solve problems 17, 19,
and 23 on pages 788-89.
3. MONDAY(01/26): Work Done by an Electric Field. HW: Read and Study
pages 772-78, then solve problems 31 and 38 on pages 789-90.
4. TUESDAY(01/27): Obtaining Electric Field Strength from the Electric
Potential. Robert Millikan and his Oil-Drop Experiment. HW: Read and Study
pages 781-86, then solve problems 42 and 49 on pages 790-91.
5. WEDNESDAY(01/28): REVIEW Ch.25 - Electric Potential. HW: Complete
HW: Complete Review Handout #1.
6. THURSDAY(01/29): TEST on Ch.25. HW: Go to website and study notes
for Ch.26 - Capacitance and Dielectrics.
Very Important: If you have any questions or miss a class, see
me before school (8:00 - 8:30 AM), during Lunch, 7th hour, or after
school. Best to send an email to rpersin@fau.edu.
Website Notes on Ch.25 - Electric Potential.
Strange But True, Electrical Sensitivity in Fish: As hard as it may be to be
believed, sharks can sense an electrical differential of one billionth of a volt.
This is the equivalent of sensing the electrical current running between two
flashlight batteries set on the ocean floor 2,000 miles apart!
1. We know that an electric field is a region in space where an electric
force is exerted on a charge. Therefore, when a positive test charge, qo,
is moved between points A and B in an electric field, E, the change in the
potential energy of the charge-field system is ΔU = -qo∫AB E·ds .
2. Electric lines of force represent the direction that a positive test charge
would move in an electric field. By convention, they originate at positively
charged objects and terminate at negatively charged objects.
3. Recall that work is done by the electric field if the electric force acting on
the charge causes it to move from one point to another, say A to B. We then
say that these two points differ in their electric potential, V, with V = U/qo .
4. The magnitude of the work done on the charge by the electric field is a
measure of this difference in potential. The electric potential difference (V)
is the work done per unit charge as a charge is moved between two points in
an electric field. Simply stated, W = U= q·V . Or better yet, the Law of
Conservation of Energy can be stated as KA + qVA = KB + qVB .
5. The Volt (V) is the unit used to measure electric potential difference.
Since a Volt measures work done per unit charge, 1 Volt = 1 Joule/Coulomb.
Other equivalent expressions for a Volt exist.
6. An electric potential difference must exist for current to flow in an electric
circuit. Current always flows from high to low potential. The potential
difference ΔV between two points A and B in an electric field E is defined as
ΔV = ΔU/qo = -∫AB E·ds .
7. As charge moves from one point to another in an electric circuit, energy
is released. This results in a decrease in electric potential. The decrease in
electric potential implies that there is an "electric potential difference" between
the two points. (This "electric potential difference" is called "voltage.")
8. The potential of the earth is arbitrarily said to be zero. An object connected
directly to the ground can be described as being "grounded". (The original
expression was "earthed".) A ground may be a common plane of zero voltage
compared with the rest of the circuit.
9. The potential at any point in an electric field can be either positive or
negative with respect to the earth, depending on the nature of the charge.
The change in electric potential over this distance is defined through the work
done by this force, where potential is shorthand for change in electric
potential, or potential difference.
10. This is analogous to the definition of the gravitational potential energy
as the work done by the force of gravity in moving a mass through a
certain distance. The potential difference between two points A and B in a
uniform electric field E where s is a vector that points from A to B and is
parallel to E is V = -Ed , where d = |s| .
11. The units of potential difference (potential) are Joules / Coulomb, which
are called Volts (V). Physically, potential difference has to do with how much
work the electric field does in moving a charge from one place to another.
12. Batteries, for example, are rated by the potential difference across their
terminals. In a 9-volt battery the potential difference between the positive
and negative terminals is precisely nine volts. On the other hand the
potential difference across the power outlet in the wall of your home is
110 volts.
13. Consider a charge placed in an electric field. Let us chose some
arbitrary reference point in the field: at this point the electric potential
energy of the charge is defined to be zero.
14. This uniquely defines the electric potential energy of the charge at every
other point in the field. For instance, the electric potential energy at some
point is simply the work done in moving the charge from one point to another
along any path, and can be calculated using V = E∙d or V = kq/r .
15. It is clear that potential depends on both the particular charge which we
place in the field and the magnitude and direction of the electric field along
some arbitrary route between points A and B. However, it is also clear that
it is directly proportional to the magnitude of the charge.
16. An equipotential surface is one on which all points are at the same
electric potential. Equipotential surfaces are | to electric field lines.
17. If we define V = 0 at rA =
∞ , the electric potential due to a point chargeat any distance r from the charges is V = kq/r . We can obtain the electric
potential associated with a group of point charges by summing the the
potentials due to the individual charges, V = k∑qi/ri .
18. The potential energy associated with a pair of point charges separated
by a distance r12 is U = kq1q2/r12 . This represents the work done by an
external agent when the charges are brought from an infinite separation to
the separation r12 . We obtain the potential energy of a distribution of
point charges by summing terms of the above equation over all pairs of
particles.
19. If we know the electric potential as a function of coordinates x, y, and z
we can obtain the components of the electric field by taking the negative
derivative of the electric potential with respect to the coordinates. For
example Ex = -dV/dx .
20. The electric potential due to a continuous charge distribution is
V = k∫dq/r .
21. Every point on the surface of a charged conductor in electrostatic
equilibrium is at the same electric potential. The potential is constant
everywhere inside the conductor and equal to its value at the surface.
And still, we need these steps to solve any problem in Physics:
(i) read the problem and identify the given variables
(ii) determine what you are asked to solve for
(iii) find the correct equation to use
(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown
(v) substitute-in the given information and simplify.
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THE
AP PHYSICS C ARCHIVES
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And Always Remember... "From Newtonian Mechanics, Through Quantum Theory, Without Physics, Life Would Be Dreary." |
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