Day 4

Tuesday, June 27, 2006

Announcements

SI sessions are now scheduled to be held in Phillips 275: Mondays at 7:00 pm, Tuesdays and Wednesdays at 4:00 pm, and Thursdays at 2:00 pm. If you have questions about SI, contact Chris Lawyer.
If you did not fill out a Student Survey on the first day of class, please do so today.

Assignments:

HW20b is due tonight at midnight.
HW21b is due tomorrow at midnight.
RWP1 is due Friday (to be handed in on paper in class).

Summary of student comments from Minute Papers - instructor responses

Main points learned:

Difference between V and U. (7X)
Electric potential and voltage are the same thing. (2X)
Equations and relationships among V, U, E, F (9X)
U and V are scalars, while F and E are vectors. (2X)
Electric field can exist in vacuum. (2X)
Energy density equation and its importance.
It is important to have a sense of the solution to the problem you are solving. (2X)
A physicist must possess physical intuition and critical thinking skills in addition to mathematical ability. (2X)
It is more important to be right than to be rigorous. (Stephen Hawking)
E = 0 inside a conductor because V is constant.
Capacitors, capacitance, and applications.
St. Elmo's fire (2X)

Lingering questions:

Still confused about the definitions and differences between V and U. (3X) - This may be somewhat unclear because we did not define gravitational potential: V = gh (elevation).
What is epsilon sub zero? Is it the same in the capacitance equation as in Gauss' law? (3X) - Yes, this is the permittivity of free space, which is a constant that indicates the ability of free space (vacuum) to support an electric field.
Is there a difference between change in potential and potential? - This is sort of like time versus change in time. Usually we assume a starting or zero point, so it is most accurate to refer to differences in electrical potential.
We examined how much work is required to assemble a collection of charges, but what about the work required to separate them? - The work is the same, but the sign is opposite.
Why is no work required to move a charge along an equipotential? - This is like a mass sliding freely over a flat frictionless surface (i.e. hockey puck on ice). No force is needed to keep it moving, so W = F*d = 0.
Not clear on the purpose of the energy density equation. (2X) - This will become more apparent later in the course.
Having trouble working out problems that involve multiple equations. - Be sure to get help in the PTC or at SI if needed.
Having difficult finding net force on a charge given other multiple charges (P19.21). (3X) - I will review this in class today.
Why does V increase near a point charge (CC 20-3)? - A positive point charge is like a mountain peak: the closer you get to the peak, the higher your gravitational potential. Note that the opposite is true for a negative charge.
Not clear on the concept of capacitance. - This is the ability to store charge.
Why isn't capacitance zero when the plates are not charged? (2X) -Just because a capacitor is not charged does not mean that it does not have the capacity to store charge.
Is there an electric field outside of the capacitor plates? - Yes, but we usually ignore this weaker field and instead focus on the strong, uniform field between the plates.
Does charge stay between capacitors? - No, the charge resides only on the plates of the capacitor.
Can all electric fields be treated as a capacitor? - No. As you will see in your first lab experiment, the field around a point charge or lightning rod is quite different.
How is energy put into a capacitor? - Some sort of power supply (like a battery) must separate the charges.
Still having trouble knowing which direction vectors should point. - E points in the direction of the force experienced by a positive test charge, so E points away from positive charges and toward negative charges.
Why is the electric field the negative gradient of the potential? - The negative sign indicates that the electric field points "downhill" from positive to negative potential.
Is k = 9e9 the same as kinetic energy? - No, k is a constant, while K is a variable.
Why don't point charges have direction for U? - Electrical potential energy is a scalar.
Could you post solutions to the homework online? - These are available on reserve in the Undergraduate and Math/Physics libraries.
When will SI start? - Yesterday.

Chapter 20: Electric Potential Energy and the Electric Potential

Comments on HW20a.

2) E = 0 means that V = constant (but not necessarily zero)
6) Just because a capacitor is not charged does not mean that it does not have the capacity to store charge.

Capacitors have the ability to store and release charge, much like a battery, but faster.
    Demo: Genecon and light bulb
Capacitance is the ratio of the charge that can be stored in a capicitor divided by the voltage. C = Q/V
The amount of capacitance is proportional to the area of the capacitor plates and inversely proportional to the distance separating the plates. C ~A/d
A dielectric is an insulating material that increases the capacitance of a capacitor by reducing the electric field in the region between the plates.
    C = kCo
Dielectric strength is the maximum electric field before breakdown occurs in a given dielectric material. Emax in air = 3 MV/m.
Ponderable: What would happen if the plates of a capacitor touched?
    Note: Just because a capacitor is not charged, does not mean that its capacitance is zero. (ref. CQ20.26 and analogy with volume of a container).
In addition to storing charge, capacitors also store energy: U = (1/2)QV = (1/2)CV^2
We can think of this energy as being stored in the electric field, electrical energy density: u = (1/2)eoE^2
Demo: Display various capacitors
Exercise: Calculate the size of a 1 F parallel-plate capacitor made from aluminum foil and paper (d = 0.1 mm)
Demo: 1 F, 5V capacitor and Genecon
    Example: How much energy can this capacitor store? Compare this energy to Ug for a 1 kg mass. Would you advise discharging this cap using your tongue or wet fingers? How about dry fingers?
Ex. 20-7 - How high could a person be lifted with 439 J of energy from a defibrilator?
What can happen to a capacitor if its maximum rated voltage is exceeded?
Why should large capacitors be stored with a wire connecting the terminals?

Problems: 51, 62, 63, 65

Concept Tests

Chapter 21 - Electrical Current and DC circuits

Electric current is the flow of electric charge. I = dQ/dt.   Physicists define the direction of the current in terms of positive charges (consistent with the direction of the electric field), even though it is negatively-charged electrons that flow in most situations. Incidently, electrical engineers define current (J not I) to be in the opposite direction.
    1 A = 1 ampere = 1 amp = 1 C/s
    Typical currents in common electrical devices.
When a switch is closed so that current can flow in a circuit, the reponse is very fast (approximately the speed of light), but the average speed of a typical electron is much slower. Why? Approximately how slow?
Demo: Rubber ball model of current.
    What could be done to increase the current in this demonstration? What are the corresponding parameters to resistance?
Prob. 21.6: What incorrect assumption is made in this problem that asks about the amount of current flowing through a TV? [assumes DC]
Many batteries are rated in mA-h. What does this unit represent? [total amount of charge (see also CQ21.5)]
When we pay for electricity in units of kW-h, what are we really paying for? [energy (but we expect a minimum amount of power)]
Electrical resistance in a wire depends on the resistivity of the conductor, the length of the wire, and its cross-sectional area: R = rL/A
Ohm's law is a useful relation that is valid for many (but not all) resistive loads: V = IR, or more properly, I = V/R (Why is this form better?)
Prob. 21.12: Find the potential difference between the feet of a bird sitting on a high-voltage power line.
    V = IR = IpL/A = 2.5 mV, which increases with L (separation between bird's feet)
The resistivity of most metals increases with temperature (ex. tungsten), but there are exceptions (ex. carbon and other semiconductors).
    Application: Thermal resistors (thermistors) are used in digital thermometers.
    Superconductivity - below a certain critical temperature, Tc, certain materials have zero resistance.
Exercise: Sketch and label a graph of current as a function of voltage (I-V plot) for a light bulb that has a cold resistance of 10 ohms and a hot resistance of 100 ohms at its operating voltage of 12 V.
Electric power is the rate at which energy must be supplied: P = IV = I*I*R = V*V/R