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Homework #5: A copy is due Friday, February 28, by 7:00am I am leaving for the Alaska trip right after that time. If I do not have that hardcopy physically in my hands via the folder on my door, or given to me personally before that, then that homework does not exist. You will keep your original to study for the test. I will have my solutions posted so you can see how I worked the problems.
That's all for homework #5.
- Sketch the charge distributions for the following charge densities in Cartesian coordinates. Make your sketches (separate graphs) in the region from x=(-)5 to +5, and y=(-)5 to +5. Indicate with an obvious (+) or (-) where the charge density is positive or negative, respectively. The constant ρ0 contains the numerical value and the appropriate units.
a. ρ=ρ0 (y+3)2
b. ρ=ρ0 (y+3)3
c. ρ=ρ0 x (y+3)2
d. ρ=ρ0 (x-2)2 (y-3)2
- Here is an electric field: E=y K y2x3, where the bold-faced y is the unit vector in the y-direction, and the constant K takes care of the magnitude and units.
a. Find the general expression for the electric potential Φ associated with this field.
b. Find the general expression for the charge density ρ associated with this field.
c. If the electric field has a magnitude of 1,600 N/C = 1,600 V/m at the point (1.25m, 2.54m) find the final numerial values for the electric potential Φ and the charge density ρ at this same point.
- Here is a spherically symmetric charge distribution: ρ=K r5 where K=1.00x10-10C/m8.
a. Find the general expressions (no numbers yet) for the electric field at an arbitrary distance 'r' from the origin. Note that both the charge density ρ and the electric field E will be spherically symmetric--include the appropriate unit vector for E.
b. If the magnitude of the electric field at a radial distance r=0.85m from the origin is 1.38N/C, determine the value of the constant that appeared in part (a).
- Here is a spherically symmetric charge distribution: ρ=K r6 where K=1.20x10-10C/m9.
a. Find the general expression for the electric potential Φ due to this charge distribution. Don't forget to include the correct number of integration constants!
b. Assuming the constants that appeared in part (a) are equal to zero, find the potential Φ at r=1.20m from the origin.
- problem 2.75. Do just the curls and divergences (show you work for each of these--no "sudden miracles" here) part. Ignore the sentence that starts out "If the curl turns out to be... ."
- Suppose that aluminum donates 1 of its electrons to the conduction band of electrons while a current is flowing through it.
a. An aluminum wire of radius r=0.120mm has a current of 2.75Amps flowing through it. Find the magnitude of the current density J.
b. Find the number density 'n' of these conduction electrons in units of #/m3. A very useful web page for this part is http://webelements.com/.
c. Find the magintude of the "drift velocity" v of the electrons in this aluminum wire.