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Homework #3: Due Friday, February 14, by 5:15pm
That's all for homework #3.
- Here are two charges and their locations: (-)22μC located at the point (x,y)=(0.90m, 1.30m); (+)22μC located at the point (x,y)=(-1.25, -3.00m). Use Mathematica (or Maple, if you still have it) to plot both the electric field vectors and the electric field unit vectors due to these charges. You are to plot this in the range x=-4.0m to 4.0m and y=4.0m to 4.0m. It should go without saying that both of these charges are present--this isn't two separate one-charge situations.
- A solid sphere of radius 90cm has a non-uniform change density given by ρ=ρ0r3 where ρ0=(+)5.60μC/m6. Find the magnitude of the electric field due to this charge at a radius of (a) 35cm, and (b) 1.25m.
- If a hole of radius 12.0cm is carved in the center of the sphere above, find the magnitude of the electric field at a radius of 72cm. Assume the same charge density function.
- A coaxial cable is shown below. The radius of the inner conducting wire is 0.50mm; the radius of the outer wire is 3.50mm. The entire cable is 2.50m long. There is a charge of (+)2.20μC on the inner wire and a charge of (-)4.5μC on the outer wire. (Recall that all charges will scurry to the surface of conductors, eliminating electric fields inside the metal of those conductors.) Assuming you are relatively far from the ends of the wire, find the magnitude of the electric field at a radius of (a) 0.25mm, (b) 1.10mm and (c) 4.70mm.
- Here is an electric field vector: E=xExx3y2 + yEyxy4. Here, Ex=1,200 N/C/m5 and Ey=1,700 N/C/m5. (a) Find the electric potential difference (voltage) between the points (-1.70m, 3.40m) and (4.50m, 3.40m). (b) Find the electric potential difference (voltage) between the points (-1.70m, 3.40m) and (-1.70m, -3.40m).
- Exercise 2.31 in the text. Ignore the last sentence in this problem, the one that starts with "Take the gradient..."