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hw3_p5406_s10

# hw3_p5406_s10 - The beam ²lls a circu-lar area of radius a...

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HW 3 Phys5406 S10 due 2/11/10 1) A solid, uniform, conducting sphere of radius a floats in a uniform, dielectric liquid of permitivity ǫ and mass density ρ with a fraction of its volume α < 0 . 5 submerged. If a charge Q is placed on the sphere, it falls until half its volume is submerged. Find Q. Can you determine the sign of the charge merely by observing the sphere dropped? 2) JDJ 5-22 3) Consider the following two separate cases concerning spheres of radius R with free charge Q.. In case (a) the sphere is a solid conductor and in case (b) it is a uniform dielectric of permitivity ǫ . In the case of the dielectric the free charge is spread uniformly throughout the volume. If each sphere were cut in half, in the plane z=0, would the hemispheres attract or repel and what force is exerted on one hemisphere by the other? 4) A beam of electrons travels in the z direction with speed v.
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Unformatted text preview: The beam ²lls a circu-lar area of radius a that is perpendicular to the z axis. The number of electrons per unit volume is n . Calculate the Poynting vector. What is the power that Fows into or out of a length L of the beam. What is the power converted to or from heat or mechanical energy in the volume. 5) Consider an ohmic conductor of the same geometry as the beam in problem 4. Let the conductor have a uniform current density J e z due to an electric ²eld in the conductor in the z direction such that the potential di³erence for a length L is V and the resistance for length L is R. The current is due to the Fow of free electrons with the usual low drift velocity. Calculate the Poynting vector.What is the power that Fows into or out of a length L of the conductor? What is the power converted to or from heat in the volume? 1...
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