hw2_p5405_f02 - if the charge on the volume’s boundary...

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HW 2 Phys5405 f02 due 9/10/02 1) Protons have a radius = 10 - 15 m. Suppose two protons are very far from each other, but heading towards each other with the same kinetic energy. What is the energy in MeV such that the protons just make contact? 2a) In a region of space E = E e x . Prove that E does not depend on y or z in this region. 2b) If there is no charge in this region, prove that E doesn’t depend on x. 3a) Charge is arranged on the surface of a sphere of radius R centered at the origin as follows: σ = σ 0 , if θ > α and σ = 0, otherwise. Here θ is the usual polar angle, 0 θ π . Find E (r = R, θ = 0). 3b) Let α 0. This e±ectively puts uniform charge density on the spherical surface. Again find E (r = R, θ = 0). You should find a field di±erent from what the Guass law would predict
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Unformatted text preview: if the charge on the volume’s boundary surface was included in the Gauss integral. That is why such charge must be excluded. 3c) What is the prediction of the Gauss law incorrectly used that was mentioned in part 2b)? 4) An infinitely long right circular cylinder has its axis along the z axis. The cylinder has radius R and throughout its volume has uniform charge density ρ . A hole of radius R’ is drilled through the cylinder parallel to its axis. The center of the hole is at x=c, where c+R’ < R and c-R’ > 0. Show that E inside the hole is constant and find its magnitude and direction? 5) JDJ chapter 1 problem 5 1...
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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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