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hw2_p5405_f05

# hw2_p5405_f05 - HW 2 Phys5405 f05 due Sept 8 1 Charge is...

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HW 2 Phys5405 f05 due Sept. 8 1) 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 . a)Find E at any point on the z axis. Hint-be careful about positive and negative z and | z | greater or less than R. b)In particular obtain E at z=R, z=0, and z= - R c)Take R=1 m and plot E( z ) / ( σR 2 / 2 0 ) as z varies from z= - 2 m to z= 2 m for cos α = 0.999, 0., -0.999. Use of a package like Mathematica makes this easy. Otherwise you can write a fortran or C++ program and make the plots by hand. Be careful about the point z= - R. Examine the plots and see if they make sense. They provide more information than just a formula. d)For E at z=R and z= - R, calculate the limits as α 0. e)When α = 0 you can use Gauss’s law to calculate E anywhere inside or outside the spherical surface. However, if you used Gauss’s law to calculate E at R, you would need to use a Gauss surface that coincided with the charges. If you did so and included the charges

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