emhw05 - Electromagnetic Theory I Problem Set 5 Due 26...

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Electromagnetic Theory I Problem Set 5 Due: 26 September 2011 17. Following the method discussed in class for the Dirichlet Green function, obtain the mixed Dirichlet/Neumann Green function for the region between two concentric spheres of radii a < b with a) Neumann conditions ( ∂G/∂r = 0) on the inner shell and Dirichlet conditions G = 0 on the outer shell, and b) vice versa. 18. Use one of the Green functions found in the previous problem to calculate a) the potential and b) the electric field in the region a < r < b for the situation in which the normal component of the electric field, E r , vanishes on the inner sphere, and the potential on the outer sphere has the behavior φ ( b, θ ) = V 0 cos θ . c) Sketch the electric field lines in the case where a/b = 0 . 5. The electric field lines are those curves that are everywhere tangent to the electric field. 19 The general electrostatic problem to find the potential in the interior of a hollow right circular cylinder of radius a and length L
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