Workshop03Images

# Workshop03Images - ECE 3030 Electromagnetic Fields and...

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ECE 3030: Electromagnetic Fields and Waves Fall 2009 WORKSHOP 3 INSTRUCTOR NOTES: Images and Poisson’s Equation Reminder: Give all hints at beginning of session. Date: Thursday 9/17 1. Ask students if they ﬁnished checking the solution to Demo Problem 4.14. They were supposed to be asked to show that the solution, namely Φ( r ) = V + ρ ( b 2 - a 2 ) 4 ε 0 ln( b/a ) ln r a - ρ ( r 2 - a 2 ) 4 ε 0 does indeed satisfy Poisson’s Equation and the boundary conditions. If they did not ﬁnish then, nor in the meantime, they should do it in this Workshop. 2. Problem 4.5 Hint: Assume solutions for the potential in each region appropriate for spherical symmetry. Deﬁne a reference for the potential. We have concentric (centers at the same location) spheres. a. Let Φ( r ) = A r + B . Two unknown constants need two boundary condi- tions to evaluate: Φ( r = a ) = 0 and Φ( r = b ) yielding Φ( r ) = bV b - a £ 1 - a r / . b.

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Workshop03Images - ECE 3030 Electromagnetic Fields and...

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