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Midterm08

# Midterm08 - Optics 287 Math 287 2:00 to 3:15 pm 1 March 4...

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Optics 287, Math 287 March 4, 2008 2:00 to 3:15 pm Midterm Exam 1. a) (10 pts.) Calculate the gradient, divergence and/or curl (all that apply) of φ ( r ) = 4 x 3 y 2 + 2 z . b) (10 pts.) Find the result of the following integral I = F ( r ) d v λ . where F ( r ) is a vector function given by one of your results from (a), and the contour is the unit circle, centered at the origin, over the xy plane. 2. a) (20 pts.) Calculate the gradient, divergence, curl, grad-div, and/or Laplacian (whichever applies) of the following functions E ( r , t ) = E 0 e i ( k r ω t ) , B ( r , t ) = B 0 e i ( k r ω t ) , where E 0 , B 0 and k are constant vectors. b) (20 pts.) Suppose that these functions are the electric and magnetic fields of a free-space monochromatic plane wave. Maxwell’s equations are given by
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