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  3. 4 total 40 pts suppose an electric field in a...

Question: 4 total 40 pts suppose an electric field in a...

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4. Total: 40 pts Suppose an electric field in a region of space is given by where T is a constant with units of time, and Bo is also a constant a) [4 pts] What are the units of the constant Bo? b) [8 pts] Sketch the electric field in the ry-plane. Do it by hand, but if you want check yourself, you can use e.g. Mathematica. c) 8 pts Calculate the closed line integral E dl where the path is a circle of radius R, parallel to the ry-plane, centered at (0,0, 20) Integrate counter-clockwise as viewed from above d) 8 pts Calculate Vx E and describe the resulting vector field in words. Show that the closed line integral value, which you obtained in part c) are equal to the corresponding surface integral of V x E. Briefly explain, why this result is related to the Stokes theorem e) [8 pts Calculate the closed line integral, Eq. (4), again, but this time where the path is a rectangle (sides of length a and b) oriented parallel to the ry-plane. Again, integrate counterclockwise as viewed from above f4 pts Determine the scalar potential that is related to the electric field E given in Eq. (3), or explain why no such potential exists.

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