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Hmwk Soln Gauss 2 (2009)

Hmwk Soln Gauss 2 (2009) - PHYS 221 General Physics II...

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PHYS 221 General Physics II - Calculus Supplement Grist Homework Solution “Gauss’ Law” Problem: A Cube with sides of length A, is in an uniform electric field E that points in the ˆ X direction. a) Find the flux through each of the six sides. b) Find the total flux through the cube. Be sure to show all of your work. Hint: Set the coordinate system so that the back left corner is at the origin as in the diagram. Solution: The flux through a side is described by Ed A  . We can first deal with the dot product by reducing the argument of the integral to ECos dA ECos dA  and then moving the Electric field term and Cosine out of the integral, as they are both constants. Each side of the cube has length A and the area of any side is simply A 2 . Because we are integrating over the area of sides of each side, the limits of integration are 0 to A 2 . This reduce the flux to a general solution of 2 EACos  .

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Hmwk Soln Gauss 2 (2009) - PHYS 221 General Physics II...

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