Physic202_hw2sols

Physic202_hw2sols - MasteringPhysics 2/27/08 1:46 PM...

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2/27/08 1:46 PM MasteringPhysics Page 1 of 16 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers Physics 202 Assignment 2 Due at 11:00pm on Wednesday, February 6, 2008 View Grading Details Exercise 22.5 Description: A hemispherical surface with radius r in a region of uniform electric field E_vec has its axis aligned parallel to the direction of the field. (a) Calculate the flux through the surface. A hemispherical surface with radius in a region of uniform electric field has its axis aligned parallel to the direction of the field. Part A Calculate the flux through the surface. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Flux through a Cube Description: Find the electric flux through a cube given an algebraic formula for the electric field in all space. Then determine the charge enclosed by the cube using Gauss's law. A cube has one corner at the origin and the opposite corner at the point . The sides of the cube are parallel to the coordinate planes. The electric field in and around the cube is given by . Part A Find the total electric flux through the surface of the cube. Hint A.1 Definition of flux The net electric flux of a field through a closed surface S is given by , where the differential vector has magnitude proportional to the differential area and is oriented outward and normal (perpendicular) to the surface. In some cases with simple geometry (like this one), you can break up the integral into manageable pieces. Consider separately the flux coming out of each of the six faces of the cube, and then add the results to obtain the net flux. [ Print ]
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2/27/08 1:46 PM MasteringPhysics Page 2 of 16 http://session.masteringphysics.com/myct Part A.2 Flux through the face Consider the face of the cube whose outward normal points in the positive x direction. What is the flux through this face? Hint A.2.a Simplifying the integral The field depends only on the spatial variable . On the face of the cube, , so is constant. Since is constant over this entire surface, it can be pulled out of the integral: . Part A.2.b Evaluate the scalar product The scalar (dot) product yields the component of the field that is in the direction of the normal (i.e., perpendicular to the surface). Evaluate the dot product . Express your answer in terms of , , , , and . ANSWER: = Part A.2.c Find the area of the face of the cube This face of the cube is a square with sides of length . What is the area of this face? ANSWER: = Express your answer in terms of , , , and . ANSWER: = Part A.3 Flux through the face Consider the face of the cube whose outward normal points in the positive y direction. What is the flux through this face? Express your answer in terms of
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This note was uploaded on 04/09/2009 for the course PHYS 202 taught by Professor Everett during the Spring '08 term at Wisconsin.

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Physic202_hw2sols - MasteringPhysics 2/27/08 1:46 PM...

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