Answered: 7. Use a surface integral to compute… | bartleby

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7. Use a surface integral to compute the flux of the vector field
leaving a unit sphere centered at the origin. Now use a volume integral to compute the flux of F leaving any
sphere that does not contain the origin. Your results might seem to contradict the divergence theorem; explain
why they in fact do not.

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4. Use the Gauss law to calculate the magnitude of the electric field from scratch. For the closed surface of integration (the "Gaussian box"), use a shape with two faces, the "caps," parallel and side or to the charged sheets. Explain all the assumptions you have to make for the electric field and back them up with symmetry arguments. sides perpendicular (a) Make a clear sketch of the system and your Gaussian box, including representative area vectors dA and electric field vectors. (b) Calculate the flux integral ƒE•dA. Include an explanation of your reasoning. (c) Calculate Qenc. Include an explanation of your reasoning. (d) Use the Gauss law to calculate the magnitude of the electric field at any point in space.
2. If you very close to the surface on a conductor it will look flat. Just as the Earth appears flat to us because we R are on the surface. We want to find the electric field at E a point P just outside the conductor. Assume the conducting surface near P has a positive charge per h area n. We draw a Gaussian cylinder of radius R and height 2h cutting through the surface. а. What is the flux through the curved portion of the Gaussian surface? Write the answer in terms of the Conductor unknown electric field E, R and/or h. b. What is the flux through the bottom endcap? С. What is the flux through the top endcap? d. Write the charge enclosed by the Gaussian surface in terms of 7, R and/or h? е. Use Gauss's law to find the electric field just outside the conductor.