Charge enclosed in uniform electric field

AI Thread Summary
The discussion revolves around calculating the charge enclosed by a cube placed in a uniform electric field of 3.00 i + 2.5 j. Using Gauss' law, the participants analyze the dot product of the electric field and the differential area for each face of the cube. They conclude that the contributions from the faces cancel out, leading to a total charge of zero enclosed within the cube. The reasoning emphasizes that a uniform electric field results in no net flux through the cube's surfaces, confirming the absence of charge inside. Thus, the final determination is that the charge enclosed by the cube is indeed zero.
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1b]1. Homework Statement

A cube oriented so that its corner lies on the origin and it extends positive 1m in the x, y, and z direction. An electric field of 3.00 i + 2.5 j passes through this space. What is the charge enclosed by the cube?

The Attempt at a Solution



Gauss' law is
integr(E . dA) = Q/epsilon

since the surface is of a cube, you can add the dot product of E and dA for every face except for the one lying in the x-y plane because there is no 'k' component of the E field.
The dot products of the faces cancel out though
So the the total charge enclosed is 0
is that right?
 
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If the electric field is uniform across the space the cube is in, then you are right that there is no charge inside, because for there to be a charge inside there would have to be a net non-zero flux through all of the faces of the cube.
 
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