Charge enclosed in uniform electric field

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SUMMARY

The discussion centers on calculating the charge enclosed by a cube in a uniform electric field defined by the vector 3.00 i + 2.5 j. Utilizing Gauss' Law, which states that the integral of the electric field E over the surface area dA equals the charge Q divided by the permittivity of free space ε, the conclusion is reached that the total charge enclosed by the cube is zero. This is confirmed by the fact that the electric field is uniform and the dot products of the electric field with the area vectors of the cube's faces cancel out, resulting in no net flux through the cube.

PREREQUISITES
  • Understanding of Gauss' Law in electrostatics
  • Familiarity with vector calculus, particularly dot products
  • Knowledge of electric fields and their properties
  • Basic concepts of charge and electric flux
NEXT STEPS
  • Study the applications of Gauss' Law in different geometries
  • Learn about electric field lines and their relation to charge distribution
  • Explore the concept of electric flux in non-uniform electric fields
  • Investigate the implications of charge distribution on electric field strength
USEFUL FOR

Students of physics, particularly those focusing on electromagnetism, educators teaching electrostatics, and anyone preparing for exams involving electric fields and Gauss' Law.

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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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