How Does Electric Flux Calculation Apply to Complex Fields and Geometries?

AI Thread Summary
The discussion revolves around calculating electric flux and net charge in complex geometries, specifically a cube and two concentric spheres. For the cube, the electric field varies with position, leading to confusion about how to apply the flux equation ∮E*dA = Q/ε0. In the case of the concentric spheres, participants are trying to understand the relationship between the charges and the electric field within the conducting materials. Clarification is sought regarding the electric field inside the conductors and how it relates to the charges on the surfaces. The conversation highlights the challenges of applying theoretical equations to non-uniform electric fields and complex geometrical shapes.
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Homework Statement


1)
A large cube has its bottom face on the x-z plane and its back face on the x-y plane. The corners on the x-axis are at (3.39 m,0,0) and (12.3 m,0,0). The cube is immersed in an electric field pointing in the positive x-direction, and given by:

E = (91.2x^2 - 2.9)i, x is the distance along the x-axis in m, and E is in N/C.

Find the net charge Q inside the cube, in μC.

2)
There are two hollow, conducting, concentric spheres, with air between the spheres:

-Sphere 1 is the inner sphere; it has inner radius a = 2.35 mm, outer radius b = 8.53 mm, and carries charge Q1 = -8.41 pC.

- Sphere 2 is the outer sphere; it has inner radius c = 3.58 cm, outer radius d = 7.92 cm, and carries charge Q2 = 5.84 pC.

- At the common center is point charge Q = -7.21 pC.

Find the charge on the outer surface of sphere 2, in pC.

Homework Equations


∮E*dA = Q/E0

The Attempt at a Solution


Q 1) I try to use equation ∮E*dA = Q/E0 to solve first question, but what I am confusing is the variable E is not a constant, should I plug in the value of x to solve it? and for the surface area since it is a cube, I should count as 6r^2? r is the slice length of the cube.
Q 2) I guess it is a simple question but I just can not figure out the relationship between two spheres.

thank you for help.
 
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psysicsfeet said:
thank you SammyS. can you give me some hints for second question?
What is the electric field within the conducting material itself?
 
SammyS said:
What is the electric field within the conducting material itself?
within the conducting material itself. do you mean inside the inner radius of inner cycle? is it kQ/a^2?
 
psysicsfeet said:
within the conducting material itself. do you mean inside the inner radius of inner cycle? is it kQ/a^2?
I mean: within the conducting material itself, for either of the shells in this problem.
 
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