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

[psysicsfeet]

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.

 

[SammyS]

For problem 1, look at this thread: https://www.physicsforums.com/posts/5221274/ .

 

[psysicsfeet]

For problem 1, look at this thread: https://www.physicsforums.com/posts/5221274/ .

thank you SammyS. can you give me some hints for second question?

 

[SammyS]

thank you SammyS. can you give me some hints for second question?

What is the electric field within the conducting material itself?

 

[psysicsfeet]

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?

 

[SammyS]

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.