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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 = (91.2

*x^*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.