Calculate the electric flux piercing a cube?

[vmr101]

Homework Statement

Consider four point charges q1, q2, q3 and q4, located at r1, r2, r3 and r4, respectively.
(a) Calculate the electric flux piercing a cube (with side a and centered at r0 = (0, 0, 0) that contains all of these charges.
(b) Calculate the electric field of the four charges as the function of r.
(c) Calculate the Coulomb forces acting on all the four charges.
(bonus) Calculate the divergence of the electric field created by these charges.

Homework Equations

Nothing is given.
Using k = 1/4∏ε

The Attempt at a Solution

a) Electric Flux ∅ = ∫E dA
Each of the size sides receive the same flux as each other, therefore one side will receive 1/6 of the flux ∅(a) = 1/6 ∫E dA

b) Due to the superposition principal E = ƩE = E1 + E2 + E3 + E4
so E = ƩE = k Ʃ q(i)/r(i)^2
E = k (q(1)/r(1)^2 + q(2)/r(2)^2 +q(3)/r(3)^2 +q(4)/r(4)^2)

c) Due to the superposition principal
F = ƩF = F1 + F2 + F3 + F4
F = kq Ʃ q(i) * (r -r(i)) / |(r - r(i))|^3

I am not sure if I am on the right track as there is not much given. We have been learning Gauss;s laws & Maxwells equations. Thanks for any guidance.

 

[PhysicsGente]

I have not checked your answers but I would too use the same reasoning. It seems to me you are in the right track.

 

[vmr101]

Anyone else have any feedback on this?

 

[bayan]

For part a) it says to find the flux piercing a cube, if cube encloses all 4 charges then you don't need integration.

I am also doing a similar assignment and for part c) I think they want us to find the forces that the other 3 charges apply to one. i.e force that charge 2,3,4 exert on 1 and 1,3,4 exert on 2 etc...