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.
Nothing is given.
Using k = 1/4∏ε
The Attempt at a Solution
a) Electric Flux ∅ = ∫E dA
Each of the size sides recieve the same flux as each other, therefore one side will recieve 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.