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 (7.93 m,0,0) and (15.9 m,0,0). The cube is immersed in an electric field pointing in the positive x-direction, and given by:
E = (44.9x2 - 9.92)i, x is the distance along the x-axis in m, and E is in N/C.
NOTE:This means that E has constant direction, but increases in magnitude with the x-coordinate.
Find the net charge Q inside the cube, in μC.
NOTE: The sign of the charge is important!
E * A = Q enclosed / ε
3. The Attempt at a Solution
E = ( 44.9 x^2 - 9.92 ) i
My first task is to find Electric field so I can use the formula that is provided in the Relevant Equations section. My question is more about math rather physics. Am I allowed to conclude that E is equal to [ ∫ 44.9 x^2 - 9.92 dx ] with lower limit being 7.93 and upper limit being 15.9? If that logic is correct then there is no other question. I got Q enc = 4.5243 Coulombs ...
Thank you Ψ