Answer: Q = ba⁴ * ε₀
Explanation:
Remember, Gauss's Law states that:
"The net electric flux through any hypothetical closed surface is equal to 1/ε₀ times the net electric charge within that closed surface" i.e
flux Φ = Q / ε₀ where
ε₀ = 8.85e-12 C²/N·m²
Also, the flux, Φ = EAcosθ, where
E = magnitude of the electric field in V/m
A = area of the surface in m²
θ = angle between the electric field lines and the normal (perpendicular) to S.
The field is directed along the x-axis, so all of the flux passes through the side of the cube at x = a. This means that θ = 0º. Thus,
Φ = EA
Then, E = bx² and we're interested in the point where x = a, so if we substitute x for a, we have
E = ba²
Since A = a² for the cube face, we have
Q / ε₀ = ba² * a²
so
Q = ba⁴ * ε₀
