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## Homework Statement

A closed surface with dimensions a = b =

0.254 m and c = 0.4064 m is located as in

the ﬁgure. The electric ﬁeld throughout the

region is nonuniform and given by ~E = (α +

β x^2)ˆı where x is in meters, α = 4 N/C, and

β = 6 N/(C m2).

Picture of object attached.

What is the magnitude of the net charge

enclosed by the surface?

Answer in units of C.

## Homework Equations

Gauss's Law: Flux = integral(E dA) = Q/permittivity constant

permittivity constant(epsilon naught) = 8.85E-12

## The Attempt at a Solution

I know that the object doesn't not have any flux through any of the sides except the left and right sides(those parallel to the electric field). So I thought to find net flux and multiply that by the permittivity constant and find the net charge enclosed.

Flux1 = (α +β (a+c)^2)*(a*b) = Electric field * area of the side(right)

Flux2 = (α +β (a)^2) * (a*b) = Electric field * area of the other side(left)

Then:

Flux1 + Flux2 = 0.709925351759

Therefore I multiply by epsilon naught:

net flux * epsilon naught = 6.28283939307E-12

However this is wrong, I believe I am messing up because of the weird way they are giving the electric field as, or possibly my entire calculations or process?