Electric flux,

$\overline{){{\mathbf{\Phi}}}_{{\mathbf{E}}}{\mathbf{=}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{E}}{\mathbf{\xb7}}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{A}}}$

Gauss' law:

$\overline{){{\mathbf{\Phi}}}_{{\mathbf{E}}}{\mathbf{=}}\frac{{\mathbf{q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{{\mathit{\u03f5}}_{\mathbf{0}}}}$

**(a)**

Flux through right side

x = L

E = (a + bL) **x̂** + c **ŷ**

A_{right} = L^{2} **x̂**

Φ_{E,right} = ((a + bL) **x̂** + c **ŷ**)•(L^{2} **x̂**) = (a + bL)(L^{2} + 0) = aL^{2} + bL^{3}

Flux through left side,

x = 0 - origin

E = (a + b•0) **x̂** + c **ŷ**

A_{left} = −L^{2} **x̂**

Φ_{E,letf} = ((a + b•0) **x̂** + c **ŷ**)•(−L^{2} **x̂**) = (a)(L^{2} + 0) = - aL^{2}

Flux through front side,

x = L

E = (a + bL) **x̂** + c **ŷ**

A_{front} = L^{2} **ẑ**

Φ_{E,front} = ((a + bL) **x̂** + c **ŷ**)•(L^{2} **ẑ**) = (0 + 0 + 0) = 0

A cube has one corner at the origin and the opposite cornerat the point (L,L,L). The sides of the cube are parallel to the coordinate planes. The electric field in and around the cube is given by **E** = (a + bx) **x̂** + c **ŷ**.

Find the total electric flux Φ_{E} through the surface of the cube. Express your answer in terms of a,b,c and L.

What is the net charge q inside the cube? Express your answer in terms of a, b, c, L, and ϵ_{0}.

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