# Electric flux through cubical box

1. Jan 31, 2015

### toothpaste666

1. The problem statement, all variables and given/known data
If the electric field is constant in direction (horizontal in the x direction) but its magnitude decreases from E1 to E2, determine the flux through a cubical box of side length L if four of the sides of the box are parallel to the field.

2. Relevant equations
∫EdA = flux

3. The attempt at a solution
$\int_0^L EdA = EA|_0^L = E_LA-E_0A = A(E_L-E_0) = L^2(E_L-E_0)$

is this reasoning correct?

2. Jan 31, 2015

### BvU

Can't find a flaw in your working. The exercise itself leaves me wondering how one could bring about such a field.

3. Jan 31, 2015

### toothpaste666

thanks. yeah it seems like a weird question. Would it be like the field between two parallel plates of opposite charge?

4. Jan 31, 2015

ε∇⋅E = ρ.

5. Feb 1, 2015

### toothpaste666

What does this mean?

6. Feb 1, 2015

### rude man

epsilon times the divergence of the E field equals the charge density (aka one of Maxwell's 4 equations). Solving that with your given E field would give you the charge distribution needed to effect the given E field. It was in answer to BvU who wondered how an E field like your given one could be produced. You could solve for ρ(x) if it amused you.

epsilon = dielectric constant

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