Electric flux through cubical box

[toothpaste666]

Homework Statement

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.

Homework Equations

∫EdA = flux

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?

 

[BvU]

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

 

[toothpaste666]

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

 

[rude man]

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

ε∇⋅E = ρ.

 

[toothpaste666]

ε∇⋅E = ρ.

What does this mean?

 

[rude man]

What does this mean?

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