- #1

oreosama

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## Homework Statement

I got home from a test, had an extra credit problem semi memorized and am wondering how I was suppose to solve.

http://i.imgur.com/cIOdSvk.png

A plane with sides [itex]L[/itex] is at [itex]x=3[/itex] . An electric field [itex]E = α y^2 x i + α z^2 y j[/itex] passes through (where [itex]\alpha[/itex] is a constant). Find the flux through the plane. (Givens are [itex] L, \alpha[/itex]

## Homework Equations

[itex]\Phi = \oint E \cdot dA[/itex]

## The Attempt at a Solution

Frankly I didn't feel like I knew what I was doing. The plane varies along y and z and the vector for dA will always go in the i direction

[itex]dA i = dydz i[/itex]

[itex]E \cdot dA = \alpha y^2 x dydz[/itex]

[itex]\int_0^L \int_0^L y^2 x dydz[/itex]

[itex]L \alpha x \frac{y^3}{3}|^L_0[/itex]

[itex] \frac{L^4}{3} \alpha x[/itex]

x=3

[itex] L^4 \alpha [/itex]

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