Flux across a plane with varying electric field

  • Thread starter oreosama
  • Start date
  • #1
51
0

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]
 
Last edited:

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
13,068
3,393
Your work looks correct to me.
 

Related Threads on Flux across a plane with varying electric field

Replies
0
Views
1K
  • Last Post
Replies
3
Views
471
Replies
1
Views
12K
  • Last Post
Replies
1
Views
16K
  • Last Post
Replies
7
Views
906
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
9
Views
5K
Replies
1
Views
17K
Replies
4
Views
5K
Top