PHYS 221
General Physics II  Calculus Supplement
Grist
Homework Solution “Gauss’ Law”
Problem:
A Cube with sides of length A, is in an uniform electric field
E
that
points in the
ˆ
X
direction.
a)
Find the flux through
each
of the six sides.
b)
Find the total flux through the cube.
Be sure to show all of your work.
Hint:
Set the coordinate system so
that the back left corner is at the origin as in the diagram.
Solution:
The flux through a side is described by
Ed
A
. We can first deal with the dot product by
reducing the argument of the integral to
ECos dA
ECos
dA
and then moving the Electric
field term and Cosine out of the integral, as they are both constants. Each side of the cube has
length A and the area of any side is simply A
2
. Because we are integrating over the area of sides
of each side, the limits of integration are 0 to A
2
. This reduce the flux to a general solution of
2
EACos
.
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 Spring '09
 G.R.GRIST
 Work, Flux, cosine function

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