Physics 230 February 13 2002

**Exercise on analyzing the result of a calculation.**

In class we obtained the electric field produced by a sheet of charge lying in
the
plane, with charge density
that is infinitely long in the
direction,
and extends from
to
On the
axis
the electric field is given
by:

Now
we want to analyze this result.

1. **Dimensions**. The angle is just a number with no
units
The charge density has dimensions of
charge/length
and so the electric field is
charge/length
and these are the correct dimensions.

2. Check the result **a large distance from the strip**.

At a great distance
from the strip, the strip looks like a line charge with line charge density
Thus we should find (Example 24.2)
In our expression,
and so
and we
have

as
expected.

3. Check the result **very close to the strip**. For
the strip "looks" infinitely wide, and so we should obtain the result of
Example 24.5,
In our expression, with
very large,
is almost
and
so

as
expected.

The result passes all three checks and so is probably correct.

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