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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