It is not clear without a picture. It takes much time.
Using the symmetry along the z axis
where
is the projection of electric field to z axis
and
This is a problem in electromagnetics applying coulomb's law, in brief, we have a disc(wire) with charges on it. We want to calculate the electric field at a point on the axis of the disc. The book had a rather annoying way of solving the problem, so I wanted to go with something simpler and went with the following:
. R is a unit vector
.
.
when we put all of that together, we get:
.
But unless we take away the 2 s from the vector we won't get to the right answer which is .
Note: integral limits and .
What did I do wrong?
Dear zzzoak,
Thanks for the reply
I know it takes a lot of time... My professor used your way but I didn't like it, I was testing a new way. Now my question is, why doesn't my way work?
Is there something we must know when integrating vectors? (integrating vectors as in sum of a very large number of vectors).
Best,