jtbell said:
B = \frac{\mu_{0} I A}{2\pi x^3}
I don't see this equation was give explicitly. What is it supposed to be describing:
a.) Field at Center of Current Loop
b.) Field on Axis of Current Loop
c.) Something elseI could also not find it anywhere on Wikipedia, but I found something which confused me even more:
http://en.wikipedia.org/wiki/Biot–Savart_law
Electric currents (along closed curve):
1.)
\mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3}
- where r is the full displacement vector from the wire element to the point at which the field is being computed and r̂ is the unit vector of r. Using this the equation can be equivalently written:
2.)
\mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2}
I think the first equation can not be without unit vector, and that it is
CIRCLE integral and should be written like this:
1.)
\mathbf{B} = \frac{\mu_0}{4\pi} \oint_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^3}
where top 'r' is unit vector which they missed to denote, and the second equation is
LINE integral and should be written like this:
2.)
\mathbf{B} = \frac{\mu_0}{4\pi}\int_L \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2}Now, if I got that right, the question is why would circle integral be 1/r^3 instead of 1/r^2?
