Show that the magnetic field at the center of the circular loop is 
and at fixed distance x far away from the loop is 
Solution:
Biot Savart's Law: 
and from the sketch:
By symmetry, total dBy = 0
From the sketch:
=\int&space;\frac{\mu_0}{4\pi}\frac{Idl}{r^2}&space;\frac{R}{r}&space;=\frac{\mu_0&space;I&space;R}{4\pi&space;r^3}\oint&space;dl&space;=\frac{\mu_0&space;I&space;R}{4\pi&space;r^3}&space;2&space;\pi&space;R=\frac{\mu_0&space;I&space;R^2}{2&space;r^3} "\rightarrow B(x)= \int \frac{\mu_0}{4\pi}\frac{Idl}{r^2} \frac{R}{r} =\frac{\mu_0 I R}{4\pi r^3}\oint dl = \frac{\mu_0 I R}{4\pi r^3} 2 \pi R=\frac{\mu_0 I R^2}{2 r^3}")
From the sketch:
=\frac{\mu_0&space;I&space;R^2}{2&space;(R^2+x^2)^{3/2}} "\rightarrow B(x)= \frac{\mu_0 I R^2}{2 (R^2+x^2)^{3/2}}")
At the center of the loop, x = 0=\frac{\mu_0&space;I}{2R} "\rightarrow B(x)= \frac{\mu_0 I}{2R}")
At fixed distance x far away from the loop, x ≫ R
Solution:
and from the sketch:
By symmetry, total dBy = 0
From the sketch:
From the sketch:
At the center of the loop, x = 0
At fixed distance x far away from the loop, x ≫ R
1 comment :
It's a nice post about Biot Savart law
. It's really helpful. I like it. Thanks for sharing it.
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