2
$\begingroup$

How do we prove the magnetic field for a circular loop is $\frac{\mu_0I}{2r}$ using Ampere's Circuital law

I proved it using Biot-Savart Law but i am getting $\mu_0I/2\pi r$ instead of $\frac{\mu_0I}{2r}$ while using Ampere's law.

Please help me where I am doing wrong

$\endgroup$

1 Answer 1

2
$\begingroup$

You probably misapplied Ampere's law. This law is usually used to find magnetic field only in special cases when the contour integral can be found as a function of single field value based on symmetry.

Magnetic field of a circular current loop is not so simple and Ampere's law cannot be easily used to find it. In such cases, the method of choice is to use the Biot-Savart law (integrate the contributions to the field due to elements of the circuit) or find vector potential as a function of position and then derive magnetic field from it.

$\endgroup$
2
  • $\begingroup$ I understand that the magnetic field is complicated but i would still like a rigorous mathematical proof $\endgroup$
    – Sayak Adak
    Commented Nov 16, 2018 at 15:07
  • $\begingroup$ I'll try brother $\endgroup$ Commented Nov 16, 2018 at 15:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.