# Homework Help: Magnetic field at the centre of a circular current loop

1. Aug 15, 2015

### dk_ch

1. The problem statement, all variables and given/known data

How to calculate the magnetic field at the centre of a circular current (I) loop of radius r using Ampere law
2. Relevant equations
B = μ0I/2r

3. The attempt at a solution
I take circulation along the circular closed path of radius r passing through the center of the loop and obtain wrong relation B = μ0I/2πr

Last edited: Aug 15, 2015
2. Aug 15, 2015

### Qwertywerty

You can not use Ampere's law to find the magnetic field at any point in the loop - nor at center , nor at any other point inside the loop .

3. Aug 15, 2015

### dk_ch

The circuital law helps to determine magnetic field due to current in case of solenoid ,toroid and straight current carrying wire. Why does it fail for circular current loop?

4. Aug 15, 2015

### Qwertywerty

Firstly , Ampere's law , is obviously valid always .

However , since it does not give us a direct relation of magnetic field with a certain quantity , it is useful in finding the magnetic field in only certain symmetric cases , whereby we are able to seperate out B , and are able to equate it to such a quantity .

In the cases you mention , we have used certain conditions to actually find the magnetic field . For example , in the case of the straight current carrying wire , we assume it is of infinte length .

Hope this helps .