Magnetic field at the centre of a circular current loop

[dk_ch]

Homework Statement

How to calculate the magnetic field at the centre of a circular current (I) loop of radius r using Ampere law

Homework Equations

B = μ₀I/2r

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
[/B]

 

[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 .

 

[dk_ch]

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 .

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?

 

[Qwertywerty]

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?

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 separate 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 infinite length .

Hope this helps .