Magnetic field at the centre of a circular current loop

In summary, the conversation discusses how to calculate the magnetic field at the centre of a circular current loop using Ampere's law. However, it is mentioned that Ampere's law cannot be used to find the magnetic field at any point in the loop, including the centre. The law is only useful in certain symmetric cases, such as solenoids, toroids, and straight current carrying wires. The reason for this limitation is due to Ampere's law not providing a direct relation between the magnetic field and a specific quantity.
  • #1
dk_ch
44
0

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]
 
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  • #2
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
Qwertywerty said:
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?
 
  • #4
dk_ch said:
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 .
 

1. What is a magnetic field at the centre of a circular current loop?

A magnetic field at the centre of a circular current loop is a region in space where a magnetic force is exerted on any magnet or moving charged particle. It is caused by the flow of electric current through a circular loop of wire.

2. How is the direction of the magnetic field determined at the centre of a circular current loop?

The direction of the magnetic field at the centre of a circular current loop can be determined using the right-hand rule. If you point your right thumb in the direction of the current flow, the direction in which your fingers curl represents the direction of the magnetic field.

3. What factors affect the strength of the magnetic field at the centre of a circular current loop?

The strength of the magnetic field at the centre of a circular current loop is affected by the magnitude of the current flowing through the loop, the number of loops in the wire, and the distance from the centre of the loop. Increasing any of these factors will result in a stronger magnetic field.

4. How does the magnetic field at the centre of a circular current loop change as you move away from the centre?

The magnetic field at the centre of a circular current loop is strongest at the centre and decreases as you move further away from the centre. This is because the distance from the centre affects the strength of the magnetic field, with the field becoming more spread out and weaker as you move away.

5. What are some real-life applications of the magnetic field at the centre of a circular current loop?

The magnetic field at the centre of a circular current loop has various applications in everyday life, including in electric motors, generators, and MRI machines. It is also used in compasses for navigation and in particle accelerators for scientific research.

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