Magnetic Field Due to a Circular Loop

In summary, the magnetic field at the center of a conductor with a circular loop of radius .0584 m and carrying a current of 9.68 A can be determined by using the formula B = (u*I)/(2*pi*r), modified by multiplying by the total length of wire around the loop. This formula differs from the one used for a straight wire, and it is important to recall the principles of Biot-Savart when solving this problem.
  • #1
JamesL
33
0
"A conductor consists of a circular loop of radius .0584 m and straight long sections. The wire lies in the plane of the paper and carries a current of 9.68 A.

Determine the magnitude of the magnetic field at the center of the loop. Answer in units of T."

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Perhaps I am not taking into account the long straight sections, but i believed that they did not affect the mag field at the center of the loop, correct?

Anyway,

using B = (u*I)/(2*pi*r), i got an incorrect answer. is this formula incorrect?
 
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  • #2
The formula you used applies for a straight wire and is thus incorrect.

You need to modify your formula by multiplying by the total length of wire around the loop.

Claude.
 
  • #3
You might want to recall what you learned about Biot-Savart.
 

1. What is a magnetic field due to a circular loop?

A magnetic field due to a circular loop is a region in space where a magnetic force is exerted on a charged particle. It is created by a circular current loop, which is a loop of wire through which an electric current flows.

2. How is the strength of the magnetic field calculated for a circular loop?

The strength of the magnetic field for a circular loop can be calculated using the formula B = (μ₀I)/(2r), where B is the magnetic field strength, μ₀ is the permeability of free space, I is the current flowing through the loop, and r is the distance from the center of the loop to the point where the field is being measured.

3. What is the direction of the magnetic field around a circular loop?

The direction of the magnetic field around a circular loop follows the right-hand rule. If you curl your fingers in the direction of the current flow, your thumb will point in the direction of the magnetic field.

4. How does the radius of a circular loop affect the strength of the magnetic field?

The strength of the magnetic field is directly proportional to the radius of the circular loop. This means that the larger the radius, the stronger the magnetic field will be.

5. What are some real-world applications of the magnetic field due to a circular loop?

The magnetic field due to a circular loop has many practical applications, such as in electric motors, generators, and MRI machines. It is also used in particle accelerators and in studying the behavior of charged particles in space.

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