Biot-Savard Law: Find Magnetic Field at Center of Loop

[lemaire]

Homework Statement

A single piece of wire is bent so that it includes a circular loop of radius a. A current I flows in the direction of the x-axis . Find an expression for the magnetic field at the center of the loop.

Homework Equations

The Attempt at a Solution

This is a problem involving the integrated Biot-Savard law

 

[Hootenanny]

This is a problem involving the integrated Biot-Savard law

You are correct, the Biot-Savart law is the way to go.

 

[lemaire]

well i can't find the right expression.

 

[Hootenanny]

well i can't find the right expression.

What have you tried?

 

[lemaire]

this is what i have: (mu_0IL)/(4pia²) with a being the radius and mu_0 being the permeability constant

 

[Hootenanny]

this is what i have: (mu_0IL)/(4pia²) with a being the radius and mu_0 being the permeability constant

Looks correct to me. However it can be simplified by noting that L = 2\pi a.

 

[lemaire]

well i am using a web software and the response you and i agreed on is not the right one. In the picture, the current I comes from the left in the x-axis goes in a circular motion and continues in the x-axis again.