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

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Homework Help Overview

The problem involves determining the magnetic field at the center of a circular loop formed by a wire carrying a current, utilizing the Biot-Savart law. The context is rooted in electromagnetism.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the Biot-Savart law and share their attempts at deriving the magnetic field expression. Questions arise regarding the correctness of the derived expression and its simplification.

Discussion Status

There is an ongoing exploration of the problem, with some participants expressing uncertainty about the derived expression. Guidance has been offered regarding potential simplifications, but there is no consensus on the correctness of the approach due to conflicting information from a web software tool.

Contextual Notes

Participants note that the current flows in a specific direction and continues in a circular motion, which may affect the interpretation of the magnetic field calculation.

lemaire
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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
 
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lemaire said:
This is a problem involving the integrated Biot-Savard law
You are correct, the Biot-Savart law is the way to go.
 
well i can't find the right expression.
 
lemaire said:
well i can't find the right expression.
What have you tried?
 
this is what i have: (mu_0IL)/(4pia2) with a being the radius and mu_0 being the permeability constant
 
lemaire said:
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.
 
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.
 

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