Calculating Magnetic Field at Center of Circular Arc | Loop Current Bending

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Homework Help Overview

The discussion revolves around calculating the magnetic field at the center of a circular arc formed by bending a straight wire carrying current. The context involves concepts from electromagnetism, specifically related to magnetic fields generated by current-carrying conductors.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the Biot-Savart law and the superposition principle to determine the magnetic field. There are questions about how to combine the magnetic fields from the arc and the straight wire, as well as uncertainties regarding the correct expressions for each segment.

Discussion Status

Some participants have provided guidance on using the superposition principle and have suggested specific formulas for the magnetic fields. There is an ongoing exploration of how to correctly sum the contributions from the arc and the straight wire, with no explicit consensus reached yet.

Contextual Notes

Participants are navigating through the problem with some uncertainty about the initial conditions and the correct application of formulas, particularly regarding the contributions from different sections of the current-carrying wire.

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iv)The magnetic field, B at the center of a circular current loop of radius r carrying current I, is given by the expression . If one of the long straight wires is bent 90o in a circular arc of radius r (refer to Figure B1). What is the magnetic field at the center of the arc P?

Can anyone help me? Help needed.
 

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Please show what you've tried.

Use the Biot-Savart law.
 
What i know is for the arc section, the magnetic field should be (miu)I / 2r and for the straight wire is (miu)I / 2(pie)r. I don't know how to start this question. Should I just sum up both magnetic field?
 
Using the superposition principle, yes you may add them together. The [tex]\frac{\mu I}{2r}[/tex] seems to be the magnetic field generated by a whole circle. Thus the field generated by the arc in the picture is [tex]\frac{1}{4}\frac{\mu I}{2r}[/tex].

EDIT: Replied the same minute :smile:.
 

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