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

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The magnetic field at the center of a circular arc can be calculated using the Biot-Savart law. For a circular arc of radius r carrying current I, the magnetic field is expressed as (μI)/(2r). When considering a straight wire bent into a 90-degree arc, the magnetic field contribution from the arc is (1/4)(μI)/(2r). The superposition principle allows for the addition of the magnetic fields from both the arc and the straight wire. This approach provides a comprehensive understanding of the magnetic field at point P.
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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 \frac{\mu I}{2r} seems to be the magnetic field generated by a whole circle. Thus the field generated by the arc in the picture is \frac{1}{4}\frac{\mu I}{2r}.

EDIT: Replied the same minute :smile:.
 
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