Calculating Magnetic Field Using Biot-Savart Law for Concentric Arcs

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SUMMARY

The discussion focuses on calculating the magnetic field at point P using the Biot-Savart Law for concentric arcs carrying a current of 6.90 A. The outer arc has a radius of 65.0 cm, while the inner arc has a radius of 41.0 cm, with an angle of 60 degrees involved in the calculation. The magnetic field is determined by integrating the contributions from both arcs, utilizing the formula db = (μI dl x r) / (4πr³) to simplify the calculations through vector cross products.

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  • Understanding of the Biot-Savart Law
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  • Ability to perform integration in physics problems
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Homework Statement


The closed loop shown in the figure below carries a current of 6.90 A in the counterclockwise direction. The radius of the outer arc is 65.0 cm, that of the inner arc is 41.0 cm. Find the magnitude of the magnetic field at point P if the angle 60 deg.

Homework Equations


Savart
[tex]db=\frac{uI dl x r}{4\pi r^3}[/tex]
dl and r are vectors
x means cross product

The Attempt at a Solution


Basically integrate the outer wire, the inner wire and add them up right?
 

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You will have to split the question into 4 parts to find the contribution of the 4 different sections. The cross product is useful here as it simplifies the different parts greatly.
 
I figured it out.
 

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