Calculating Force from Two Circular Rings | Exam Prep

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To calculate the force between two circular rings carrying current, the magnetic field produced by one ring at the location of the other can be determined using the formula B = μ₀I/(2πr). The force on one ring due to the magnetic field of the other can then be calculated using F = IL x B. However, integrating around the entire circle may be necessary for an accurate result, especially given the separation distance of 0.10 cm. The approach of using the magnetic field and force equations is valid, but attention to the geometry and integration may be required for precise calculations. Proper understanding of these concepts is crucial for exam preparation.
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Consider two circular rings, each of radius R = 25.0 cm ,
separated by 0.10 cm as shown. Each ring carries a current
I = 3.0 A. What is the magnitude of the force exerted on one ring by
the other ring?

is there any way to do this without integrating around the whole circle??

I have an exam tomorrow and some advice would be greatly appreciated.
 
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i tried using B=u0I/2Pi*r to get the magnetic field, then using F = ILxB to get force on one ring to another, but I don't think Its right
 
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