Flux induced in a circular loop

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Homework Help Overview

The discussion revolves around calculating the magnetic flux induced in a circular loop due to an infinitely long current-carrying wire. The loop has a radius of 1 m and is positioned 2 m away from the wire, with the current being alternating. Participants are exploring the relationship between the magnetic field and the geometry of the setup.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formulation of the integral for calculating the magnetic flux, with one participant noting their approach based on examples with square loops. Questions arise regarding the derivation of the integral used for the flux calculation and the clarity of the setup's geometry.

Discussion Status

There is an ongoing exploration of the mathematical formulation involved in the problem. Participants are questioning the derivation of the integral and clarifying the spatial relationship between the circular loop and the wire. No consensus has been reached, but there is active engagement with the mathematical aspects of the problem.

Contextual Notes

One participant emphasizes the importance of a diagram for clarity, indicating that the spatial arrangement of the loop and wire is crucial for understanding the problem. The discussion reflects a focus on the assumptions regarding the plane in which both elements lie.

meaghan
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Homework Statement


I have a circular loop with a radius of 1 m. The center of the loop is located 2 m away from a infinitely long current carrying wire, with ac current I. Find the flux in the circular loop

Homework Equations


Φ = ∫ B ds

The Attempt at a Solution


I've found a lot of examples with square loops, so the magnetic field in the loop will depend on both the x and y direction.
I got that Φ = ∫ uo I / π(2+y) *√(1-y2) since the magnetic field will change according to the point on the circle.
 
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A diagram is always helpful. From your statement, it is not clear if the circular loop and the long wire are in one plane.
 
upload_2017-10-29_14-5-4.png


it's all in one plane
 

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How did you write the integral for the flux?
 
Chandra Prayaga said:
How did you write the integral for the flux?
Φ = ∫ uo I √(a2+y2) / (π (2a+y)) dy
 
My question was, do you know how that integral was derived?
 

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