Understanding the Use of Magnetic Field in MIT Problem 4 31-9

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Homework Help Overview

This discussion revolves around an MIT problem related to the magnetic field and its application in a specific scenario involving a current-carrying wire and a loop. Participants are examining the setup and the mathematical treatment of the magnetic field in relation to the loop's dimensions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the use of variables and the setup of the problem, particularly the designation of 'x' for the B-field and the distance from the rod to the loop. There is also discussion about the integration of the magnetic field over the area of the loop and the implications of the loop's dimensions.

Discussion Status

Some participants are seeking clarification on specific terms and dimensions, while others are attempting to reconcile their understanding with the mathematical expressions provided in the problem. There is an ongoing exploration of the relationships between the variables involved, and guidance has been offered regarding the integration process necessary for calculating magnetic flux.

Contextual Notes

Participants are working without a visual aid, which has led to some confusion regarding the problem's setup. The discussion includes references to specific dimensions (h, w, L) and the need for integration to accurately assess the magnetic flux through the loop.

flyingpig
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what is h?

can you tell me via some image?
 


They are integrating the B field over the area inside the loop. (Since I don't have the figure, I must go by the mathematics in their solution.) The loop must be distance, h, from the current carrying wire. The loop extends a distance, w, in the x direction and a distance L in the y direction.
 
Last edited:


Hm you are right, let me get the picture.
 


What do you mean "x direction"?

When I first did it I did this

\Phi = B \cdot A = \frac{\mu_0 I}{2\pi (h + w)} \cdot Lw
 


flyingpig said:
What do you mean "x direction"?

When I first did it I did this

\Phi = B \cdot A = \frac{\mu_0 I}{2\pi (h + w)} \cdot Lw

The magnetic field you used only applies at the very bottom of the loop. In general, B is given by mu_0*I/(2*pi*r), where r is the distance from the wire. You have to integrate over the area of the loop to get the flux.
 

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