Length of sides of a wire loop in a uniform magnetic field

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Homework Help Overview

The discussion revolves around calculating the length of the sides of a wire loop in a uniform magnetic field, utilizing the torque equation involving the number of turns, current, magnetic field strength, and angle. Participants are exploring the relationships between these variables and the implications of their calculations.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the side length of a wire loop using the torque formula, but expresses uncertainty about their result. Some participants point out dimensional inconsistencies in the calculations, while others reflect on potential errors in using their calculator settings.

Discussion Status

The discussion is ongoing, with participants providing feedback on the calculations and addressing errors. There is an acknowledgment of mistakes made in the calculations, particularly regarding the square root and calculator settings, which may influence the results.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can share or the methods they can use. There is a focus on ensuring the calculations align with the physical principles involved.

cestlavie
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Homework Statement
A wire loop with 60 turns is formed into a square with sides of length 𝑠. The loop is in the presence of a 1.00 T uniform magnetic field 𝐵 that points in the negative 𝑦 direction. The plane of the loop is tilted off the 𝑥-axis by ##\theta=15##. If 𝑖=1.30 A of current flows through the loop and the loop experiences a torque of magnitude 0.0727 N⋅m , what are the lengths of the sides s of the square loop, in centimeters?
Relevant Equations
## A=x^2##
## \tau=NIABsin\theta##
If ##\tau= 0.0727, N=60, i=1.3, B=1.0,## and ##\theta=15##, I tried the following calculation:
##\tau=NIABsin\theta##
##\tau=NIs^2Bsin\theta##
##s^2=\frac {\tau} {NIBsin\theta}=\frac {.0727} {60*1.3*1*sin(15)}=0.0632 m=6.32 cm##
The answer is probably right in front of me, but I don't know what I am doing wrong.
 
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One thing, the dimensions of the last equation is length squared.
 
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Keith_McClary said:
One thing, the dimensions of the last equation is length squared.
Oops! I forgot to add the square root! But my answer is for s, not s squared.
##s^2= \frac {\tau} {NIBsin\theta}##
##s=\sqrt {\frac {\tau} {NIBsin\theta}}=0.0632m = 6.32 cm##
 
I feel all kinds of stupid. I tried doing a different set of numbers and realized that my calculator was not in degrees. Thank you @Keith_McClary for your help.
 

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