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

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SUMMARY

The calculation of the length of the sides of a wire loop in a uniform magnetic field was addressed using the formula ##\tau=NIABsin\theta##. With values ##\tau=0.0727##, ##N=60##, ##i=1.3##, ##B=1.0##, and ##\theta=15##, the correct calculation for side length ##s## was derived as ##s=\sqrt{\frac{\tau}{NIBsin\theta}}=0.0632 m (6.32 cm)##. The initial confusion stemmed from neglecting to take the square root of the result, and a misconfiguration of the calculator's mode (degrees vs. radians) was also identified as a source of error.

PREREQUISITES
  • Understanding of torque in magnetic fields
  • Familiarity with the formula for torque: ##\tau=NIABsin\theta##
  • Basic proficiency in using scientific calculators
  • Knowledge of trigonometric functions and their applications
NEXT STEPS
  • Review the principles of electromagnetism related to torque and magnetic fields
  • Practice calculations involving torque using different values for ##N##, ##i##, ##B##, and ##\theta##
  • Learn about the implications of calculator settings on trigonometric calculations
  • Explore advanced applications of wire loops in magnetic fields, such as in electric motors
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Physics students, electrical engineering students, and professionals working with electromagnetic systems will benefit from this discussion.

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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