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

AI Thread Summary
The calculation for the length of the sides of a wire loop in a uniform magnetic field was initially incorrect due to a missing square root in the final equation. The correct formula is s = √(τ / (NIB sin θ)), which yields a length of 0.0632 m or 6.32 cm. The user also discovered that their calculator was set to radians instead of degrees, which contributed to the confusion. After correcting these errors, the user expressed relief and gratitude for the assistance received. Accurate calculations are crucial in physics problems involving magnetic fields and loops.
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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