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

In summary, the conversation involved a calculation using variables ##\tau=0.0727, N=60, i=1.3, B=1.0,## and ##\theta=15##. The first attempt at the calculation was using the equation ##\tau=NIABsin\theta##, while the second attempt used ##\tau=NIs^2Bsin\theta##. After realizing a mistake in the calculation, the correct answer was found using ##s=\sqrt{\frac{\tau}{NIBsin\theta}}=0.0632m=6.32cm##. The conversation also mentioned an issue with the calculator being set to degrees.
  • #1
cestlavie
10
3
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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  • #2
One thing, the dimensions of the last equation is length squared.
 
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Likes cestlavie
  • #3
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##
 
  • #4
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.
 

1. How does the length of sides of a wire loop affect its interaction with a uniform magnetic field?

The length of sides of a wire loop does not directly affect its interaction with a uniform magnetic field. However, it can indirectly impact the strength of the induced current in the wire loop, which is determined by the rate of change of the magnetic flux through the loop.

2. What is the formula for calculating the induced current in a wire loop in a uniform magnetic field?

The formula for calculating the induced current in a wire loop is I = -nA(dB/dt), where I is the induced current, n is the number of turns in the loop, A is the area of the loop, and dB/dt is the rate of change of the magnetic field.

3. How does the orientation of the wire loop in a uniform magnetic field affect the induced current?

The orientation of the wire loop in a uniform magnetic field can affect the induced current. If the loop is perpendicular to the magnetic field, the induced current will be at its maximum. If the loop is parallel to the magnetic field, the induced current will be zero.

4. Can the length of sides of a wire loop be changed to increase the induced current?

Yes, the length of sides of a wire loop can be changed to increase the induced current. Increasing the length of the loop will increase the area, which in turn will increase the rate of change of the magnetic flux and therefore increase the induced current.

5. How can the length of sides of a wire loop be measured accurately?

The length of sides of a wire loop can be measured accurately using a ruler or caliper. It is important to ensure that the measurement is taken from the same point on each side of the loop to avoid any discrepancies. Additionally, multiple measurements should be taken and averaged to increase accuracy.

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