Current passing through a loop

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A current of 5 A through a wire loop generates a magnetic field of 3.4 x 10^-3 T at the center, leading to the need for calculating the loop's radius using the formula B = μNi / 2r. The permeability (μ) is identified as the magnetic constant, typically approximated by vacuum permeability. Initial calculations yielded an incorrect radius, prompting a reevaluation that corrected the magnetic field value to 6.28 x 10^-6, resulting in a more plausible radius of 0.924 m. Further verification using an online calculator confirmed the revised calculations, indicating that earlier errors were present. Accurate calculations are essential for determining the correct radius in magnetic field problems.
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Homework Statement



A current of 5 A is passed through a single wire loop, producing a magnetic field of 3.4 x 10^-3 T at the center. What is the radius of the loop?

Homework Equations



B = μNi / 2r

The Attempt at a Solution



B = 3.4 x 10^-3
N = 1
i = 5

B = μNi / 2r
3.4 x 10^-3 = (__)(1loop)(5 A) / 2r

what is this u variable ? what does it represent
 
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it's the greek letter, mu, and it's the permeability of the substance with respect to the magnetic field. Often, your substance is air, which can be (very accurately) approximated by the vacuum permeability.

Try googling "magnetic constant" ;)
 
i found a value for it.. 4∏ x10^-7
but the rest of the question goes like this then
= (3.14x10^-6)/2r
= 1.57 x 10^-6/r

3.4 x 10^-3 = 1.57 x 10^-6/r

1.57 x 10^-6 = 3.4 x 10^-3 r
4.62x10^-4 = r

0.0004617647059 m

this doesn't seem right
 
Your first line (with =) looks wrong 3.14x10^-6?
 
redid the first line got the new answer of 6.28x10^-6 not sure of my miscaculation. this resulted in the new answer of .924m seems more plausible.
 
i actually tried using that but not to sure on all of its function, as soon as i enter 5 A it calculates everything
 
you have to enter I and R and it will give you B. Don't need to worry about z, since you're doing center of loop.
 
i entered my .9m and 5 A to get a B of 0.000003399992 what does this tell me ?
 
  • #10
let's assume hyperphysics is right, first. What does that tell you?
 
  • #11
well that somewhere in my calculations i am wrong. redid it to get 9.2x10^-4 which when plugged into the site is correct
 
  • #12
congrats :)
 
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