Current passing through a loop

[AdsBerger]

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

 

[Pythagorean]

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" ;)

 

[AdsBerger]

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

 

[Pythagorean]

Your first line (with =) looks wrong 3.14x10^-6?

 

[AdsBerger]

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.

 

[Pythagorean]

You could always check it:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

 

[AdsBerger]

i actually tried using that but not to sure on all of its function, as soon as i enter 5 A it calculates everything

 

[Pythagorean]

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.

 

[AdsBerger]

i entered my .9m and 5 A to get a B of 0.000003399992 what does this tell me ?

 

[Pythagorean]

let's assume hyperphysics is right, first. What does that tell you?

 

[AdsBerger]

well that somewhere in my calculations i am wrong. redid it to get 9.2x10^-4 which when plugged into the site is correct

 

[Pythagorean]

congrats :)