What Is the Range of Magnetic Field Values Inside a Toroid?

[Angie K.]

Homework Statement

A toroid has a 49.4-cm inner diameter and a 57.4-cm outer diameter. It carries a 23 A current in its 500 coils. Determine the range of values for B inside the toroid.

A) Bmaximum = ?
B) Bminimum = ?

Homework Equations

B = mu0/2pi * NI/r[/B]

The Attempt at a Solution

I tried plugging in the values from the problem but I am not sure where I am going wrong.

B minimum = Mu0 * 500 * 23 / 2 pi * (.494/2)

B maximum = Mu0 * 500 * 23 / 2 pi * (.572/2)

Am I doing something wrong with the radius? Is the B minimum not thre inner r and the maximum the outer r?

 

[CWatters]

Is the B minimum not the inner r and the maximum the outer r?

No it's the other way around.

http://physics.aalto.fi/pub/kurssit/Tfy-3.15xx/Tp_ohjeet/33en.pdf

..the magnetic field strength decreases inversely proportional to the distance from the torus center

If you divide by a smaller number (eg inner radius) you get a larger result (eg maximum B).

 

[Angie K.]

No it's the other way around.

http://physics.aalto.fi/pub/kurssit/Tfy-3.15xx/Tp_ohjeet/33en.pdf
If you divide by a smaller number (eg inner radius) you get a larger result (eg maximum B).

So the equation becomes

B maximum = Mu0 * 500 * 23 / 2 pi * (.494/2)

B minimum = Mu0 * 500 * 23 / 2 pi * (.572/2)

?

 

[CWatters]

Yes.