Find field intensity at center of toroid?

[D.B0004]

Homework Statement

I really think my answer is correct - could someone verify this or let me know where I went wrong? This is problem submitted online, the "correct" answer looks like my teacher accidentally hit the button 3 twice.
PROBLEM:
The toriod in example 5-1 from the textbook has an inner diameter of 3.1 cm and an outer diameter of 4 cm. 8 amps are flowing through 41 turns on the toroid.

What is the field intensity very close to the inside diameter (A/m)?

See attachment for figure.

Homework Equations

Rm = 0.5*(Di+Do)/2
H = Ni/L
L = 2*PI*Rm

Simply find H.

The Attempt at a Solution

I plugged in the numbers many times and keep getting 367.62. My teacher got 3367.92. Looks like the 3 was clicked twice? Any help appreciated.

 

[TSny]

I'm getting the same answer as your teacher. Note that you are asked to find the field "very close to the inside diameter".

 

[D.B0004]

Okay. Here are my steps
1) Find Rm = (0.01775)/4= 0.01775
2) Find H = Ni*I/(2*PI*Rm) = 42*8/(2IPI*.01775 = 3012.8

I forgot to put the I in my first answer.

I don't see the importance of the "very close to the inside diameter" part and how that effects the equation.

 

[TSny]

Okay. Here are my steps
1) Find Rm = (0.01775)/4= 0.01775
2) Find H = Ni*I/(2*PI*Rm) = 42*8/(2IPI*.01775 = 3012.8

You are using the mean value of R: Rm. But you need to use the value of R that corresponds to being close to the inner diameter.

Did you derive the formula for H in class using Ampere's law, or were you just given the formula without a derivation?

 

[D.B0004]

We were not given it. Maybe they just assume I could derive it? Not sure. But I think I see what you are saying. So rather than going to the Rm, I should just use Ri -->
Ri = .031/2
Didn't derive it but that gives the right answer. Thanks.