How Strong is the Magnetic Field Inside a Toroid?

[hellogirl88]

You are going to wrap a toroid with 273 m of copper wire that can carry a current of I = 1.7 A. The toroid has radius R = 16 cm and cross sectional diameter D = 1.2 cm. How large a magnetic field (T) can you make at the average toroidal radius?

I have been using the formula B = (\mu*N*I)/2*\pi*R
where \mu = 4\pi*10^-7, N = number of windings of the coil, and I is the current...I have no idea how to figure out N though. Any help would be greatly appreciated.

 

[Doc Al]

You know how long the wire is and the size of the toroid. How many turns can you make with that much wire?

 

[hellogirl88]

well L = 272m, and I am given R and the cross sectional diameter, and I know I need to combine those to get the size of the toroid, but I don't know how to combine them. I've attached a picture that associated with the problem.

 

[Doc Al]

Hint: What's the circumference of the toroid cross-section?

 

[hellogirl88]

Well, circumference = diameter time pi, so would the cross sectional circumference = pi * 1.2cm ? Even so, I am still really confused how to incorporate that into finding the total area of the circle. I understand I should essentially be thinking of the toroid as an inner circle and outer circle, but I can visualize how to incorporate both into the total area...

 

[Doc Al]

Well, circumference = diameter time pi, so would the cross sectional circumference = pi * 1.2cm ?

Good. So how many times can you wrap the wire around that circumference?

Even so, I am still really confused how to incorporate that into finding the total area of the circle.

You don't need the area of the circle, just the circumference.

 

[hellogirl88]

Thank you so so much! It makes much more sense to me now. Another student in my class explained it in a way that implied needing the area of the circles, which is what confused me. Thanks again