Magnetic Field of Toroid

In summary, You can make a magnetic field of B = 5.58*10^-5 T at the average toroidal radius using the given information of 273 m of copper wire, current of I = 1.7 A, toroid radius R = 16 cm, and cross sectional diameter D = 1.2 cm. By calculating the circumference of the toroid cross-section, you can determine the number of windings N and use it in the formula B = (\mu*N*I)/2*\pi*R to find the maximum magnetic field.
  • #1
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 = ([tex]\mu[/tex]*N*I)/2*[tex]\pi[/tex]*R
where [tex]\mu[/tex] = 4[tex]\pi[/tex]*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.
 
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  • #2
You know how long the wire is and the size of the toroid. How many turns can you make with that much wire?
 
  • #3
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.
 

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  • #4
Hint: What's the circumference of the toroid cross-section?
 
  • #5
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...
 
  • #6
hellogirl88 said:
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.
 
  • #7
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
 

1. What is a toroid?

A toroid is a type of three-dimensional geometric shape that resembles a donut or a tire. It is formed by rotating a circle around an axis that is parallel to the circle's plane.

2. What is the magnetic field of a toroid?

The magnetic field of a toroid is a circular magnetic field that is produced by a current flowing through a wire that is coiled around the toroid's surface. The strength of the magnetic field depends on the number of turns in the wire and the amount of current flowing through it.

3. How is the magnetic field of a toroid calculated?

The magnetic field of a toroid can be calculated using the formula B = (μ0 * N * I) / (2π * r), where B is the magnetic field strength, μ0 is the permeability of free space, N is the number of turns in the wire, I is the current, and r is the radius of the toroid.

4. What is the direction of the magnetic field in a toroid?

The direction of the magnetic field in a toroid is always tangential to the circle formed by the wire. This means that the magnetic field lines are always perpendicular to the plane of the toroid and point in a clockwise or counterclockwise direction, depending on the direction of the current in the wire.

5. What are the applications of a toroid's magnetic field?

The magnetic field of a toroid has many practical applications, including in transformers, inductors, and electromagnets. It is also used in various electronic devices such as speakers, motors, and generators. Additionally, the magnetic field of a toroid is important in understanding the behavior of magnetic materials in physics and engineering.

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