Magnetic Field Inside a Toroid

In summary, the magnetic field strength inside a toroid with a 49.4-cm inner diameter and a 57.4-cm outer diameter carrying a 23 A current in its 500 coils can be calculated using the equation B = mu0/2pi * NI/r. The range of values for B inside the toroid is Bmaximum = Mu0 * 500 * 23 / 2 pi * (.494/2) and Bminimum = Mu0 * 500 * 23 / 2 pi * (.572/2), with Bmaximum being the magnetic field strength at the inner radius and Bminimum being the magnetic field strength at the outer radius.
  • #1
Angie K.
108
1

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?
 
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  • #2
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).
 
  • #3
CWatters said:
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)

?
 
  • #4
Yes.
 

1. What is a toroid?

A toroid is a donut-shaped object with a circular cross-section, often made of a ferromagnetic material, that is used to create a magnetic field.

2. How is a magnetic field created inside a toroid?

A magnetic field is created inside a toroid when an electric current is passed through its windings. This current generates a magnetic field that is concentrated inside the toroid due to its shape and the alignment of the windings.

3. What is the direction of the magnetic field inside a toroid?

The magnetic field inside a toroid is always perpendicular to the direction of the current in the windings. It is also circular, with the field lines wrapping around the toroid in a concentric manner.

4. How does the magnetic field inside a toroid compare to other shapes?

The magnetic field inside a toroid is much stronger and more concentrated than the field inside other shapes, such as a straight solenoid. This is due to the closed loop of the toroid, which allows for more windings and a more concentrated magnetic field.

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

The magnetic field inside a toroid is used in various applications, such as in transformers, motors, and generators. It is also used in medical devices such as MRI machines, as well as in particle accelerators and other scientific instruments.

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