Square toriods vs. circula toroids

[blindnz]

Homework Statement

Just a question when determing the B-field inside the volume of a toroid as a function of its radius.
Does it change the problem if the toroid has a non circular cross section i.e a square rather then a circle?

 

[qspeechc]

No. Do the electromagnetic laws say anything about the shape? Only about the space of the area or volume you choose, nothing about what the current is doing inside or outside that.

 

[Shooting Star]

Homework Statement

Just a question when determing the B-field inside the volume of a toroid as a function of its radius.
Does it change the problem if the toroid has a non circular cross section i.e a square rather then a circle?

Do you mean a toroid around which a wire is wound?

If so, then the cross-section has to be the same all along. The shape does not matter. Also, the wire has to be tightly wound, i.e., very less gap between the turns.

If the question pertained to something else, then just ignore all this.

 

[MATHLETE1]

When you say that the square toroid will have the same calculation for the B-field as a circular one do you mean that it will depend on the radius or would it depend on the width of the rectangular cross section. Such as if the cross sectional dimensions were of height of a and length of b the B-field would be:

∫B(dA)= μNI → B∫(dA)=μNI → B(ab)=μNI → B=μNI/(ab) where B is dependent on b.

Or do you mean that B=μNI/(2piR)?

 

[asteriatic]

Yes, the shape of the cross section of a toroid can affect the calculation of the B-field inside. In a circular toroid, the B-field is constant throughout the cross section and can be easily calculated using the formula B = μ0IN/2πr. However, in a square toroid, the B-field may not be constant throughout the cross section and will require a different approach for calculation. This is because the shape of the cross section can affect the distribution of current and magnetic flux within the toroid, ultimately impacting the B-field. Therefore, it is important to take into consideration the shape of the cross section when determining the B-field inside a toroid.