Direction of magnetic field due to a toroid

[Pushoam]

Homework Statement

To find the direction of magnetic field due to a toroid.

Homework Equations

The Attempt at a Solution

Taking the cross - sectional shape of toroid circular, the toroid could be turned into a solenoid. A solenoid's magnetic field is along its axis. When the solenoid gets turned into a toroid, its axis becomes circumferential.
So, the direction of magnetic field is circumferential. Is this correct?

 

[cnh1995]

So, the direction of magnetic field is circumferential. Is this correct?

Yes.

 

[Pushoam]

Yes.

I want to know about the argument. Is the argument correct?
And is there anyway to generalize it for any cross-sectional shape?

 

[cnh1995]

I want to know about the argument. Is the argument correct?

Yes. In fact, there is no magnetic field outside the toroid.

And is there anyway to generalize it for any cross-sectional shape?

I'm not an expert, but I don't think so. Factors like shape, symmetry, permeability of the material affect the field.

 

[Pushoam]

Thanks.