Magnetic field at centre and inside the toroid

[Saitama]

Homework Statement

$N=2.5\times 10^3$ wire turns are uniformly wound on a wooden toroidal core of a very small cross-section. A current $I$ flows through the wire. Find the ratio $\eta$ of the magnetic induction inside the core to that at the centre of the toroid.

Homework Equations

The Attempt at a Solution

The field inside the core has some finite value and at the centre it is zero. So the ration should be infinite but this wrong. I don't see what I have missed.

 

[mfb]

The toroid is like a second coil, the wire goes around it once.

 

[Saitama]

The toroid is like a second coil, the wire goes around it once.

I still don't understand what you mean.

 

[haruspex]

mfb means that because the wooden core is very thin, when viewed from the centre, O, of the torus you can take the core as having zero thickness. This means that the toroid can be thought of as a simple loop of wire around O.

 

[Saitama]

mfb means that because the wooden core is very thin, when viewed from the centre, O, of the torus you can take the core as having zero thickness. This means that the toroid can be thought of as a simple loop of wire around O.

The magnetic field inside the toroid is $\mu_0NI/(2\pi R)$ where $R$ is the radius of toroid.

Magnetic field at center of a loop is $\mu_0NI/(2R)$. If I find the ratio $\eta$ using these two expressions, it comes out to be independent of N but this is wrong.

 

[mfb]

For the magnetic field at the center, you do not have N turns.

 

[Saitama]

For the magnetic field at the center, you do not have N turns.

Thank you!