# Magnetic field at centre and inside the toroid

#### Saitama

1. 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.

2. Homework Equations

3. 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.

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#### mfb

Mentor
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

Homework Helper
Gold Member
2018 Award
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

Mentor
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!

"Magnetic field at centre and inside the toroid"

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