# Magnetic field at centre and inside the toroid

1. May 25, 2013

### Saitama

1. The problem statement, all variables and given/known data
$N=2.5\times 10^3$ 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. Relevant 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.

2. May 25, 2013

### Staff: Mentor

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

3. May 25, 2013

### Saitama

I still don't understand what you mean.

4. May 26, 2013

### 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.

5. May 26, 2013

### Saitama

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.

6. May 26, 2013

### Staff: Mentor

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

7. May 26, 2013

Thank you!