Question

A toroid is made of 2 000 turns of wire of radius 2.00 cm formed into a donut shape of inner radius 10.0 cm and outer radius 14.0 cm. When a 30.0-A current is present in the toroid, the magnetic field at a distance of 11.0 cm from the center of the toroid is___________

Answer 1

To solve this problem we will apply the concepts related to the magnetic field in a Toroid, this can be defined as the product between the free space permeability, the number of turns and the current, due to the change in the perimeter of the Toroid. In mathematical terms this is,

$B = \frac{\mu NI}{2\pi r}$

N = Number of turns

$\mu$= Permeability of free space

I = Current in the Toroid

r = Distance from the wire to the field point

Our values are given as,

$\mu = 4\pi *10^{-7}T \cdot m/A$

$I = 30A$

$N = 2000$

$r = 11.0cm = 11.0*10^{-2}m$

Replacing,

$B = \frac{(4\pi *10^{-7})(2000)(30)}{2 \pi (11.0*10^{-2})}$

$B = 0.109T$

$B = 109mT$

Therefore the magnetic field at a distance of 11.0cm from the center of the Toroid is 109mT