Question

A tightly wound 1000-turn toroid has an inner radius 1.00 cm and an outer radius 2.00 cm, and carries a current of 1.50 A. The toroid is centered at the origin with the centers of the individual turns in the z = 0 plane. Determine the magnitude field at a distance of 1,10 cm from the origin.

Answer 1

Therefore, the magnitude of magnetic field at a distance 1.10cm from the origin is 27.3mT

Step-by-step explanation:

Given;

Number of turns, N = 1000

Inner radius, r₁ = 1cm

Outer radius, r₂ = 2cm

Current, I = 1.5A

Magnetic field strength, B = ?

The magnetic field inside a tightly wound toroid is given by B = μ₀ NI / 2πr

where,

a < r < b and a and b are the inner and outer radii of the toroid.

The magnetic field of toroid is

`B = (u_oNI)/(2\pi r)`

Substituting the values in the formula:

`B (1.10cm) = ((4\pi X 10^-^7 ) ( 1000)(1.5))/(2\pi (1.10) ) \\\\`

`B (1.10cm) = 27.3mT`

Therefore, the magnitude of magnetic field at a distance 1.10cm from the origin is 27.3mT