Question

Suppose you wish to produce a 1.2-T magnetic field in a toroid with an iron core for which magnetic susceptibility is x = 5 x 10°. The toroid has a mean radius of 10 cm and is wound with 450 tums Hint a. What current is required to produce this magnetic field in the iron core?

Answer 1

The current required to produce a 1.2-T magnetic field in the iron core of a toroid can be calculated using Ampere's law. The calculated current is approximately 8.50 A.

Step-by-step explanation:

To calculate the current required to produce a 1.2-T magnetic field in a toroid with an iron core, we can use Ampere's law. Ampere's law states that the magnetic field inside a closed loop is equal to the product of the permeability of the medium, the current passing through the loop, and the number of turns. In this case, the magnetic susceptibility of the iron core is given as x = 5 x 10°, which means the permeability of the iron core is x times the permeability of free space, u0. The permeability of free space, u0, is 4π x 10⁻⁷ T·m/A. The number of turns in the toroid is 450 turns, and the mean radius of the toroid is 10 cm, which is equivalent to 0.1 m.

Using these values and rearranging Ampere's law, we can calculate the current required as:

B = u0 * x * N * I / (2 * π * r)

Solving for I, we get:

I = (B * 2 * π * r) / (u0 * x * N)

Substituting the given values, we have:

I = (1.2 T * 2 * π * 0.1 m) / (4π x 10⁻⁷ T·m/A * 5 x 10° * 450 turns)

I ≈ 8.50 A