Question

The current in the windings of a toroidal solenoid is 2.400 A. There are 500 turns, and the mean radius is 25.00 cm. The toroidal solenoid is filled with a magnetic material. The mag- netic field inside the windings is found to be 1.940 T. Calculate: (a) the relative permeability

(b) the magnetic susceptibility of the material that fills the toroid.

Answer 1

The relative permeability of the magnetic material is 1.213 x 10^5 and the magnetic susceptibility is also 1.213 x 10^5.

Step-by-step explanation:

To calculate the relative permeability of the magnetic material that fills the toroidal solenoid, we can use the formula:

μ = B / (μ0 × N × I)

Where μ is the relative permeability, B is the magnetic field, μ0 is the permeability of free space (4π×10-7 T·m/A), N is the number of turns, and I is the current. Plugging in the given values, we get:

μ = 1.940 T / (4π×10-7 T×m/A × 500 turns × 2.400 A) = 1.213 × 105

To calculate the magnetic susceptibility, we can use the formula:

χ = μ - 1

Where χ is the magnetic susceptibility. Plugging in the calculated value of μ, we get:

χ = 1.213 × 105 - 1 = 1.213 × 105

Answer 2

(a) The relative permeability of the solenoid is 321.6.

(b) The magnetic susceptibility of the material that fills the toroid is 320.6.

How to calculate the relative permeability?

(a) The relative permeability of the solenoid is calculated by applying the following formula.

B = μNμrI/L

μr = BL/μNI

where;

• B is magnetic field strength
• L is the mean radius
• N is the number of turns
• I is the current

μr = BL/μNI

μr = (1.94 x 0.25) /(4π x 10⁻⁷ x 500 x 2.4)

μr = 321.6

(b) The magnetic susceptibility of the material that fills the toroid is calculated as;

X = μr - 1

X = 321.6 - 1

X = 320.6