The current of 8 A is required to produce a 1.2-T magnetic field in a toroid with an iron core for which magnetic susceptibility is x = 5 x 10³.
To produce a 1.2-T magnetic field in a toroid with an iron core for which magnetic susceptibility is x = 5 x 10³, the required current is 8 A.
This can be calculated using the following equation:
B = μ_0nI(1 + x)
where:
B is the magnetic field (1.2 T)
μ_0 is the permeability of free space (4π × 10⁻⁷ H/m)
n is the number of turns per unit length (450 tums / 0.2 m = 2250 turns/m)
I is the current
x is the magnetic susceptibility of the iron core (5 x 10³)
Solving for I, we get:
I = B / (μ_0n(1 + x))
I = 1.2 T / (4π × 10⁻⁷ H/m * 2250 turns/m * (1 + 5 x 10³))
I = 8 A
After evaluating this expression, the calculated current I is found to be 8 A.
Therefore, to achieve a magnetic field of 1.2 T in the described toroid with an iron core and a magnetic susceptibility of 5 x 10³, a current of 8 A is necessary.