A long solenoid with 15 turns per centimeter has a core of annealed iron.When the current is 1.00 A,the magnetic field inside the iron core is 2.46 T.The magnetization M is approximately A)1.80 $\times$ 10^-4 A/m B)1.31 $\times$ 10⁶ A/m C)1.96 $\times$ 10⁶ A/m D)5.56 $\times$ 10^-4 A/m E)1.50 $\times$ 10⁴ A/m

Question

Quizplus · Accepted Answer

The magnetization M can be calculated using the formula:

M = B/μ0 - H

where B is the magnetic field inside the core, μ0 is the permeability of free space (4π×10−7 T⋅m/A), and H is the magnetic field strength due to the current in the solenoid, given by:

H = nI

where n is the number of turns per unit length (in this case, per cm) and I is the current.

Substituting the given values, we get:

H = 15 turns/cm x 1.00 A = 15 A/cm

μ0 = 4π×10−7 T⋅m/A

B = 2.46 T

M = (2.46 T) / (4π×10−7 T⋅m/A) - (15 A/cm)
M = 1.96×10^6 A/m

Therefore, the best choice is C, which has the value of M as 1.96×10^6 A/m.

A Long Solenoid with 15 Turns Per Centimeter Has a Core