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 relative permeability K_m is approximately A)1800 B)1310 C)7.64 $\times$ 10^-4 D)5.56 $\times$ 10^-4 E)1500

Question

Quizplus · Accepted Answer

The magnetic field inside the solenoid is given by:

B = μ₀μ_rnI

where μ₀ is the permeability of free space, μ_r is the relative permeability of the material, n is the number of turns per unit length, and I is the current.

Rearranging this equation to solve for μ_r, we get:

μ_r = B/(μ₀nI)

Substituting the given values, we get:

μ_r = (2.46 T)/(4π×10⁻⁷ T·m/A × 15 turns/cm × 0.01 m/cm × 1 A) ≈ 1310

Therefore, the relative permeability of the annealed iron core is approximately 1310, which is closest to choice B.

A Long Solenoid with 15 Turns Per Centimeter Has a Core