A solenoid has a core made of material with relative permeability $400$ . The magnetic field produced in the interior of solenoid is $1.0$ T. The magnetic intensity in SI units is $\alpha \times 10^5$ . The value of $\alpha$ is ______.
(Free space permeability $\mu_0=4\pi \times 10^{-7}$ SI units.)

Question

A solenoid has a core made of material with relative permeability

400

. The magnetic field produced in the interior of solenoid is

1.0

T. The magnetic intensity in SI units is

\alpha \times 10^5

. The value of

\alpha

is ______.
(Free space permeability

\mu_0=4\pi \times 10^{-7}

SI units.)

Quantrex Academy · Accepted Answer

Correct answer: B. (1)/(16π)

The magnetic field B inside the solenoid is related to the magnetic intensity H by the formula: B = μ H = μ_0 μ_r H Rearranging for H , we get: H = (B)/(μ_0 μ_r) Substituting the given values ( B = 1.0 T, μ_r = 400 , and μ_0 = 4π × 10^ -7 T m/A): H = 1.0 4π × 10^ -7 × 400 H = 1.0 1600π × 10^ -7 H = 1 16π × 10^ -5 H = (1)/(16π) × 10^5 A/m Comparing this with the given expression H = α × 10^5 , we find: α = (1)/(16π) Answer: (1)/(16π)

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