In a material, the magnetic field B and the magnetic intensity H are observed to be 1.6 T and 1000 A m^ -1 , respectively. Determine the relative permeability μ_r and the susceptibility of the material.

Correct answer: C. μ_r 1.3 × 10^3 , 1.3 × 10^3 The relation between magnetic field B , magnetic intensity H , and relative permeability μ_r is given by: B = μ H = μ_0 μ_r H μ_r = (B)/(μ_0 H) Substituting the given values, B = 1.6 T , H = 1000 A m^ -1 , and μ_0 = 4π × 10^ -7 T m A^ -1 : μ_r = 1.6 4π × 10^ -7 × 1000 = (1.6 × 10^4)/(4π) μ_r = (4000)/(π) 1273.2 1.3 × 10^3 The magnetic susceptibility is related to relative permeability by: = μ_r - 1 1273.2 - 1 = 1272.2 1.3 × 10^3

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Magnetic Properties of Matter

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Magnetic Properties of Matter

In a material, the magnetic field B and the magnetic intensity H...

In a material, the magnetic field

B

and the magnetic intensity

H

are observed to be

1.6 \text{ T}

and

1000 \text{ A m}^{-1}

, respectively. Determine the relative permeability

\mu_r

and the susceptibility

\chi

of the material.

Options

A $\mu_r \approx 1.6 \times 10^3$ , $\chi \approx 1.6 \times 10^3$
B $\mu_r \approx 6.3 \times 10^2$ , $\chi \approx 6.3 \times 10^2$
C $\mu_r \approx 1.3 \times 10^3$ , $\chi \approx 1.3 \times 10^3$
D $\mu_r \approx 1.6 \times 10^{-3}$ , $\chi \approx 1.6 \times 10^{-3}$

Correct answer

C. $\mu_r \approx 1.3 \times 10^3$ , $\chi \approx 1.3 \times 10^3$

Step-by-step solution

The relation between magnetic field

B

, magnetic intensity

H

, and relative permeability

\mu_r

is given by:

B = \mu H = \mu_0 \mu_r H

\mu_r = \dfrac{B}{\mu_0 H}

Substituting the given values,

B = 1.6 \text{ T}

H = 1000 \text{ A m}^{-1}

, and

\mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}

\mu_r = \dfrac{1.6}{4\pi \times 10^{-7} \times 1000} = \dfrac{1.6 \times 10^4}{4\pi}

\mu_r = \dfrac{4000}{\pi} \approx 1273.2 \approx 1.3 \times 10^3

The magnetic susceptibility

\chi

is related to relative permeability by:

\chi = \mu_r - 1

\chi \approx 1273.2 - 1 = 1272.2 \approx 1.3 \times 10^3

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