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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

Suppose each iron atom possesses a permanent magnetic moment of 2...

Suppose each iron atom possesses a permanent magnetic moment of 22 Bohr magnetons (where 11 Bohr magneton equals 9.27imes10−24extAm29.27 imes 10^{-24} ext{ A m}^2). The density of atoms in iron is given as 8.52imes1028extatomsm−38.52 imes 10^{28} ext{ atoms m}^{-3}. Determine the maximum magnetic field BB on the axis inside a long cylinder of iron.

Options

  1. A4.0extT4.0 ext{ T}
  2. B2.0extT2.0 ext{ T}
  3. C1.0extT1.0 ext{ T}
  4. D0.5extT0.5 ext{ T}

Correct answer

B. 2.0extT2.0 ext{ T}

Step-by-step solution

The maximum magnetization MM is achieved when all atomic magnetic moments are aligned parallel to each other.

M=nmM = n m

Substituting the given values:

n=8.52×1028 m−3n = 8.52 \times 10^{28} \text{ m}^{-3}

m=2×9.27×10−24 A m2=1.854×10−23 A m2m = 2 \times 9.27 \times 10^{-24} \text{ A m}^2 = 1.854 \times 10^{-23} \text{ A m}^2

M=(8.52×1028)×(1.854×10−23)≈1.58×106 A m−1M = (8.52 \times 10^{28}) \times (1.854 \times 10^{-23}) \approx 1.58 \times 10^6 \text{ A m}^{-1}

For a long cylinder, the demagnetizing factor is zero, so the maximum magnetic field on the axis is given by B=μ0MB = \mu_0 M.

B=4π×10−7×1.58×106B = 4\pi \times 10^{-7} \times 1.58 \times 10^6

B=4×3.1416×0.158≈1.98 TB = 4 \times 3.1416 \times 0.158 \approx 1.98 \text{ T}

Rounding to the nearest given option, we get B≈2.0 TB \approx 2.0 \text{ T}.
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