# A magnetizing field of 2 × 103 Am-1 produces a magnetic flux density of 8π T in an iron rod. Then the relative permeability of the iron rod will be:

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A magnetizing field of 2 × 103 Am-1 produces a magnetic flux density of 8π T in an iron rod. Then the relative permeability of the iron rod will be:
1. 102
2. 1
3. 104
4. 103

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Correct Answer - Option 3 : 104

CONCEPT:

Magnetizing field intensity (H):

• The ability of the magnetizing field to magnetize a material medium is expressed by a vector  $\vec H$, called magnetizing field intensity or magnetic intensity.
• Its magnitude may be defined as the number of ampere-turns (nI) flowing around the unit length of the solenoid required to produce the given magnetizing field. Thus

H =nI

Bo = μoIA = μoH  or $H = \frac{{{B_o}}}{{{μ _o}}}\;$

CALCULATION:

Given -  B = 8π T and H = 2 × 103 Am-1

• The relation between magnetic field intensity (H) and magnetic flux density (B) is given by

⇒ B = μ H = μoμr

$\Rightarrow \mu_r=\frac{B}{\mu _oH}$

$\Rightarrow \mu_r=\frac{8\pi}{4\pi \times 10^{-7}\times2 \times 10^{3}}=10^{4}$