Question

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

Answer 1

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 = μ_oμ_rH 

\(\Rightarrow \mu_r=\frac{B}{\mu _oH}\)

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