Question

The relative permeability of iron is 2000. Its absolute permeability in SI unit will be [$\frac{\mu_0}{4\pi} = 10^{-7}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$]

• A. $8\pi \times 10^{-7}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$
• B. $4\pi \times 10^{-5}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$
• C. $8\pi \times 10^{-4}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$
• D. $500\pi \times 10^{-7}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$

Hint:

When combining a large multiplier with a small power of ten, group the zeros with the exponent first to avoid arithmetic mistakes: $2000 \times 10^{-7} = 2 \times 10^3 \times 10^{-7} = 2 \times 10^{-4}$. Then simply multiply by the remaining factor of $4\pi$ to get $8\pi \times 10^{-4}$ instantly!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Iron has relative permeability μ_r = 2000; find its absolute permeability μ in SI units given μ₀/4π = 10⁻⁷.

Step 2: Key Formula or Approach:
μ = μ_r × μ₀. Substitute μ₀ = 4π × 10⁻⁷.

Step 3: Detailed Explanation:
μ = 2000 × 4π × 10⁻⁷ = 8000π × 10⁻⁷ = 8π × 10⁻⁴ T·m/A.

Step 4: Final Answer:
μ = 8π × 10⁻⁴ T·m/A, matching option (C).