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:
We are given the dimensionless relative permeability of an iron core sample, $\mu_r = 2000$. We need to compute its absolute magnetic permeability ($\mu$) expressed in standard SI units.

Step 2: Key Formula or Approach:
The absolute magnetic permeability of a medium is defined as the product of its relative permeability and the permeability of free space (vacuum permeability, $\mu_0$): $$\mu = \mu_r \times \mu_0$$ From the given standard constant ratio $\frac{\mu_0}{4\pi} = 10^{-7}$, we can substitute $\mu_0 = 4\pi \times 10^{-7}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$.

Step 3: Detailed Explanation:
Let's substitute the values of $\mu_r$ and $\mu_0$ into the definition formula: $$\mu = 2000 \times \left(4\pi \times 10^{-7}\right)$$ Multiply the constants together: $$\mu = 8000\pi \times 10^{-7}$$ Convert the expression to standard scientific notation by moving the decimal point three places to the left: $$\mu = 8\pi \times 10^3 \times 10^{-7} = 8\pi \times 10^{-4}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$$ This matches option (C).

Step 4: Final Answer:
The absolute permeability of iron is $8\pi \times 10^{-4}\text{ T}\cdot\text{m}\cdot\text{A}^{-1}$, which corresponds to option (C).