Question

If the permeability of a substance is $616 \times 10^{-5} \, NA^{-2}$, then the susceptibility of the substance is

• A. 3899
• B. 5899
• C. 4899
• D. 6899

Hint:

Remember the value of $\mu_0 = 4\pi \times 10^{-7}$. Approximation $\pi \approx 22/7$ often simplifies calculations involving multiples of 11 or 7.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The magnetic susceptibility ($\chi$) is related to the absolute permeability ($\mu$) and the permeability of free space ($\mu_0$) by the relation: \[ \mu = \mu_0 (1 + \chi) \] Or using relative permeability ($\mu_r$): \[ \mu_r = \frac{\mu}{\mu_0} = 1 + \chi \implies \chi = \frac{\mu}{\mu_0} - 1 \]
Step 2: Substitution and Calculation:
Given: $\mu = 616 \times 10^{-5} \, NA^{-2}$ $\mu_0 = 4\pi \times 10^{-7} \, NA^{-2} \approx 4 \times \frac{22}{7} \times 10^{-7} \, NA^{-2} = \frac{88}{7} \times 10^{-7} \, NA^{-2}$ Calculate relative permeability $\mu_r$: \[ \mu_r = \frac{616 \times 10^{-5}}{\frac{88}{7} \times 10^{-7}} \] \[ \mu_r = \frac{616 \times 10^{-5} \times 7}{88 \times 10^{-7}} \] \[ \mu_r = \frac{616}{88} \times 7 \times 10^{2} \] We know that $88 \times 7 = 616$. So, $\frac{616}{88} = 7$. \[ \mu_r = 7 \times 7 \times 100 = 49 \times 100 = 4900 \] Now, calculate susceptibility $\chi$: \[ \chi = \mu_r - 1 \] \[ \chi = 4900 - 1 = 4899 \]
Step 3: Final Answer:
The susceptibility is 4899.