A solenoid has a core of a substance with relative permeability 600. What is the magnetic permeability of the given substance?

Options

A. `20pixx10^(-5)NA^(-2)`
B. `21pixx10^(-5)NA^(-2)`
C. `22pixx10^(-5)NA^(-2)`
D. `24pixx10^(-5)NA^(-2)`

Explanation

To find the magnetic permeability (\( \mu \)) of the given substance in the solenoid, we can follow these steps:

### Step 1: Understand the relationship between magnetic permeability and relative permeability
The magnetic permeability of a material is related to its relative permeability and the permeability of free space (\( \mu_0 \)) by the formula:
\[ \mu = \mu_r \cdot \mu_0 \]
where:
- \( \mu \) is the magnetic permeability of the substance,
- \( \mu_r \) is the relative permeability of the substance,
- \( \mu_0 \) is the permeability of free space.

### Step 2: Identify the given values
From the problem, we know:
- The relative permeability (\( \mu_r \)) is given as 600.
- The permeability of free space (\( \mu_0 \)) is a constant value given by:
\[ \mu_0 = 4\pi \times 10^{-7} \, \text{N/A}^2 \]

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula for magnetic permeability:
\[ \mu = \mu_r \cdot \mu_0 = 600 \cdot (4\pi \times 10^{-7}) \]

### Step 4: Calculate the magnetic permeability
Calculating the above expression:
\[ \mu = 600 \cdot 4\pi \times 10^{-7} \]
\[ \mu = 2400\pi \times 10^{-7} \, \text{N/A}^2 \]

### Step 5: Express the answer in a simplified form
To express this in a more standard form:
\[ \mu = 24\pi \times 10^{-4} \, \text{N/A}^2 \]

### Final Answer
Thus, the magnetic permeability of the given substance is:
\[ \mu = 24\pi \times 10^{-4} \, \text{N/A}^2 \]