An iron bar of permeability `8.2 xx 10^(-3)` Wb/A-m is placed in a magentic field of strongth 150 A/m . what is induction in the iron rod ?

Answer

To find the magnetic induction \( B \) in the iron rod, we can use the relationship between magnetic induction, permeability, and magnetic field strength. The formula is given by:

\[ B = \mu H \]

Where:
- \( B \) is the magnetic induction (in Weber per square meter, Wb/m²),
- \( \mu \) is the permeability of the material (in Weber per ampere meter, Wb/A·m),
- \( H \) is the magnetic field strength (in ampere per meter, A/m).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Permeability \( \mu = 8.2 \times 10^{-3} \, \text{Wb/A·m} \)
- Magnetic field strength \( H = 150 \, \text{A/m} \)

2. **Substitute the Values into the Formula**:
\[ B = \mu H = (8.2 \times 10^{-3} \, \text{Wb/A·m}) \times (150 \, \text{A/m}) \]

3. **Perform the Multiplication**:
- First, calculate \( 8.2 \times 150 \):
\[ 8.2 \times 150 = 1230 \]
- Now, include the exponent from the permeability:
\[ B = 1230 \times 10^{-3} \, \text{Wb/m}^2 \]

4. **Convert to Standard Form**:
\[ B = 1.23 \, \text{Wb/m}^2 \]

5. **Final Answer**:
The magnetic induction \( B \) in the iron rod is:
\[ B = 1.23 \, \text{Wb/m}^2 \]