Inductance

Relative Permeability and Inductance

When an air core in an inductor is replaced by an iron core, the self-inductance increases from 0.02 mH to 40 mH. We want to find the relative permeability of the iron.

Step 1: Inductance and Permeability

The inductance ( ) of an inductor is directly proportional to the permeability ( ) of the core material. The formula for the inductance of a solenoid is:

Where:

• is the inductance.
• is the permeability of the core material.
• is the number of turns in the coil.
• is the cross-sectional area of the coil.
• is the length of the coil.

Step 2: Relative Permeability

The relative permeability ( ) is the ratio of the permeability of a material ( ) to the permeability of free space ( ):

Therefore, .

Step 3: Ratio of Inductances

Let be the inductance with the air core, and be the inductance with the iron core. Then:

Taking the ratio of the two inductances:

Step 4: Calculate

We are given and . Therefore:

Conclusion

The relative permeability of the iron is 2000.