An iron-cored solenoid has self- inductance. 2.8 H. When the core is removed, the self inductance becomes 2 mH. What is the relative permeability of the core used?

Explanation

To solve the problem of finding the relative permeability of the iron core used in the solenoid, we will follow these steps:

### Step 1: Understand the relationship between self-inductance with and without the core
The self-inductance \( L \) of a solenoid with a core is given by:
\[ L = \mu \cdot n^2 \cdot \pi r^2 \cdot L \]
where \( \mu \) is the permeability of the core material, \( n \) is the number of turns per unit length, \( r \) is the radius, and \( L \) is the length of the solenoid.
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