You build a solenoid containing 500 windings over a 0.20-m length, with a loop radius of 0.025 m for each winding. the current in the unit is 3.0 a. what is the inductance of the solenoid?

The inductance of a solenoid is given by:

where
is the vacuum permeability
N is the number of turns of the solenoid
A is the area of one loop of the solenoid
l is its length

For the solenoid in our problem, N=500, and the radius of one loop is r=0.025 m, so the area of one loop is

and its length is l=0.20 m

So the inductance of the solenoid is