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

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.