Coil length or Solenoid length?

[kaosAD]

This is not a homework. I am just pretty confused about a problem (with solution!) I saw in the internet found here:
http://www.transtutors.com/physics-homework-help/electromagnetism/Electromagnetic-induction.aspx

The part I am confused is the mutual inductance part. Here I repeat the question:

Homework Statement

A long solenoid of length 1 m, cross sectional area 10 cm2, having 1000 turns has wound about its centre a small coil of 20 turns. Compute the mutual inductance of the two circuits. What is the emf in the coil when the current in the solenoid changes at the rate of 10 Amp/s?

Homework Equations

I am assuming in the question, both coils are wound such that both has the same coil length as the solenoid.

The Attempt at a Solution

The mutual inductance M is given as:

<br /> M = \frac{\mu N_1 N_2 I_2 A}{l}<br />

where l is the length is the solenoid length. Suppose the 20 turns coil has shorter coil length. Would that affect the mutual inductance value?

 

[kuruman]

No. As long as the coil is near the midpoint of the solenoid and its ends do not extend very far from the midpoint, the length of the coil does not matter much. This is an approximate calculation which assumes that the magnetic field generated by the solenoid is uniform at the location of the coil. It is most accurate at the solenoid's midpoint. As you move the coil closer to the ends of the solenoid, the field generated by the solenoid is less and less uniform which makes the approximation less and less valid.