On-axis field degradation of solenoid

[Orlando]

1. The problem statement, all variables and given/known data

I have to calculate the induced current in a coil a known distance from a solenoid (the secondary coil is on the axis of the solenoid). As the magnetic flux from the solenoid weakens with distance, I have applied biort-savart law to determine the stength of the magnetic field at a point from the solenoid. My question is, when I am calculating the induced current in the second coil, do I do so by considering the magnetic field stength at the center of the second coil, or do I find an average field strength by considering the field strength at all the points along the axis of the coil?

2. Relevant equations
Equation for thin shell solenoid field degradation: http://www.netdenizen.com/emagnet/solenoids/thinsolenoid.htm


3. The attempt at a solution
I think that it's more appropriate to consider the average field strength throughout the second coil, but I am not sure. Can anyone help me please?

[cragar]

wouldn't you just integrate the B field over the area. And how is the field changing with time .