re - "how to apply the ampere's law to the infinite solenoid...
how we find the equation for the magnetic field ??
who can help..."
Construct an amperian loop around the windings and along the axis. Hard to describe - easier to draw.
Let the solenoid be
<-----<-----<--B--<-----<-----<--
------------
| |
--------|----------|------------/
------------ /
------>------->-------->---->-/
/
----------------------------/
Then integrate around the loop. It's been years since I've done this stuff so let me know how you do. This should start yoiu off. Keep in mind the number of turns per unit length in the solebnoid and the current in the filiment. I think you may assume that the field inside the solenoid is uniform. The answer should come easy after that.
Pete