(English is not my native language, kindly ignore certain grammatical errors.)

Reference: Problems in General Physics - IE Irodov Q 3.241 A very long straight solenoid carries a current I . The cross-sectional area of the solenoid is equal to S, the number of turns per unit length is equal to n.

Find the flux of the vector B through the end plane of the solenoid.

Doubt: As far as I can remember when we make simplifying assumptions about a solenoid we say that it should have tight winding, no resistance, and be very long (relative to the radius). In such a case the feild lines are almost parallel, and uniform. There is no magnetic feild leakage outside the solenoid and hence the feild strength is 0 outside and N(mu0)I inside.

If that is the case then why exactly the feild strength becomes half at the edge? If I take a surface deep within the solenoid or at the surface, it should not make much of a difference. Since there is no leakage of the lines. There is one reasoning I have heard, "You add two semi infinite solenoids to make an infinite one hence the feild strength of each should be half." But my problem is that the "loss" of half of the strength at the edges makes the assumption we take dubious. As the results we get do not match. Those feild lines must escape through the solenoid itself. Therefore, the above assumptions become pointless.

Kindly correct me if I am wrong. Thank You.