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WHY IS THE MAGNITUDE OFMAGNETIC FIELD OUTSIDE A SOLENOID TAKEN AS 0?
Magnetic field lines only exist as loops, they cannot diverge from or converge to a point like electric field lines can .The magnetic field lines follow the longitudinal path of the solenoid inside, so they must go in the opposite direction outside of the solenoid so that the lines can form a loop. However, the volume outside the solenoid is much greater than the volume inside, so the density of magnetic field lines outside is greatly reduced. Now recall that the field outside is constant. In order for the total number of field lines to be conserved, the field outside must go to zero as the solenoid gets longer.


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