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If we take a point with in the solenoid, the magentic fields due to the current carrying loops to the right of the point and to the left of the point , both, are in the same direction.  So they add.  So the magnetic field inside becomes strong.

The magnetic fields due to various turns in the solenoid, oppose each other, for all the points outside the solenoid.  So they cancel out nearly, and hence the magnetic field strength outside the solenoid is too small or negligible.

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