The diagram shows an electromagnetic actuator used in an electronic security door lock system. The system uses a solenoid with a soft iron core to control the movement of an armature (plunger).

Describe the shape and direction of the magnetic field lines produced by this solenoid when the switch is closed, both inside the core and outside of it.
Explain the physical effect of using a soft iron core rather than an air core inside the solenoid.
A technician replaces the soft iron core with a hard steel core. When the switch is closed, the lock engages. Explain why the door remains locked even after the switch is opened and the current is switched off.