GAL: Gradient Adaptive Lattice: GAL: Guggenheim Aeronautical Laboratory: GAL: Gas Analysis Laboratory: GAL: George A. Lincoln (WWII General) Gal: Galindian (linguistics) GAL: Guinea Airways, Ltd. GAL: Groupe Antiterroristes de LibÃ©ration (French: Anti-Terrorist Liberation Group) GAL: Gathering Arm Loader (mining) GAL: Graphics Adapter Language: GAL: Gimbal Angle Loss: GAL
1 If the distance between two magnets is doubled the magnetic force between them will fall to a quarter of the initial value. #(F//4)#.  If the distance between two magnets is halved the magnetic force between them will increase to four times the initial value. #(4F)#.
This you see as the north pole forming near the north pole of the solenoid. Like poles repel, unlike poles attract is kind of a misleading analogy(I find it strange that I realized this after reading your question). What actually is happening is that the tiny magnetic dipoles inside the magnetic material(a bar of iron, for example) align with the direction of the magnetic field.