Final answer:
Reducing the distance between two bar magnets to half its original value will increase the force between the poles by four times, due to the inverse square law governing magnetic forces.
Step-by-step explanation:
If the distance between two long bar magnets is reduced to half of its original value, the force between them will change according to the inverse square law. This law states that the magnitude of the force between two magnetic poles is inversely proportional to the square of the distance between them. Therefore, if the distance is reduced by half, the magnetic force between the poles will increase by a factor of four (2 squared).
The magnetic force is akin to Coulomb's Law in electrostatics, where the electrostatic force between two charged objects also follows the inverse square law, which implies a similar proportional increase in force when distance is decreased.
It's important to note that magnetic poles always come in pairs; if you cut a bar magnet in half, you will end up with two smaller magnets, each with a north and south pole.