[Subhadeep Roy]

A bar magnet has been cut vertically from the middle into two equal pieces,will the magnetic strength of the two cut pieces remain the same,if not,why?

[Unknown008]

What do you think about it?

[leechaolan]

No, the magnetic field strength will be halved. Magnets, like most other matter consists of atoms which are electrons orbiting a nucleus in some sense. (orbit is not a classical continuous ellipse but that's beyond the scope of this question)

According to the Biot-Savart law, electric currents cause the formation of external magnetic fields. Each electron orbiting a nucleus is like a closed loop of electric current which causes an external magnetic field vector parallel to it's angular momentum vector. (the actual angular momentum in these particles are permanent intrinsic built in angular momenta however)

In non-magnetized materials, the spin directions of any two pairs of atoms are directed opposite to each other so the magnetic effects of each field cancel out. In magnetized materials, there's an uneven balance of spin direction. (so that there's a net field in one direction) The more unbalanced it is, the greater the overall field strength.

Because there are only a finite number of particles in a magnetic structure of a certain volume, there is a maximum attainable magnetic field strength. Let's assume that a magneti is "magnetically saturated". If you break the magnet in half, there are less resultant fields per piece of material. (exactly half that amount) Breaking the magnet even further will just keep lessening the amount of resultant field available.

If you want to look at it another way, Ampere's law (neglecting displacement currents) states that the total magnetic field integrated through any closed loop is directly proportional to the current causing it. Each "domain particle" can be considered as a unit of current. More available fields depends on proprtionally more domains which depends on proportionally more volume for a constant density material.

Hope that cleared things up.