Question

What happens if a bar magnet is cut into two pieces: (i) transverse to its length and (ii) along its length?

Answer 1

(i ) Magnet moment will reduced to half and magnetic strength remain same and length(2l)become half i.e(l). 
(ii ) magnetic strength reduced to half and also Magnetic moment reduces to half but length remains same(2l).

Answer 2

A couple of different things can happen when you cut a magnet in half.If you do it gently you can end up with two magnets. You can think of a magnet as a bundle of tiny magnets, called magnetic domains, that are jammed together. Each one reinforces the magnetic fields of the others. Each one has a tiny north and south pole. If you cut one in half, the newly cut faces will become the new north or south poles of the smaller pieces. You could keep slicing smaller and smaller slices like a loaf of bread and keep getting thinner magnets, each with a new set of poles.