(i) Use:
(i) the Ampere's law for H and
(ii) continuity of lines of B, to conclude that inside a bar magnet,
(a) lines of `overset(to)(H)` run from the N pole to S pole, while
b) lines of `overset(to)(B)` must run from the S pole to N pole.

Explanation

Let us consider a magnetic field line of `overset(to)(B)` through the bar magnet as given in the figure below.

It must be a closed loop as shown in figure.
Let C be the amperian loop, then
`int_(Q)^(P) overset(to)(H). overset(to(d) l = int_(Q)^(P) ( overset(to)(B) )/(mu_(0) ). overset(to)(d) l " "[because B= mu_(0) H]`
The angle between `overset(to)(B) and overset(to)(d) l` is less than `90^@` inside the bar magnet, so it is positive hence `cos theta gt 1`
`int_(Q)^(P) overset(to)(H). overset(to)(d) l = int_(Q)^(P) ( overset(to)(B))/(mu_0) . overset(to)(d) l lt 0`
Hence, the line of `overset(to)(B)` must run from south pole (S) to north pole (N) inside the bar magnet.
According to Ampere.s law,
`oint_("PQP") overset(to)(H). overset(to)(d) l = 0`
`oint_("PQP") overset(to)(H). overset(to)(d)l = int_(P)^(Q) overset(to)(H). overset(to)(d)l + int_(Q)^(P) overset(to)(H). overset(to)(d)l =0`
but `int_(Q)^(P) overset(to)(H). overset(to)(d) l gt 0 " "` (outside magnet)
Hence `int_(P)^(Q) overset(to)(H). overset(to)(d) l lt 0" "` (Inside magnet)
If angle between `overset(to)(H) and overset(to)(d) l` is more than `90^@` , so that `cos theta` is negative. It means the line of `overset(to)(H)` must run from N pole to S pole inside the bar magnet.