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(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. |
Answer» Solution :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) LGT 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^@`, sothat `cos theta` is negative. It means the line of `overset(to)(H)` must run from N pole to S pole inside the bar magnet. |
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