1.

Use (i) the Ampere's law for vecHand (ii) continuity of lines of vecB , to conclude that inside a bar magnet, (a) lines of vecHrun from the N pole to S pole, while (b) lines of vecBmust run from the S pole to N pole

Answer»

SOLUTION :
We will consider here the magnetic field line of B through the bar magnet as shown above. The field line must be a closed LOOP. Let us consider it as amperian loop. Then,
`int_(P)^(O) vecH .vecdl= int_(P)^(O) (vecB)/(mu_0). vecdl gt 0 `
It will be positive because the ANGLE between `vecB`and dl is less than `90^@`inside the bar magnet, so that COS `theta`is positive. So, the lines of `vecB`must run from south pole (S) to north pole (N) inside the bar magnet. According to Ampere.s law,
`oint_(OPO) vecH.vecdl = 0`
` oint_(OPO) vecH.vecdl = int_(O)^(P) vecH.vecdl + int_(P)^(O) vecH.vecdl = 0 `
As ` int_(P)^(O) vecH.vecdl gt 0`
` rArr int_(O)^(P) vecH.vecdl lt= 0 `
This is because the angle between `vecH` and `vecdl`is greater than `90^(@)` . It means that the lines of H must run from north pole (N) to south pole (S) inside the bar magnet.


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