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  • 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 H run from the N pole to S pole, while b lines of B must run from the S pole to N pole

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 H run from the N pole to S pole, while (b) lines of B must run from the S pole to N pole.

 

Answers (1)

Consider a magnetic field line going through the bar magnet. We know that it must be a closed-loop.

\int_{Q}^{P}H.dl=\int_{Q}^{P}\frac{\overrightarrow{B}}{\overrightarrow{\mu_{0}}}\overrightarrow{dl}

B and dl are at an acute angle to each other inside the magnet.

i.e., \int_{Q}^{P}H.dl=\int_{Q}^{P}\frac{\overrightarrow{B}}{\overrightarrow{\mu_{0}}}\overrightarrow{dl}>0  i.e. positive  

 Hence, the lines of B must run from south pole S to north pole N inside the bar magnet.

 According to ampere's law 

\\\oint \overrightarrow{H}.\overrightarrow{dl} =0\\\oint \overrightarrow{H}.\overrightarrow{dl} =\int_{P}^{Q}\overrightarrow{H}.\overrightarrow{dl}+\int_{Q}^{P}\overrightarrow{H}.\overrightarrow{dl}

 As \int_{P}^{Q}\overrightarrow{H}.\overrightarrow{dl}>0 so ,\int_{Q}^{P}\overrightarrow{H}.\overrightarrow{dl}<0 negative 

 If angle between H and dl is more than 90^{\circ}, so that \cos \theta is negative 

(meaning that the lines run from N pole to S pole inside the bar magnet)
 

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