Express the dependence of strength of magnetic field due to a bar magnet on distance from it in mathematical form

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Solution

$M a g n e t i c f i e l d d u e t o t h e b a r m a g n e t a t a d i s \tan c e r f r o m t h e b a r m a g n e t i s : B = \frac{μ_{o} m}{2 π r^{3}} w h e r e m i s t h e m a g n e t i c m o m e n t o f t h e b a r m a g n e t . m = M_{o} π a^{2} l w h e r e l i s t h e l e n g t h o f t h e b a r m a g n e t a i s t h e r a d i s u o f t h e b a r m a g n e t (t a k i n g c y l i n d r i c a l i n s h a p e) . M_{o} i s t h e s t r e n g t h o f t h e m a g n e t i s a t i o n o f t h e b a r m a g n e t . H e n c e M a g n e t i c f i e l d a t a p o i n t r f r o m b a r m a g n e t i s i n v e r s e l y p r o p o r t i o n a l t o t h e c u b e o f t h e d i s \tan c e o f t h e b e t w e e n t h e m .$

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