why does iron rod increase the mutual inductance while iron sheet decreases the mutual inductance

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Solution

$I r o n r o d w o r k s a s a s o f t i r o n c o r e w h i c h e n h a n c e s t h e m a g n e t i c f l u x l i n k e d w i t h t h e c o i l w h e r e a s i r o n s h e e t i s a b e a t e n i r o n i n w h i c h w h e n f l u x i s l i n k e d e d d y c u r r e n t s a r e p r o d u c e d w h i c h d e c r e a s e t h e n e t f l u x l i n k e d w i t h a n d t h u s r e d u c e s t h e m u t u a l i n d u c \tan c e .$

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