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(a) Definethe term 'self-inductance' and write theS.I. unit. (b) Obtainthe expression for the mutualinductance of twolong co-axialsolenoidsS_(1) and S_(2)wound one over the other, each of length L and radii r_(1) and r_(2) andn_(1) and n_(2)number of turnsper unit length , when acurrent I is set up in the outersolenoid S_(2). |
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Answer» Solution :(a) Self induction is the PROPERTY held by the coil byvirtue of which it opposes any changein strengthof the current flowingthrough it(an emf is inducedin it)S.I., is called inertiaof electricity, is its unit is Henery, `1H = (1V)/(1Am//s) = 1 W//A`. (b) `S_(1)` and `S_(2)` are the solenoidwith same length las shown`n_(1)` and `n_(2)` through `S_(1)phi_(2)1Flu`lined with `S_(2)`DUE to currentthrough S. `phi_(21) prop I_(1)`. `phi_(21) = m_(2), I_(1)` Where, `M_(21)` is co-efficientof mutual inductionof the two solenoid. As the current pass through `S_(1)`, emf is inducedin `S_(2)`. Magnecticfield inside `S_(1) = B_(1) = mu_(0)n_(1)O_(1)` Magneticflux linkedwith each turn of `S_(2) = B_(1)A` So total magneticflux linkedwith `S_(2)phi_(21) = B_(1)An_(2)I` `= mu_(0)n_(1)I_(1) xx A xx n_(2)l` `= phi_(21) = mu_(0)n_(1)n_(2) AI_(1)` `M_(21) = mu_(0)n_(1)n_(2)Al` Mutual inductancebetweenthe twosolenoidswhen currentis passed through `S_(2)`and inducedemf is producedin `S_(1)` `M_(12) = mu_(0)n_(1)n_(2)Al` Mutual inductance betweenthe two solenoidsthe two solenoidswhen current is passed through`S_(2)`and indcued emf isproduced in `S_(1)`. `M_(12) = mu_(0)n_(1)n_(2)Al` So, `M_(12)= M_(21) = M`(say) Hence, co-efficient of mutual inductionbetween the long solenoids `M= mu_(0)n_(1)n_(2)Al`. 
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