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Obtain the expression for the magnetic energy stored in a coil (solenoid). |
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Answer» Solution :When a current is established in a coil , work has to be done against the BACKEMF. This work done is stored in the form of magnetic energy in the coil. LET dw be the work done in ESTABLISHING a currentI in the coil in a time dt. Then dw=-`epsilon` I dt Where `epsilon` is induced emf. Since `epsilon=-L(DI)/(dt)` We have `dw=L(dI)/(canceldI)Icanceldt rArr dw=L I dI` The total work done is establishing current is `w=int dw = int_0^1L I dI = L[1^2/2]_0^I=1/2LI^2` This work is stored in the coil in the form of magnetic potential energy `U=1/2LI^2` |
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