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www.GOALias.blogspot.comPhysicsM 11is the self-inductance and is written as L 1. Therefore,ε =−LdIdt−MdIdt1 21 1 12Interactive animation on ac generator:http://micro.magnet.fsu.edu/electromagnet~java/generator/ac.htmlEXAMPLE 6.10Example 6.10 (a) Obtain the expression for the magnetic energy storedin a solenoid in terms of magnetic field B, area A and length l of thesolenoid. (b) How does this magnetic energy compare with theelectrostatic energy stored in a capacitor?Solution(a) From Eq. (6.19), the magnetic energy isUB1= LI2221 ⎛ B ⎞= L B0nI2 ⎜=⎝μn ⎟⎠01 2⎛ B ⎞= ( μ0n Al )2 ⎜⎝μn ⎟⎠02( since μ ,for a solenoid)[from Eq. (6.17)]1 2= B Al2μ0(b) The magnetic energy per unit volume is,uUVBB= (where V is volume that contains flux)=U BAl2B= (6.20)2μ0We have already obtained the relation for the electrostatic energystored per unit volume in a parallel plate capacitor (refer to Chapter 2,Eq. 2.77),1 2uΕ= ε0E(2.77)2In both the cases energy is proportional to the square of the fieldstrength. Equations (6.20) and (2.77) have been derived for specialcases: a solenoid and a parallel plate capacitor, respectively. But theyare general and valid for any region of space in which a magnetic fieldor/and an electric field exist.2246.10 AC GENERATORThe phenomenon of electromagnetic induction has been technologicallyexploited in many ways. An exceptionally important application is thegeneration of alternating currents (ac). The modern ac generator with atypical output capacity of 100 MW is a highly evolved machine. In thissection, we shall describe the basic principles behind this machine. TheYugoslav inventor Nicola Tesla is credited with the development of themachine. As was pointed out in Section 6.3, one method to induce an emf