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B) With our s ign convention , a positive J gives a posi tive B . At t 0 , dB /dt 0 and J = O . Then , as B decreas es , J increases as per Lenz ' s law , etc . = = 11- 7 ( 11 . 2 ) INDUCTION HEATING a) -d� /dt - Tfr 2 (d /dt) ( V o N ' I 0 coswt) b ) The length of the conductor is 2 Tfr and its cros s-section is Ldr . = 50 Hence R c) dP av = 21Tr /crLdr 2 2 ( 11 U WN ' I 0 ) o 2x2 rrr /crLdr = [Ilo2rrcrw2N ' 2 1 0 ) 2 / 4 Lr 3 dr , Th e average va 1ue 0 f S ln equa 1 to 0 . 5 . , 2 wt b elng ' R d) P av ( ) L r 3 dr ( ) LR4 / 4 = ( 4rr x lO -7 x 21T x 60 x 5000 x 2 ) 2 J = o ( 1T x lO 5 /16) ( 6 x lO -2 ) 4 x l = 5 .
10-1 7 ( lO . 8) V vBa ELECTROMAGNETIC FLOWMETERS = CHAPTER 11 11-1 ( 11 . 1) a) Bv 9, b) Zero . = BOAT TESTING TANK 2 x 10 -5 x 20 x 3 1 . 2 mV = 11-2 ( 11 . 1) EXPANDING LOOP a) I = Bvs /R b ) (B ls ) v (Bvs) 2 /R c) I 2 R = (Bvs ) 2 /R. The power exp ended to move the bar appears as heat in the resis tance R . = 11-3 ( 11 . 2) INDUCED CURRENTS t t Reference : Rev . S ci . Ins trum . , � , 1581 ( 19 7 7 ) . 49 11-4 ( 11 . 1) INDUCED CURRENTS a) Counterclockwise b ) Counterclockwise c) S ince the flux linkage is con -+ -+ s tant , and s ince v x B = 0 , the induced electromotance is zero .
9 3 pF /m A / 2Tr r , E = A / 2TrE E r r o On the inner s urface of the diel ectric , On the outer surface , 29 6-8 ( 6 . G " ' oA , J E A o r 1 l- ( t / s ) ( 2 / 3 ) 6-9 ( 6 . 7 ) a) S ince the only free charge is Q , Eq . 6 - 1 7 g ives us tha t Z -9 Z -11 2 Z 10 / 4 rrr = 7 . 9 6 x lO / r C /m D = Q / 4Tfr = b o th in s ide and outside the die l ectri c . Ins ide the die le c tric , Z Q / 4TfE E r r o -11 2 -11 2 7 . 9 5 x 10 /3r 2 . 6 5 x 10 /r D/E E r o E. 1= = = Out s ide th e diele c t ri c , 2 2 D/E Q / 4TfE r 8 .
an introduction to magnetohydrodinamics by Davidson