Question

on a 1311 HA5.4 Self- and mutual - inductance 10 coefficients of long solenoids. [40 points) this is a very simple problem single long solenoid and two concentric long solenoids. Consider a long solenoid with n= 100 loops per deci- meter of lenght °C 1 decimeter (dm) = 10^m') and loop ross-section S=100 cm? 1) Calculate the self-inductance I per urnit lenght of the solenoid. [20 points) >

Answer 1

LE MONRA e ne no: self Inductance of solenoid to given! ; N= total ho. of tumo l=length of solenoid no: Oftusna perunit L=llone Aal langre L=477157 foro) fr01z 100X16 (me) n= 1000 loop/om x (107 m) A-s=loome L=47X107 x 106 x 102x10t looxlot Nanol 4 = 4 T7X16 1- 26m H Ano' perunit length = 126 167 늘 = 126 H Aro e

Let coaxial solenoid P is wound over an another solendid. P 11 12 12 S (1) Let 1 = length of both solenoid. 1 and 2 = radii of Pand S A2 = trị [area of secondary coil, S] Magnetic induction in solenoid, P B₂ =homh (1) N where, in= number of turn per unit length. .. Total flux linked with solenoid S 02 = B, A, N2 02 = B, (nr?) N2 = (Mon, 4) Ter2 N2 N 11 πιΝ = Ho 2= Hot LN, N2 11

5oon M12 Mompilo Now mutual Inductance of two solenoid to giren apl- NowAlo sa e A M = no. of turno pew amit length so/m. é no. Ostturno neutral Inductance l perumit lengst berunit length for amooolenoid nalou MIL Monni Al di 107 Clown e nic ni n1=500 =8000 ol M12 = 47TX 10 7 1000x500x x50x104 Q = 477X50 10-5x5 1000 7 X 105H 3 HXS = 6 200 x 10 26.28 mH x 5 Ars' = 31.4.MH Ano' frial answer. 5.41- 12 mit And =12.6 mH 2-31-404 As' = 31.4 mH.