Question

on a Self- and mutual - inductance coefficients of long solenoids. this is a very simple problem single long solenoid and two concentric long solenoids. Consider a long solenoid with n = 100 loops per deci- I meter of lenght °(1 decimeter Cem )=104m) and loop ross-section S= 100 cm 1) Calculate the self-inductance I per urut lenght of the solenoid. 2) Consider to insert a second long solenoid inside the first solenoid and coaxial with it Caf. rig. HA 5.4). The second solenoid har n'= 500 loop pure dm of lenght and loop cross-section 5=50cm? Calculate the mutual-inductance M per unit lenght between the two solenoids and discuss its sign.

Answer 1

Criven a solenoid with n=100 loops I am : 1 dm = 10-1 n=1000 loops Im Area s = 100 cm? m. - 100x10 2 { lcm = 10²m 10-2 m² 1) We know that the self inductance L is given as where, L = 4 n²e A Permeability of free space self indirectance n number of turps per per unit length unit length - L = lon²A e length of solenoid A Area of of woss section = xx107x (03) X10 of loop Moy l -2 - 3 H = 48x 10 - 4x3.14 x 103 1.256 x 10 -2 y Crinen second solenoid has n'= 500 loopldm. 5000 loop Im. s = 50cm² = 50x10 ma 2 5X10 We know that the mutual inductance is given as M = Mo nanals' Mutual inductance per unit length .. M = Monon's 42x107x 103 x 5 x 10² x 5x10 B. 14 x 10 -2 H