Question

1. a. One solenoid is centered inside another. The outer one has a length of 47.0 cm and contains 6700 coils, while the coaxial inner solenoid is 5.00 cm long and 0.170 cm in diameter and contains 17.0 coils. What is the mutual inductance of these solenoids? The current in the outer solenoid is changing at 38.0 A/s. b. Find the emf induced in the inner solenoid. c. A toroidal solenoid has a mean radius of 18.0 cm and a cross-sectional area of 5.00 cm2 and is wound uniformly with 120 turns. A second coil with 490 turns is wound uniformly on top of the first. What is the mutual inductance of these coils? d. At the instant when the current in an inductor is increasing at a rate of  7.00×10⁻² A/s , the magnitude of the self-induced emf is 2.80×10⁻² V . What is the inductance of the inductor? e. What would have to be the self-inductance of a solenoid for it to store 10.0 J of energy when a 1.50 A current runs through it? f. If this solenoid's cross-sectional diameter is 3.80 cm , and if you could wrap its coils to a density of 10 coils/mm , how long would the solenoid be?

Answer 1

Given,

Lo = 47 cm ; No = 6700 ; Li = 5 cm ; di = 0.17 cm ; Ni = 17 ; I/t = 38 A/s

ri = 0.17/2 = 0.085

a)We know that the mutual inductance if coils is guven by:

M = u0 A N1 N2/l

A and l are Area and length of inside the solenoids and outer respectively

M = 4 pi x 10^-7 x 3.14 x (0.00085)^2 x 6700 x 15/0.47 = 6.1 x 10^-7 H

Hence, M = 6.1 x 10^-7 H

b)E(inner) = M Io/t

E = 6.1 x 10^-7 x 38 = 2.31 x 10^-5 V

Hence, E = 2.31 x 10^-5 V