Question

A long solenoid (cross-sectional area = 0.79 x 10-6 m2, number of turns per unit length = 3523 turns/m) is bent into a circular shape so it looks like a doughnut. This wire-wound doughnut is called a toroid. Assume that the diameter of the solenoid is small compared to the radius of the toroid, which is 0.041 m. Find the emf induced in the toroid when the current decreases from 2.5 A to 1.1 A in a time of 0.15 s. Number Units the tolerance is +/-2%

Answer 1

Given cross sectional area 0.79 times 10^- 6 m^2 number of turns per unit length 3523 Diameter of solenoid 0.041 m To find emf induced in the toroid current decreases from 2.5 A to 1.1 A Time 0.155 Now self - inductance of straight solenoid L = mu_0 n^2 l A To find radius of toroid R inductance L = 2 pi mu_0 n^2 R A According to Faraday is law, induced emf epsilon = -Delta Phi/Delta t = -Delta (L I)/Delta t = -L Delta I/Delta t = -2 pi mu_0 n^2 R A (I - I_0/t) = -[2 pi times 4 pi times 10^- 7 times (3.46)^2 times (0.054) (0.77 times 10^- 6) (1.1 - 2.5/0.15)] = 2.84 times 10^- 5 v Therefore Emf induced in toroid epsilon 2.84 times 10^- 5 v .