Question

1. (20 points) Consider a toroid of made of N square loops of wires (side length a) with current i. The mean radius of the toroid is R. You may express your results in terms ofN, R,a, i, and natural constants. Use Ampere's Law, prove that the magnetic field at a point inside the toroid and a distance r from the center is given by ue Ni/ (2 r). Find the magnetic flux through the cross section of the toroid. Find the inductance of the toroid. d. The toroid is used in a radio LC circuit, which is tuned to receive radio signal from KUSC (91.5 MHz). The capacitor is a pair of parallel square plates of the same size as the cross section of the toroid, with plate separation of 2.50 mm. The mean radius of the toroid is the same as the side length of its loops (R a), and it contains 150 loops. Find the numerical value of a. a. b. C. Top View a a Cross Section

Answer 1

Each step is done one by one. Note for part d, the circuit works as a tuned circuit. In the problem R and r are same (typing error as there are no 2 uses of R anywhere)

OJ a We apply Ampere Laur i the Langth l no 2r n. NC 27r lua = BA en A= a2 No 2r


c) Indutave 7 N 7- Na 2 2 a 27r aN d Gwen .N=150 ra Fa a paalet ptats A a 2. EoA Cuhere 1 d 2.5X 17 12 8.854 X10a2 -5osh2.5x 13 3.5416X10Xa


L= N2 a2 27r 150 x a2 =3580.986a 27 Xa Tunuy duguny f= 91.5x 10 HZ T 2 C ラLC= 422 3580.926 a X3.5416X1Xa 2 472x91.52)ol2- a 6-20aX10 m 6.2 1