Question

A toroidal solenoid with N turns of wire, has inner radius a, outer radius b, and a rectangular cross section of height h. Make a diagram of the toroid and its cross section and show that the self-inductance of this solenoid is given by L = [µ0N^2h/( 2π )]*ln(b/a).

Answer 1

€ot Giren: a = inner radices b = Outer radius h = height of toroid. - Magnetic field torcoid can be inside a rectangular comitten as angla ho da da B- MONIL b- 2110 torcoid Loherce N= No. of tuuong o I - Cererent. r = distance frcom We need to calculate the inside toroid changes. the central axix of the torond. flex because the field (Magnetic field) LE det da - Small Cross-Sectional crea element infinitesimal) - da = Lengh x Width = hadz & pla=hdo] Pm = Fleex - flex can be obtained by integrating magnetic field over an area. >> Om ſe da bi - MONI ). NONI h har bdo tr 27 S » doo - MONID 1ngb २४ Ho NIG m = MONID (In b-ha) - Pm = 21 28 = selt enductance = Nom N No Nih >> L 1 217 MoN b in (b) 218