Question

A toroidal ring, having 100 turns per cm of a thin wire is wound on a nonmagnetic metal rod of length 1 m and diameter 1 cm. If the permeability of bar is equal to that of free space (µ₀), calculate the magnetic field inside the bar (B) when the current (i) circulating through the turns is 1 A. Also determine the self-inductance (L) of the coil.

Answer 1

Data : l = 1 m, d = 1 cm, n = 100 cm^-1 = 10⁴ m^-1 , 

I = 100 A, µ₀ = 4π × 10^-7 H/m

The radius of cross section, r = d/2 = 0.5 cm

= 5 × 10^-3 m

(a) Magnetic field inside the toroid,