# Inductance in a toroidal coil

**1. The problem statement, all variables and given/known data**

A toroidal coil of 500 turns is wound on a steel ring of 0.5 m mean diameter and 2*10^-3 m^2 cross-sectional area. An excitation of 4000 A/m produces a flux density of 1.0 T. Find the inductance in the coil.

**2. Relevant equations**

W=0.5LI^2= 0.5∫BH dV

**3. The attempt at a solution**

B= 1T, H=B*μ so W=0.5*(1)*1*μ∫dV

∫dV= cross-sectional area * mean circumference of toroid= .002*.5*pi= ∏*10^-3

So W= 2∏^2*10^-10

I/l=4000 A/m, I’m assuming length here is the total length of the coil?

l=N(2pi*r)+2pi*R (to account for the thickness of the wire, essentially the circumference of the toroid

Area of cross-section is 0.002, so r=0.0252

l=500*2pi*0.0252 + 2*pi*0.025=80.84

So I=4000*80.84= 323,000A

L=2W/I^2=2∏^2*10^-10/(323000)^2= 1.89*10^-20, which seems way too small to me…did I do something wrong?

http://ift.tt/1oymqBM

## Leave a comment