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?