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Homework Help
Introductory Physics Homework Help
Toroid Air Gap: MMF, B-H Curve, Flux Density & More
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[QUOTE="sarahgarden, post: 2768913, member: 250283"] [h2]Homework Statement [/h2] (I have done parts i) through v) correctly. It is the remaining two I'm stuck on. A toroid of rectangular cross-section has a height of 10mm, an inner diameter of 68mm and an outer diameter of 82mm. It is made of iron and is wound with 118 closely-spaced turns. When a current of 2A flows, calculate; i)the mmf around the toroid ii)the magnetic field-strength within the toroid iii)Using B-H curve determine the flux density and flux in the ring, iv)the relative permeability at this point on the curve A 1mm air gap is then cut in the toroid. The current is still 2A. Calculate; v)the new flux density in the ring, vi)the mmf around the ring, and across the air gap. vii) It is then required to establish a flux density of 0.75T in the air gap. Calculate the current needed to do this. Answers to parts vi) and vii) vi) 53, 183 A-t vii) 8.0 A[h2]Homework Equations[/h2] [tex]m.m.f.=NI=BS(R_{m}iron+R_{m}air)[/tex] [tex]R_{m}=\frac{l}{\mu_{0}\mu_{r}S}[/tex] where [tex]\mu_{r}=557[/tex], I have [tex]B=0.21T[/tex] (although the answer gives it as 0.23) [tex]R_{m}(iron)=4.787*10^6[/tex] and [tex]R_{m}(air)=11.365*10^6[/tex] [tex]S [/tex]= cross-sectional area = [tex]7*10^{-5}[/tex][h2]The Attempt at a Solution[/h2] I get the m.m.f. across the air gap correct if I use the value of B = 0.23T in answers. My answer was 0.21T and I found this was significant: [tex]R_{m}(air)=\frac{l}{\mu_{0}S}[/tex] [tex]m.m.f.=BS(R_{m}(air))[/tex] [tex]=0.23*7*10^-5*11.365*10^6=183.5At[/tex] I did as before with the iron, subtracting the 1mm from \piD for l (in metres) [tex]m.m.f.=BS(R_{m}(iron)[/tex] where [tex]R_{m}(iron)=\frac{l}{\mu_{0}\mu_{r}S}[/tex] but I get 70, which is far from the answer of 53. For the last part (vii) I don't know why it isn't simply [tex]I=\frac{BS}{N}R_{m}(air)[/tex] with this I get 5A rather than 8Your help is much appreciated. [/QUOTE]
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Introductory Physics Homework Help
Toroid Air Gap: MMF, B-H Curve, Flux Density & More
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