m A toroidal (doughnut shaped) sample of ferromagnetic material with relative permeability u has a mean radius R. The to

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M A Toroidal Doughnut Shaped Sample Of Ferromagnetic Material With Relative Permeability U Has A Mean Radius R The To 1 (61.85 KiB) Viewed 45 times

m A toroidal (doughnut shaped) sample of ferromagnetic material with relative permeability u has a mean radius R. The toroid is cut into two halves and the parts separated by a small distance l. A single wire is overwound on the two halves and around the air gaps separating them, with a total of N, turns. B a) If the wire carries current I, show that the magnetic field in the material of this electromagnet is μμο NI 2(TR+ul) In your answer indicate clearly the physics and any assumptions considered in the derivation. Consider all relevant Maxwell equations and the field conditions at boundaries between media. b) If the relative permeability u of the material of the toroid is 1700, the mean radius R of the original un-cut toroid is 5 cm, the cross-sectional area of the toroid is 1.1 x 10-4 m², the total number of turns N, is 800, the current I is 0.2 A and the length of each gap is 3 mm determine: 1) the magnitude of the magnetic field, li) the magnitude of the magnetic intensity inside the material, ii) the magnetic flux through all turns of the wire. c) A student says that the magnetic field is inversely proportional to length 1, and so the magnitude of the field can be changed by altering the length of the air gaps. Discuss whether this statement is correct. d) Another student says that the magnetic field at a radial distance larger than the outer radius of the toroid is zero. State whether this statement is correct, justifying your answer.