Answer to Question #90946 in Electric Circuits for Sino

Question #90946
a coil of resistance wire of 500turns and of resistance 4ohms is closely wound on time ring. the ring has mean diameter of 0.25m and a uniform cross-sectional area of 700mm^2 calaculate the flux in the ring when supply of 6v is applied to end of the wedding. assume a relative permeability of 550
1
Expert's answer
2019-06-24T09:18:19-0400

The current in the windings of the toroidal solenoid will be


"I=\\frac{V}{R}."

Consider why it is a toroidal solenoid. The length along the axis of the ring will be


"L=\\pi D=3.142\\cdot0.25=0.785\\text{ m},"


while its diameter is


"d=\\sqrt{\\frac{4A_{cs}}{\\pi}}=\\sqrt{\\frac{4\\cdot700\/10^6}{3.142}}=0.03\\text{ m},"


therefore "L>>d".

The magnetic field of the solenoid:


"B=k\\mu_0I\\frac{N}{L}."

The flux is


"\\Phi=BA_{cs}."

Combining this all together gives


"\\Phi=\\frac{k\\mu_0VNA_{cs}}{\\pi DR}="

"=\\frac{550\\cdot4\\pi\\cdot10^{-7}\\cdot6\\cdot500\\cdot700\/10^6}{3.142\\cdot0.25\\cdot4}=4.62\\cdot10^{-4}\\text{ Wb}."




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