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

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


L=πD=3.1420.25=0.785 m,L=\pi D=3.142\cdot0.25=0.785\text{ m},


while its diameter is


d=4Acsπ=4700/1063.142=0.03 m,d=\sqrt{\frac{4A_{cs}}{\pi}}=\sqrt{\frac{4\cdot700/10^6}{3.142}}=0.03\text{ m},


therefore L>>dL>>d.

The magnetic field of the solenoid:


B=kμ0INL.B=k\mu_0I\frac{N}{L}.

The flux is


Φ=BAcs.\Phi=BA_{cs}.

Combining this all together gives


Φ=kμ0VNAcsπDR=\Phi=\frac{k\mu_0VNA_{cs}}{\pi DR}=

=5504π1076500700/1063.1420.254=4.62104 Wb.=\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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