Answer to Question #90946 in Electric Circuits for Sino

Question

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

Answer 1

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

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

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