Answer to Question #164410 in Electricity and Magnetism for pappu

Question

An iron ring has a X-section of 2 cm2 and a mean diameter of 20 cm. An air-gap of 0.4 mm has been cut across the section of the ring. The ring is wound with a coil of 300 turns . If the total magnetic flux is 0.20 mWb. The relative permeability of iron is 1000. Determine the current flowing through the coil

Answer 1

Answer

Given data

Φ = 0.24 mWb;

A = 2cm²

= 0.0003 m² ;

 B = Φ/A

= $1Wb/m^2$

AT for iron ring = H × l

=$(B/µ0 µr ) × l$

= $(\frac{1}{12.57\times10^{−7 }× 1000} )\times0.20\\=1592$

AT for air-gap

= H × l

= (B/µ0) × l

$(\frac{1}{12.57× 10^{−7}}) × 0.4 × 10^{−3}\\ = 318$

total AT provided = 300 × I = 300 I

∴ $300I=1592+318$

$I=6.37A$