## Magnetic circuit with an air gap

Q) An iron ring has its mean length of flux path as 60 cm and its cross-sectional area as 15 cm². If relative permeability is 500. Find the current required to be passed through a coil of 300 turns wound uniformly around it to produce a flux density of 1.2 T. What would be the flux density with the same current if the iron ring is replaced by an air core.

Given: l = 60 cm; a = 15 cm²; $\mu_r = 500$ ; N = 300; B=1.2 T.

$MMF(F) = \dfrac{Bl}{\mu_0 \mu_r}$

$F = \dfrac{1.2 \times 60 \times 10^{-2}}{4\pi \times 10^{-7}\times 500}$

F = 1145.9155 AT

If iron ring is replaced by air core.

$MMF(F) = \dfrac{B_{air}l}{\mu_0 \mu_r}$

$B_{air} = 2.4 \times 10^{-3} T$