Concept of leakage flux, useful flux and fringing:
Leakage flux: Some flux while passing through the magnetic circuit, leaks through the air surrounding the core. This flux is called as leakage flux.
Useful flux: The flux in the air gap which is actually utilized for various purposes depending upon the application is called as useful flux
Fringing: When the magnetic flux passing or crossing an air gap then it tends to bulge outwards the iron ring, this effect is called as “Fringing”.