Why does magnetic flux leak outside an electromagnet’s core?

Magnetic flux leaks outside an electromagnet’s core because the magnetic field is not perfectly confined within the coil or the core material. While the design of an electromagnet aims to concentrate magnetic lines of force within the core, there is always a portion of the magnetic field that exists as leakage flux around the exterior of the coil.1

This leakage occurs because magnetic lines of force naturally tend to spread out when moving between regions of different permeability. Although high-permeability materials are used to "crowd" these lines into the core, they are not absolute insulators for magnetic fields, and some flux inevitably extends into the surrounding space. This leakage flux does not contribute to the magnetization of the core. The amount of leakage is generally small, provided the magnetic core possesses relatively high permeability.1