It seems there might be a confusion in your question. Refraction is a term typically associated with the behavior of light or other waves as they pass from one medium to another, causing a change in direction due to a change in the medium's properties. However, the concept of refraction is not commonly used in the context of magnetic circuits and electromagnetism.
Magnetic circuits and electromagnetism deal with the behavior of magnetic fields, flux, and their interactions with materials. Let me briefly explain these concepts:
Magnetic Circuit: Similar to how electrical circuits are composed of various components like resistors, capacitors, and inductors, a magnetic circuit consists of different elements that guide the flow of magnetic flux. These elements can include magnetic materials (such as iron cores), air gaps, and coils carrying electric current. Just as voltage drives current in an electrical circuit, magnetic potential difference (magnetomotive force, or MMF) drives the flow of magnetic flux in a magnetic circuit.
Magnetic Flux: Magnetic flux is a measure of the quantity of magnetic field lines passing through a given area. It's analogous to electric flux for electric fields. The magnetic flux passing through a surface is determined by the strength of the magnetic field and the area it passes through. Mathematically, it's defined as the product of the magnetic field strength (B) and the area (A) perpendicular to the field.
Electromagnetism: Electromagnetism is the branch of physics that studies the behavior of electric and magnetic fields, their interactions, and their effects on charged particles. Maxwell's equations are the fundamental equations that describe the behavior of electromagnetic fields and form the foundation of electromagnetism.
If you're looking for information about how magnetic fields interact with different materials or how they can be manipulated using magnetic circuits, I'd be happy to provide more information on those topics. However, if you intended to ask about something specific related to "refraction of magnetic flux," please provide more context or clarify your question so I can assist you accurately.