# Faraday's Law and Magnetic Induction: cause and effect, experiment and theory

## TL;DR

This paper critically examines Faraday's Law, highlighting the distinction between causality and mathematical expression, and explores how explicit causal equations might be formulated within electromagnetic theory.

## Contribution

It analyzes various approaches to explicitly incorporate causality into Faraday's Law, clarifying the relationship between experimental causality and mathematical formulation.

## Key findings

- The standard equation does not directly encode causality.
- Explicit causal formulations are possible but complex.
- The distinction impacts understanding of electromagnetic induction.

## Abstract

Faraday's Law of induction is often stated as "a change in magnetic flux causes an EMF"; or, more cautiously, "a change in magnetic flux is associated with an EMF"; It is as well that the more cautious form exists, because the first "causes" form is incompatible with the usual expression $V = - \partial_t \Phi$. This is not, however, to deny the causality as reasonably inferred from experimental observation - it is the equation for Faraday's Law of induction which does not represent the claimed cause-and-effect relationship. Here I investigate a selection of different approaches, trying to see how an explicitly causal mathematical equation, which attempts to encapsulate the "a change in magnetic flux causes ..." idea, might arise.