What is the universal definition of 'inertia' in fields?

Question

In my physics class we recently did the Gravitational Field unit, and the idea of gravitational field strength was introduced: $$g=\frac{F}{m}=\frac{GMm}{r^2}\frac{1}{m}=\frac{GM}{r^2}$$ After doing that unit, now we're on to Electric Fields, and the idea of electric field strength was introduced: $$E=\frac{F}{q}=\frac{kQq}{r^2}\frac{1}{q}=\frac{kQ}{r^2}$$ I saw the main similarity; mass was replaced with charge (and a different proportionality constant). My teacher explained that phenomenon in general for all fields as: $$Field \,\,Strength=\frac{F}{Intertia}$$ He said in the gravitational field, the inertia is mass. In electric fields, the inertia is charge. My understanding of inertia was the classical mechanics one; the property of matter that resists change in motion. But my teacher explained that each field has it's own 'inertia'. I've been searching the web about specifically this, the formal definition of inertia across all fields, and have not come across anything. Does such a definition even exist?

Answer 1

This is an odd use of the term inertia. I would usually define the field strength as the force per unit charge, where the word charge refers to the property generating the field. Note that electrical charge is one form of the general term charge - the terminology can be a bit confusing. The term charge has a precise definition, though this is probably a bit involved for many readers.

For gravity the charge is mass, so the gravitational field strength is the force per unit mass i.e. Newton's per kilogram (which is just the gravitational acceleration).

For electric fields the charge is electrical charge, so the field strength is the force per unit charge i.e. Newtons per Coulomb.