# Differences between a field, its field strength, and the force an object experiences within this field

My question is what are the conceptual and intuitive differences between these things. For example, the magnetic field B = F/(|q|v). In this case, B IS the field, and when a charged particle is travelling within this field, it experiences some magnetic force F. In this case, what is the magnetic field strength? Does it even matter, if from B we can calculate the the force the particle experiences anyway? More generally, what is the conceptual difference between a field, its field strength, and the force an object experiences when in this field? Thanks in advance, and I apologise if this question has already been answered, although I couldn't find anything answering this question precisely!

A field is usually a tensor field of arbitrary order, so a function from space(-time) to the corresponding tensor space. For example, in your case, $\vec{B}$ is a vector field, a function from time and space to three dimensional vectors. The field strength is in my experience usually used for the norm of a vector field. And usually, the field gives the force vector that an object of unit mass/charge/... experiences, so to obtain the force of an actual object in the field, you usually need to multiply the field vector with the objects "scaling value" - the mass/charge/...