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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!

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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/...
Was this the kind of answer you were looking for?

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  • $\begingroup$ Hi, yes that made some sense to me! It just clicked in my head that, say, the electric field is just some fundamental component of the universe, in that charged particles create these fields, and that our way of interacting and explaining these fields is to describe them in terms of what we can observe, i.e. Force acting on a unit charge in this case. Unfortunately I still don't quite understand what the field strength is, or is useful for? $\endgroup$ – masiewpao Jul 5 '16 at 9:14
  • $\begingroup$ It is useful if you look only at the component in the field's direction or if the field is just along the, say, x-axis - then the field is field strength multiplied by the unit vector in x-direction. $\endgroup$ – Sanya Jul 5 '16 at 10:30

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