Question

Magnetic flux Phi = B.A is not a vector quantity. Is flux density Phi/A a vector quantity?
Can we define magnetic field, B as magnetic flux density. Are the expressions, magnetic field B and magnetic flux density, Phi/A, magnetic induction interchangeable?

Answer 1

well magnetic flux density will give the projection of B in a certian direction (normal to the surface u've chosen)

since phi is a product of two vectors, u can't really go backward with it.
there is no "reverse" action to taking the product of two vectors,
since it is not an injective action (or tranformation)
U can get the same flux in the same area, from two (or more) different B fields

so u can't really go back from phi and A and discover B


(the two B fields are at the same angle (but opposite) with the surface

Answer 2

The various definitions of vector B are (i) B = F div (v q) where vector F is force on a moving charge q, v is the velocity vector (ii) B =phi div A where phi is the flux and A is the area and (iii) \[B = mu H\] where mu is permeability and H is the strength of the magnetising field. It is easy to explain to students in the first and third cases the vector nature of B since F, v, H are all vectors. But in the second definition flux density is not a vector. So how can it be explained?
The three ways of defining B also lead to referring to it as (i) Magnetic field/Intensity of the magnetic field/ Magnetic field strength [analogous to electric field strength Vector E = F/q] (ii) Magnetic flux density (iii) Magnetic Induction. Are these terms interchangeable or are they to be used in particular contexts?

Answer 3

this is an intersting way of thinking. After all u can't define something by itself, only with interaction with other object or concepts. In physics u can usually just describe an object or idea by it outcomes, and somtimes it's sources.

By the way if u want to disccus this using skype I'll be very happy to shre my thougths and hear yours. I appriciate very much theaching.

So if we define electric field as somethong that exserts a force on charged particales,
than we can define the magnetic field as something that exeserts a force on moving charged particales
As I see it, this is the best and most accurate defenition.
[and it's the described by the Lorentz force F=q(v x B) ]
Faraday's law is some kind of a relative applaince of the same law (if the magnet is movig and not the charged particles)

The source of the magnetic field is usually a moving charged particle or current

I think indeed the magnetic field is a bit abstract concept, but it does exist,
so
To define it I think the best way is it's outcome's (like lorentz law) and it's source
not using equations, which comes later to a basic description of the phenomenon
All the best!
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