Physics Help Forum Definition of a Magnetic Field

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 Apr 25th 2011, 05:12 PM #1 Junior Member   Join Date: Oct 2010 Posts: 21 Definition of a Magnetic Field What is the fundamental definition of magnetic (B) field? For example, gravitational field is defined as the gravitational force acting on an arbitrary mass divided by that mass. Electric field is electric force acting on an arbitrary positive charge divided by the charge's magnitude. And both their directions are parallel to the would-be force on the hypothetical charge or mass. My Physics B textbook from last year defined the magnetic field in terms of the direction that a compass would point. As far as direction goes this is valid but it is not sufficient to calculate magnitude, so I rejected what rather seemed to me like an amateur definition. My Physics C textbook goes more theoretical, claiming that the magnetic field is defined such that the force induced on a unit charge due to magnetism alone is equal to the cross product of the velocity and the field. Under this definition, if we knew the force (which needs not be defined in terms of magnetism since force is mechanical concept and not an electrical one) and we knew the velocity, we would backward be able to find the field and call it a definition. This is my understanding. Its just the fact that two prominent textbooks would give me conflicting definitions that threw me off guard. And also, the cross product definition makes it seem like the magnetic force is being defined in terms of the field which I do not hold to be the case because forces are mechanical concepts that are defined only in terms of mass and acceleration. But the equations are laid out in such a way that you don't really know whether it is the field being defined or the force or what magnetism even is. It does make me confused as far as definitions go. Sorry for the miscommunication. Sky Last edited by Skyrim; Apr 25th 2011 at 09:10 PM.
Apr 25th 2011, 05:46 PM   #2

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 Originally Posted by Skyrim Is the B-Field defined in terms of the B-Force (Magnetic Force) or in terms of the compass needle? Thanks.
Are you talking about in theory, or how you would actually go about measuring it?

Theoretically it is determined by something called the "vector potential" A. We use this because it is a form that is more conducive to gauge invariance.

Experimentally I really cannot say. I would take a guess that it is determined by the force, but I could be wrong. A simple way to measure the E field is to map out equipotential lines. I have not heard of this being done with the magnetic field, but then I stink at labs.

-Dan

Edit: Upon further reflection you could map out magnetic field lines using a compass...
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Apr 25th 2011, 09:01 PM   #3
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 Originally Posted by topsquark Are you talking about in theory, or how you would actually go about measuring it? Theoretically it is determined by something called the "vector potential" A. We use this because it is a form that is more conducive to gauge invariance. Experimentally I really cannot say. I would take a guess that it is determined by the force, but I could be wrong. A simple way to measure the E field is to map out equipotential lines. I have not heard of this being done with the magnetic field, but then I stink at labs. -Dan Edit: Upon further reflection you could map out magnetic field lines using a compass...
Sorry I guess I did not clarify enough. I will edit the OP.

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