[Phys-L] Re: Definition of electric field

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi-
        I can avoid John Denker's caveats by resorting to the approach
taken in the discussion labs of the kind advocated by Hake and by myself.
Definitions, in this approach, are operational:  I define a quantity by
telling you how to measure it (See Bridgeman, <The Logic of Modern
Physics>).  I can measure forces (with standard springs), positions, time
lapses, and, perhaps, if I am clever, velocities.  An electric field is a
fiction, deduced from mapping a certain force field in a region.
        "Field" here, is short for "vector field".  A vector field
consists of a set of vectors, each vector associated with a point in space
(or spacetime, if you want to get fancy).  Thus, a force field can be
mapped by measuring forces in a region.  An E-vector can be calculated by
measuring the force on a static electric charge at a point.
                                        Regards,
                                                Jack


On Mon, 30 May 2005, Savinainen Antti wrote:

> Hello,
>
> I was engaged with a discussion on electric field,
> force and test charge in another list. Some interesting
> points were raised and I'd like to have your responses
> to them.
>
> I have understood that the concepts of interaction
> and field are more fundamental in modern physics than
> the concept of force. However, in the definition of
> the electric field strength the force concept plays
> a central role along with a positive test charge:
> the eletric field is defined as the ratio between
> the force due to the field on "small" positive test
> charge divided by the value of that charge.
>
> 1) Is it possible to define electric field with no
> reference to forces? Is it so that one can not discuss
> fields without referring to forces? (I know that the
> electric field can be calculated from the potential
> in cases where potential can be defined. This does not
> seem to involve forces, or perhaps it does through
> the concept of work!).
>
> We define the electic field by making use of the
> positive test charge which is small enough not to
> distort the original charge distribution of the
> field that is measured. Then we continue using
> this defined electric field to determine force on
> any charge placed in the field. Now, there is no
> guarantee that this new "test" charge would not
> distort the original charge distribution and hence
> change the defined electric field strength!
> Nevertheless, many textbook exercises are presented
> with no discussion of this possibility.
>
> 2) So why is it so important to use "small" test charge
> in defining the field if it does not matter in textbook
> applications later on? I understand that the electric
> field strenght is the property of the field, not the
> property of a charge placed in the field. However,
> how realistically this is achieved in textbook
> presentations and in real measurements?
>
> Interestingly, as my colleague pointed out, Wikipedia
> defines electric field as
> (<http://en.wikipedia.org/wiki/Electric_field>):
>
> “Suppose one of the charges is taken to be fixed,
> and the other one to be a moveable "test charge". […]
> The electric field is defined as the proportionality constant between charge and force: F = qE”.
>
> This definition does not require that the test charge should be small; it is unnecessary because the other
> charge creating the field is assumed to be "fixed".
>
> 3) Do you think that Wikipedia's definition is better
> that the standard definition? How can we make the other
> charge "fixed" in practise?
>
>
> Regards,
>
> Antti
>
> Antti Savinainen, Ph.D., B.Ed.
> Senior Lecturer in Physics and Mathematics
> Kuopio Lyseo High School
> Finland
> E-mail: <antti.savinainen@kuopio.fi>
> Website: <http://kotisivu.mtv3.fi/physics/>
>
>
> --
> Tämä viesti on tarkastettu MailScanner ohjelmistolla
> virusten ja roskapostien suodattamiseksi.
> Kuopion kaupunki / ATK-keskus
> --

--
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