Talk:Ampère's force law

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[edit] A timely article

The addition of this page on Ampere's Force Law deserves warm applause. The lack of it has caused problems in other Wikipages dealing with electromagnetism. The following suggestions might improve it.

1) Change the units for the infinitessimals from amperes to metres (or 'meters', if you favour, sorry favor, the US spelling).

Rationale: The left hand side of the equation for F12 must have units of newtons. The units of mu0 are correctly stated as newtons / (ampere)2. Therefore the dimensions of the subexpression between the equals sign and the integral are also newtons. Consequently the integral part needs to be a dimensionless expression. If the infinitessimals, dI1 and dI2, both had units of length then it's easy to see how they drop out against the R2 on the denominator. If, on the other hand, the infinitessimals really had units of amperes then how is a dimensionless expression reached? All writers agree that the infinitessimals are called 'current elements', so the natural (but incorrect) assumption is that their units should be amperes.

2) Change the symbol for the infinitessimals from I to s.

Rationale: The confusion above is compounded because a lower case letter l (ell) is easy to mistake for an upper case I (eye) - a problem which still afflicts my own page on AFL, and also the BIPM (reference 6). At least one writer of repute, Brebis Bleaney, avoids the problem by using lower case s (ess) for the infinitessimals. It's then much clearer that you are dealing with a distance.

3) Change the definition of AFL from 'The force of attraction or repulsion between two current-carrying wires' to the equation for F12.

Rationale: Encyclopedic definitions require concision; and mathematics is the most concise language we have. This is the stance taken by, for example, David Cheng who states that the F12 equation is Ampere's Law.

The paradigm is surely Coulomb's law, which no one defines as 'The force of attraction or repulsion between two charge carrying spheres'. Definitions of CL always emphasise the key concepts of inverse square falloff and the product q1 q2.

4) Change the definition of AFL to that given by the BIPM: the integrand of the F12 equation.

Rationale: For one thing, the differential version looks less intimidating than the double integral one.

d^2\mathbf{F}_{12} = \frac{\mu_0 I_1 I_2}{4 \pi r^2} \left \lbrace d\mathbf{s}_1 \times \left ( d\mathbf{s}_2 \times \hat \mathbf{r}_{12} \right ) \right \rbrace

The main reason is to maintain consistency with CL.

Consider that CL relates hypothetical 'point charges'. It doesn't directly correspond to any real-world electrostatics apparatus (even an electron isn't a point). This ought to be reflected in our thinking about magnetostatics. We can't verify AFL directly because an isolated current element is physically impossible. However, we don't much care about that because AFL supplies the fundamental basis on which the force between practical current carrying thick wire circuits is calculated.

Bleaney avoids the phrase "Ampere's Force Law" but he starts with the differential form as, I think, should Wikipedia. BIPM uses the phrase 'the corresponding (to CL) equation for the magnetic force'. Well, I feel that that is what AFL really is: the magnetostatics counterpart to CL. There are higher level discussions in electromagnetism which rely on linkage of CL and AFL. These will be facilitated by treating AFL in this way. True, Ampere may not have used the differential form; but then he didn't give the same double integral that the present page does.

Certainly, both the parallel wires equation and the general integral form should be retained; but as derived cases and not as starting points.


RAClarke (talk) 23:13, 15 March 2008 (UTC)

Well I agree with 1 and 2, and just implemented those changes. As for the other suggestions, I'd be fine with it either way, for my part. Go for it, if you want. :-) --Steve (talk) 22:26, 16 March 2008 (UTC)
I favor a definition in words followed by the equation because math just turns most people off immediately. Could use dℓ d \ell for elementary length to avoid use of dl dl. Brews ohare (talk) 00:56, 17 March 2008 (UTC)


Hi Brews,

I favor a definition in words followed by the equation because math just turns most people off immediately.

Speaking as an engineer whose grasp of vector calculus is shakier than Galloping Gertie, I have much sympathy with your viewpoint. The CL page indeed uses words first. The challenge, though, is to devise words that mean something more specific than the present vagueness yet are less mind numbing than an end user licence agreement:

Ampere's Force Law states that the electromechanical force exerted upon a conductor of negligible thickness, length and curvature is inversely proportional to the square of the distance separating that conductor from a second, separate, such conductor and is directly proportional to both the product of the current magnitudes and the sine of the angle made by a line joining the conductors.

I admit this is neither watertight nor snappy. Have you anything better?

Usually, a picture is worth a thousand words but the vectors, being necessarily three dimensional in nature, when drawn in 2D (by Bleaney, for example) just confuse. In the very long term I'd like to try something with Java 3D. Does Wikipedia support that?


RAClarke (talk) 13:05, 20 March 2008 (UTC)