Maxwell's equations VS. Lorentz & Coulomb force equations

[varga]

X.) Yes. Though I should say its not that it SHOULD be replaced, it just can be replaced. We normally use Vector Identities to simplify things, and not substitute directly. For example, we can take the curl on both sides of 3, then sub in the curl(B) from 4.

Y.) No.

Z.) No.

Q.) Yes. Though I think it would be more precise to say that depending on the situation, the equations in Y.) and Z.) are solutions for B.

THANK YOU! Finally... thank you, whooo. Let me clarify, Q; do you mean to say if velocity is non-relativistic we can use Biot-Savart and Coulomb's law with good accuracy? Do you mean to say there are situations where Y.) and Z.) are applicable but Maxwell's equations are not? Basically, what do you mean by "depending on the situation, the equations in Y.) and Z.) are solutions for B.", it sounds exclusive of everything else, like nothing else IS solution, but they ARE.


I'll just leave this like that for a while so everyone get a chance to disagree with what you said and hence avoid any confusion and "going in circles". For a start, I can say that I generally agree and I thank you again for making this much more clear.

 

[Repainted]

THANK YOU! Finally... thank you, whooo. Let me clarify, Q; do you mean to say if velocity is non-relativistic we can use Biot-Savart and Coulomb's law with good accuracy?

Thats right, Biot-Savart and Coulomb's law are good approximations for the E-fields of slow moving charges, obviously the faster the charges are moving, the less accurate they become.

Do you mean to say there are situations where Y.) and Z.) are applicable but Maxwell's equations are not? Basically, what do you mean by "depending on the situation, the equations in Y.) and Z.) are solutions for B.", it sounds exclusive of everything else, like nothing else IS solution, but they ARE.

I don't get what you mean. Your first statement contradicts your second. Y.) and Z.) are solutions from Maxwell's equations, so how can Maxwell's equations not be applicable to the situations Y.) and Z.) are?

Maybe I wasn't clear. What I meant was, when we solve Maxwell's equations for B, we get Y.) or Z.) or something else, it depends on the situation.

 

[varga]

What part ofdon't you understand. If you cannot do something as simple as follow a link and find Equation 21 I don't know how you think anyone can possibly help you over the internet. IMO, you are in serious need of classroom instruction; internet instruction is not likely to be successful in your case.

Sorry to anger you, kiddo. Do you understand this particular effect of "retarded time" is not even experimentally confirmed?


http://maxwell.ucdavis.edu/~electro/magnetic_field/images/bptchrg.jpg

Anyway, have I ever told you what I actually do? Do you know what that is? -- B field: The magnitude potential and its density distribution of B field does change during this time proportionally to velocity. Geometrically this potential is toroidal and its magnitude drops off uniformly with the inverse square law in a plane perpendicular to velocity vector, but it decreases as this angle goes from 90 degrees to 0 when it aligns with the velocity vector and where magnetic potential is zero, directly in line behind and in front of the charge. If we trace the magnitude potential around the charge with some arbitrary but constant radius it will describe a "ball squeezed from the front and behind" (doughnut). Therefore, I can say this field does have rotation (curl) defined by the cross product, and that divB != 0.

Has anyone ever told you that is how magnetic field of a moving charge looks like? What do you say is the divergence of that field? -- In any case, we are not going in circles - I accept all these equations, answers - but now, are you ready to pick one of those "correct" ones and solve that basic problem numerically so we can actually compare and see how big this error really is?

 

[Frame Dragger]

Sorry to anger you, kiddo.

*winces* Oh boy... this is going to get so ugly.

EDIT: Varga... do yourself a favour and learn to take criticism with more grace than this.

 

[varga]

Thats right, Biot-Savart and Coulomb's law are good approximations for the E-fields of slow moving charges, obviously the faster the charges are moving, the less accurate they become.

Thank you. All I'm trying to do here is to plot one of those CORRECTED equations as velocity goes up against classical Coulomb and Biot-Savart, all I want to see just how big this error is at 800m/s, 2,900m/s, 18,475m/s...

I don't get what you mean. Your first statement contradicts your second. Y.) and Z.) are solutions from Maxwell's equations, so how can Maxwell's equations not be applicable to the situations Y.) and Z.) are?

Maybe I wasn't clear. What I meant was, when we solve Maxwell's equations for B, we get Y.) or Z.) or something else, it depends on the situation.

Hmmm. That sounds as if Maxwell's equations produce other equations and not actual numerical results. Maybe we should use real words instead of X, Y, Z. Can you please rephrase your original statement and be more specific what situations did you have in mind and what would be suitable equation for each of those particular situations, that should settle it: - "Though I think it would be more precise to say that depending on the situation, the equations in Y.) and Z.) are solutions for B."

 

[ZapperZ]

This thread is closed because there is no hope.

Zz.