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  1. M

    B Holonomic basis

    Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?
  2. M

    In magnetism, what is the difference between the B and H fields?

    When the cylinder is embedded, a secondary layer of bound densities is formed around it which oppose those of the P or M whose influence would otherwise be prevalent. That is why the method will measure H or D rather than E or B Too see what I mean you can try a thought experiment using my...
  3. M

    In magnetism, what is the difference between the B and H fields?

    ...and so they are the usual assumptions for a good reason-they are the correct assumptions for the subject matter under discussion.
  4. M

    In magnetism, what is the difference between the B and H fields?

    And besides, trying to discuss vector H on the quantum level doesn't even make any sense. H is defined as: H = B/μ° - M And M is by definition a macroscopic value. It is the magnetic dipole moment per unit volume. Undefined on the quantum level, and hence so too is H.
  5. M

    In magnetism, what is the difference between the B and H fields?

    Yes, the usual assumptions in the macroscopic model.
  6. M

    In magnetism, what is the difference between the B and H fields?

    The boundary condition which states that the discontinuity in the tangential component of the H at the border between two mediums is equal to the free surface current density J follows directly from the relation ∇ x H = Jfree + ∂D/∂t
  7. M

    In magnetism, what is the difference between the B and H fields?

    But inside of a perfect conductor, there is no "polarization/magnetization" by definition. All charges/currents are "free charges/currents" and are at the surface. Where does choice come in? ...And what would you "shuffle" to change the conclusion you would be unavoidably directed to about...
  8. M

    In magnetism, what is the difference between the B and H fields?

    Nope. https://en.wikipedia.org/wiki/Interface_conditions_for_electromagnetic_fields#Interface_conditions_for_magnetic_field_vectors At the interface between two mediums, the free surface current J is equal to the difference between the tangential components of H, on either side of the...
  9. M

    In magnetism, what is the difference between the B and H fields?

    The only problem with saying H is just a mathematical construct and not a real field is that H can actually be directly measured by experiment at a particular point in space, and all without needing to know either B or M or even J locally. In this respect it is just as fundamental as E or B...
  10. M

    Factoring polynomials

    Can any polynomial in any degree of x be factored into a product of the form (leading coefficient)(x-a)(x-b) ... (x-z) as long as we can use complex numbers for a,b, etc.? Thanks
  11. M

    Can the basis minor of a matrix be the matrix itself?

    Thanks Geofleur. I thought so but just wasn't sure.
  12. M

    Can the basis minor of a matrix be the matrix itself?

    Hello I am trying to learn linear algebra, and I came across this definition of basis minor on this webpage: https://en.wikibooks.org/wiki/Linear_Algebra/Linear_Dependence_of_Columns "The rank of a matrix is the maximum order of a minor that does not equal 0. The minor of a matrix with the...
  13. M

    I Gravity on Einstein's train

    https://www.physicsforums.com/threads/need-help-understanding-electromagnetics-and-relativity.835867/ post #2: "Increasing the momentum in the y direction while keeping the momentum in the x direction fixed will actually decrease the velocity in the x direction"
  14. M

    I Gravity on Einstein's train

    ... and another question: Wouldn't it actually require a y-directed force just to keep this train moving at v in the y-direction? I ask because if the accelerating rocket's floor were the only force acting on the train, then in order for the train to conserve its momentum in the y-direction as...
  15. M

    I Gravity on Einstein's train

    Hello A couple of questions. Would a marble placed on the floor of the train roll towards the back? Would a string attached to a penduluum-like mass hung from the ceiling of the train make an acute angle facing the rear wall, and an obtuse angle facing the front wall, rather than hang...
  16. M

    Need help understanding electromagnetics and relativity

    Thanks Ben No real academic or professional background in either. But what I do know today, I've learned mostly on my own, having become fascinated with electromagnetic theory. Some years back I read a textbook on electromagnetics by an author/physicist named Nannapaneni Narayana Rao called...
  17. M

    Need help understanding electromagnetics and relativity

    Thanks so much, everybody! I'm wondering if there are any tutorials out there on understanding some of the mathematical language that has been used throughout this thread involving matrices, tensors and suchlike to describe vectors, because I'm sure I'd find it helpful. I know I'm missing out...
  18. M

    Need help understanding electromagnetics and relativity

    Okay. So in K, its velocity in the x-direction is not constant, as my non-relativistic model led me to incorrectly conclude, but actually decreases. And I'm guessing, this is having something to do with the mass increase of the particle as its acceleration in the y-direction increases its...
  19. M

    Need help understanding electromagnetics and relativity

    Hello I'm having a little trouble understanding how two observers in two different inertial frames of reference would view the same simple electromagnetic event. Let's call the first frame K, and we can use cartesian coordinates x, y, z, and t for time in K. There is an electric field E in K...
  20. M

    Ampere's circuital law

    But if in the local rest frame of each wire element there is a magnetic field B-prime, then presumably a compass situated one of the elements and riding along with it would be accordingly deflected. With no B-field in the lab frame, what is there in the body of electromagnetic law to account...
  21. M

    Ampere's circuital law

    Not an imaginary artifact. We have to be able to determine, yes or no, if compasses situated along the perimeter of the shrinking loop in the constant E field would deflect. Either they would or they wouldn't.
  22. M

    Ampere's circuital law

    is this a yes?
  23. M

    Ampere's circuital law

    The amount of E passing through a surface enclosed by the shrinking loop is lessening even though E itself is time-constant inside of it. Would that be like a displacement current through it? After all, in a Faraday law analogy, if it were a loop perpendicular to a B field, there would be 2...
  24. M

    Ampere's circuital law

    Imagine an E field coming out of your screen that is constant everywhere in space and time (∂E/∂t=0). And in your reference frame, let's say that this the only field there is -- there is no B. Say there is a loop in the plane of your screen, and so the plane of this loop is perpendicular to...
  25. M

    Maxwell's curl equations

    ∂∂∂ Thank you very much for your reply! Getting back to my shrinking loop of wire in an area of time-constant B field, would the following analysis be correct, in light of what you've said? (Let us assume either no induced current, or negligible induced current in my shrinking loop, so it...
  26. M

    Maxwell's curl equations

    If I may make a quick correction, I should have presented the integral form as ∫(closed)E⋅dl=-d/dt[∫B⋅dA], and not as ∫(closed)E⋅dl=-d/dt[∫(closed)B⋅dA] like I did, because the surface integral on the right is NOT around a closed surface. (sorry).
  27. M

    Maxwell's curl equations

    I first learned Maxwell's equations in their integral form before I was introduced to the differential form, i.e. w/curl & divergence. As I understand, in order to derive the curl form from the integral form, apply Stokes Theorem to the integral form of ∫(closed)E⋅dl=-d/dt[∫(closed)B⋅dA], and...
  28. M

    Relativistic transformation of the Lorentz force (E + v x B)

    oh wait a minute ... [duhh] ... time still dilates. ha-ha. I guess a clock moving with my test charge would tick less than a clock situated on one of the plates as the charge is accelerated in the positive z direction by either E or E'. I still really have to mull this over & study before I'm...
  29. M

    Relativistic transformation of the Lorentz force (E + v x B)

    but the force in my question is created by an E field whose only component is in the positive z-direction, and this, along with any acceleration it may create, is also in the positive z-direction. The transformation of these frames parallel to the x-y plane the test charge moves in doesn't...
  30. M

    Relativistic transformation of the Lorentz force (E + v x B)

    Thank you for your reply. I apologize if my understanding of the subject matter is not advanced enough for me to know what you mean. How can the force on something, which is a 'real event', change simply because change our inertial frame of obervation?
  31. M

    Relativistic transformation of the Lorentz force (E + v x B)

    Here is a problem: Imagine two equally charged capacitor plates parallel to the x-y axis, whose area is large enough compared to the distance between them that fringe effects can be ignored. The bottom plate (at z=0) is + charged, and the top is - charged. The vector field E is therefore...
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