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...
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.
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
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...
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...
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...
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
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...
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"
... 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...
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...
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...
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...
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...
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...
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...
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.
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...
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...
∂∂∂
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...
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).
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...
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...
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...
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?
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...