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mathperson
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What is the electric field outside a steady state current loop?
Why is this not discussed in textbooks?
Why is this not discussed in textbooks?
0 (provided the usual case of an uncharged wire)mathperson said:What is the electric field outside a steady state current loop?
Because 0 is boring, even for textbooks.mathperson said:Why is this not discussed in textbooks?
That depends on the properties of the wire itself. There will be no e-field inside a perfect conductor, there will be an e-field inside a resistor.DaTario said:and what about inside?
That is not quite true. The relativistic corrections to the E field of a rotating charged ring are of the same order of magnitude as the B field. A rotating charged ring is not the same as a ring with a current.Phrak said:The motion of the charge will have no additional effect.
clem said:That is not quite true. The relativistic corrections to the E field of a rotating charged ring are of the same order of magnitude as the B field. A rotating charged ring is not the same as a ring with a current.
clem said:The E and B fields of a moving electric charge are the Lienard-Wiechert fields.
See an advanced EM text.
Yes......Phrak said:Are you claiming that the field solution of a ring that is charged and rotating in not the same as the superposition of a static ring of charge and a ring of current, classically treated?
This is completely incorrect. A single moving charge is in fact a current. For a uniform ring of current the magnitude of the current is given by J DiracDelta(x²+y²-R²,z). For a single moving point charge the magnitude of the current is given by qv DiracDelta(x-X,y-Y,z-Z). In the limit of a continuum of charges moving in a ring given by X²+Y²=R² and Z=0 it is clear that the above two expressions are the same. And the description for both are handled by Maxwell's equations.clem said:The motion of charged particles is in many textbooks. It does not matter if you have one particle or billions. One particle in motion or many are not the same as a current.
That is why you can't use the fields of a current for one or many moving moving particles.
Note the key word "superposition" that you used above. Don't forget that you can get both constructive and destructive interference in superposition. These radiation components from anyone point charge are eliminated by the principle of superposition by destructive interference from the contributions of all of the other charges.mathperson said:trying again: A charged particule going in a circle generates an electric field in part due to its acceleration. Yet the acceleration from a classical current loop does not contribute to the electric field? What hypotheses are used to decide this either way? Isn't a classical wire a superposition of an equal amount of + & - charge continuously distributed along a curve?
Vanadium 50 said:Radiation requires a changing multipole moment. This system has exactly one non-zero moment, the magnetic dipole moment, and it's static.
The argument that a single accelerating charge radiates neglects a very important fact: this is not a single accelerating charge. Suppose I had a rotating plate, and I place a charge at 0 degrees. This plate radiates. Now, I put another charge at 180, and now I no longer have any electric dipole radiation. I do still have quadrupole radiation, so I place charges at 90 and 270. Now the highest surviving moment is electric octopole, which can be zeroed out with charges every 45 degrees. In the limit of a continuous ring of charge, there is no radiation: radiation from any point on the ring is canceled by radiation from other points on the ring.
This has nothing to do with superconductivity. It's true if you simply glued charges to a ring. It's all in Chapter 9 of Jackson.
Now, you might ask, "yes, but we know charges aren't continuous: they're discrete - doesn't that wreck your argument?" Yes, but they are really, really close to [continuous]: you have millions of electrons, so it all cancels except for the million-pole terms, and those radiate very, very little power. Possibly the age of the universe per photon.
Certainly not, what would make you think that? It would be astounding indeed for a linear system to have the same output for a "point" input as for an arc of points. Like finding that 1+1=1 instead of 2.mathperson said:If a charge going in a circle generates such a field, then wouldn't an arc of charge do the same?
Yes, this is the correct approach. The ring can be treated as a superposition of a continuous circle of point charges in uniform circular motion. In terms of the principle of superposition, do you understand the concept of destructive interference that I mentioned in my previous post and that Vanadium described implicitly the quote?mathperson said:Also on page 489 he treats a wire a a superposition of + & - continuous line charges with no acceleration.
Yes.mathperson said:Divide a circle of charge into small enough arcs so that each arc may be regarded as a point charge. If the circle is rotating, each point has a velocity cross acceleration vector pointing in the same direction. Apply eq(9.107) page 424 (electric field of a point charge equation) to each point charge and take the vector sum.
Although I don't know enough to follow the superposition argument, my guess is that it shows that there is no time varying electric field.
How so?mathperson said:Consider a ring of - charge superimposed on a ring of + charge of equal value. If both rings are stationary, there is no net field anywhere. If the - ring rotates and the + one doesn't, the above argument shows there is an electrostatic field.
The electric field of a current loop refers to the force field that surrounds a current-carrying loop of wire. It is created by the movement of electric charges within the loop and can affect other charged particles in its vicinity.
The electric field can be calculated using the formula E = (μ0/4π) * (2πIR²)/r³, where μ0 is the permeability of free space, I is the current flowing through the loop, R is the radius of the loop, and r is the distance from the center of the loop to the point where the electric field is being measured.
The strength of the electric field of a current loop is affected by the current flowing through the loop, the radius of the loop, and the distance from the center of the loop. It is also influenced by the medium in which the loop is placed and any nearby electric charges.
The direction of the electric field of a current loop changes with distance according to the inverse-square law. This means that the strength of the electric field decreases as the distance from the loop increases, and the direction of the field lines becomes more radial.
The electric field of a current loop has various applications, such as in electric motors, generators, and transformers. It is also used in medical imaging techniques such as magnetic resonance imaging (MRI) and in particle accelerators to control the motion of charged particles.