New answers tagged

1

Here is an explicit way to see why $\vec{A}$ is defined at all points. The vector potential $\vec{A}$ is given by the following: $$\vec{A}(\vec{r},t)=\int d^3r’ \frac{\mu_0}{4\pi}\frac{\vec{J}(\vec{r}’,t)}{\big| \vec{r}-\vec{r}’\big|}$$ As is evident from the RHS of the above equation, the vector potential at a point is a result of integrating over all ...


0

Maxwell's equation $\textrm{curl} \textbf{E}=-\frac {\partial\textbf{B}}{\partial t}$ is true irrespective of the current, hence you always have $\textrm{div}\frac {\partial\textbf{B}}{\partial t}= \frac {\partial}{\partial t} \textrm{div}\textbf{B}=0$ hence $\textrm{div}\textbf{B}=constant-of-time$. But we also know that $\textrm{div}\textbf{B}=0$ always ...


1

I think you can agree that the magnetic field $\mathbf B$ can be defined in regions where $\mathbf J$ is $0$ (think of the field around a current carrying wire). Since the vector potential $\mathbf A$ relates to the magnetic field by $$\mathbf B=\nabla\times\mathbf A$$ the curl of $\mathbf A$ must also be able to be defined in regions where $\mathbf J=0$, ...


1

In the early universe the density would be so large that space would be effectively filled with a medium. Today the universe is so sparse you need to travel for millions of miles to get from one chunk on matter to another. On a smaller distance scale where molecular bonding occurs one can have acoustic vibrations, on the smallest scale lattice vibrations ...


0

The dashed lines are the ones that arise from the S state (n=2, l=0, j=1/2). The other lines all arise from P states. This graph ignores the lamb shift. According to Dirac (not quantizing the EM field), the state (n=2, l=1, j=1/2) has the same zero-field energy, splits also in two at non-zero fields, but has a smaller g-factor and thus smaller splitting. ...


0

But the definition of a surface is via a normal vector to that surface $d\vec{A}$ at every point on it. The only ambiguity is the 180 degree ambiguity of which way it points (always outward if it is a closed surface, or you can choose otherwise). The total flux through that surface is $\Phi = \int \vec{B} \cdot d\vec{A}$, which reduces to $BA \cos{\theta}$ ...


0

The answer is yes. However, the reason why people did not do it this way is because it is lengthy to calculate the angle $\alpha$. Think about it, when we have a surface, the mathematical description is always given as the normal vector to that surface. Meanwhile, if you want to find out $\alpha$, you need to first determine the projection of $\vec{B}$ on ...


0

As this electron undergoes circular motion, it emits EM radiation, so it goes through a spiral trajectory with a continuously decreasing orbital radius. What is electromagnetic radiation at the particle level of an electron ( a quantum mechanical particle)? The emission of photons. The probability of emitting a photon which will take away energy and thus ...


0

The whole question is perfectly formulated, but allow me to reconsider these formulations nevertheless. As far as I know, when electrons travel perpendicular to a uniform magnetic field, the Lorentz force makes the electron undergo circular motion. The Lorentz force is the expression for the observed phenomenon that moving charges are deflected under ...


0

The constant speed of electron is by assuming electron does not emit EM radiation.You just mixed up with it.


-1

Using Ampere's circuital law for a single loop of the solenoid, we have $$B*L=(\mu)(i)$$ where: L is the length of the solenoid. $\mu$ is the (permeability of free space) i is the enclosed current This implies that if there are N windings in the solenoid, $$ B=(\mu)(N)(i)/L$$


4

There is a medium: the plasma which filled space in those early times. And on a large enough distance scale, space is 'full of stuff' even now, though at a low average density.


0

Ampère's circuital law states that the line integral of the magnetic field around some closed curve $C$ is equal to the enclosed current $I_{enc}$ : $$\oint_c\vec{B} \cdot d\vec{l} = \mu_0I_{enc}$$ By solving the integral you should be able to obtain the relationships that you are looking for


0

What you are asking for is the period of the wave. Electromagnetic waves have the same fundamental wave characteristics as all other harmonic waves. At every point through which the wave passes the electric field oscillates with a fixed frequency - in this case $f=5GHz$. The time between the wave reaching consecutive peak values is the period $T$. As ...


0

lets start here : Electromagnetic waves carry energy as they travel through empty space. There is an energy density associated with both the electric field E and the magnetic field B. As wavelength $λ=c/ν$ , so if you know the frequency you know the wavelength. Highest to lowest is 1/2 wavelength as seen in the figure, talingthe y axis.. Now if you ...


1

A line does not have to be straight, that is not part of the definition of the word.


1

Lenz's law states: $$ \varepsilon = - \frac{d\Phi}{dt} $$ Where $\Phi$ is the magnetic flux, and $\varepsilon$ the electromotive force. However, the problem gives us not the change in the magnetic flux, but the change in flux density, i.e. the magnetic field $B$. You can rewrite Lenz's law as: $$ \varepsilon = -\frac{d}{dt} \int B \cdot dA, $$ Where $A$ ...


2

As pointed out in the comments, Lenz's law is only a qualitative statement, while Faraday's law is the appropriate quantitative statement. It says that a changing magnetic flux $\Phi_\mathrm{enc}$ induces an EMF ("electromotive force", i.e. a kind of "voltage around the ring" $$ \mathcal{E} = \oint \vec{E} \cdot d\vec{\ell} = -\frac{d\Phi_\mathrm{enc}}{dt}. $...


1

Today we all know that at the lowest known level, the quarks, that build up the nucleons, these are held together by the strong force, and it is much stronger then any other force at this distance, that is why quarks exist in confinement, in our universe (except maybe inside black holes). Now the nucleons are held together by the residual strong force (...


0

The OP is completely, totally, correct. There are many common objects, example https://en.wikipedia.org/wiki/Magnetar where the "self-" magnetic field is so strong that it easily rips apart objects, molecules, atoms, and even photons. Such things are the common state of the universe. In really rare, unusual, conditions (eg, your fridge magnets, on ...


10

That does look like there are real lines, doesn't it? It's because each iron filing becomes its own magnet which affects the others. Notice how they're all crowded together close to the ends of the magnet, and then there's a region where they're thin, and then they get closer together farther away? I think that's because close up, the magnetic field of ...


0

What is happening when iron filings form a "field line" pattern, is actually an energy minimisation process, somewhat akin to the reason that solar systems form out of rotating clouds of dust. Each individual iron particle becomes magnetised by the applied field, much more so than the surrounding medium. There are then forces acting on the adjacent iron ...


0

Magnetic field lines show the direction of force a magnetic mono-pole would experience if it were free to move under the influence of a magnet, but unfortunately, we all know that mono-poles are just a thing of imagination and don't exist in reality. This is given by Gauss' law for magnetism which states $$\oint \mathbf B\cdot\text d\mathbf s=0$$ Whenever ...


20

Magnets are held together the same way all solids are held together: chemical bonds between the particles that make up the magnet, which are ultimately due to electromagnetism. Take two fridge magnets that attract each other, stick them together, and pull them apart. Then take an ordinary piece of metal, and pull on its ends with about the same force. This ...


77

The chemical bonds of the material keep it together. If the magnets you're thinking of are made of metal, then the chemical bond is the metallic bond, which is quite strong. You can get a sense of how strong it is if you try to rip a metal bar into two. Unless you are exceptionally strong, you probably won't manage – but you are probably able to pull a bar ...


1

The iron filings themselves repel each other and create a pattern that can be observed visually as lines. Liquid metals create mountains that end with peaks as the active forces dissipate, so you can see the concentration is highest nearest the origin.


1

Note: I'm assuming that you want to levitate the 600 kg object to the center of it's container, leading to the following comments. Force from a magnet follows the inverse square law, meaning that if you try to use a constant magnetic field from an adjustable electromagnet, the position of your 600 kg object will be unstable. As you slowly increase the ...


0

A body need to be charged or magnetic to be affected my a magnetic field. A charged body can be contained in something like a cyclotron where it can be forced to follow a circular path. If the body is magnetic, it can easily be levitated by surrounding it with other magnets Humans are not affected by large magnetic fields upto around $20$T as evidenced by ...


77

Individual iron filings will align their long dimension with the magnetic field. But then they will also feel the induced magnetization in other iron particles nearby, and they will tend to move toward each other till their points touch. This is what creates the strings of iron particles. When the needles cannot move from their site, one does not get lines.


0

Force, like all vectors, is not a Lorentz invariant. It is therefore not surprising that the force between two protons depends on which frame of reference is considered. The calculation is simple to do by calculating the electric and magnetic fields observed in the frame in which the protons are seen to be moving. Both fields appear different in the moving ...


6

When we say that magnetic field lines don't exist we mean that there is no physical form of them. Magnetic field lines just represent the direction of force which a ferromagnetic substance like iron would experience in the vicinity of a magnet (the pattern formed by iron filings). The specific lines or pattern is formed because that the the actual ...


81

Here's a map of the barometric pressure in the United States. The map contains isobars, which are lines of constant pressure. These are constructed by starting from an arbitrary point, and following the direction where the pressure doesn't change. Isobars don't "exist", in the sense that there isn't literally a big white line in the sky hovering over New ...


4

It is true that magnetic field is a vector, and if you have two magnets, the resultant field is the vector sum of the fields from each magnet. But that isn't what your teacher is talking about when he says field lines never cross. Iron filings line up with the magnetic field like little compass needles. They show the direction of a field from a single ...


9

You are correct. But so is your teacher. If two magnetic fields are added at a point then the direction of the magnetic field at that point is given by the resultant, which is the same as the direction of the compass needle. Magnetic fields are vectors and there is always only one resultant no matter how many vectors are added together. Magnetic field ...


7

As others have pointed out, this is not an erratum. It can sometimes help to skip the fancy products and use a more sophisticated notation. So that is what this answer will do. Abstract Index Notation In one, called abstract index notation, we denote vectors with raised indexes, and covectors (linear mappings from vectors to scalars) with lowered indexes. ...


-1

Fire radiates light. Nobody cared how it happens. With the help of electrochemical potential and later electrical induction, electrons were moved in electrical circuits that became hot. Edison perfected the light bulb, and inside the bulb the circuit became so hot from the moving electrons that it glowed. In the end it turned out that the emission of light ...


0

The answer to your question is photons, which create an electromagnetic field, no matter if vacuum or not. In a vacuum, the speed of photons is c=299792458 m/s and is also related to electromagnetic wave/ light shape.


-1

You are asking how there can be fields in vacuum, even though as you say there are no electrons present to create the EM field itself. You are confused because of the definition of vacuum. Even though vacuum in some context might mean sometimes the same as empty space, the fields still fill the fabric of spacetime throughout, that is, for example the EM ...


0

according to Maxwell's equations, the time derivative of the electric field is equivalent to a rotation of the magnetic field, which makes a pair of electric and magnetic fields self-propagating through a vacuum. So, for example, the rapid movement of charges back and forth along a wire in a vacuum will create a rapidly-varying magnetic field in the ...


0

Why does it change its direction above and below the wire? What is the reason ? First of all, it is an experimental result. The postulated existence of a magnetic field around a conductor, and how it changes in direction and intensity according to angle and distance, is a consequence of that result.


0

The magnetic field of a wire is circular around the wire, so it changes direction continually if you go around the wire.


1

It is unclear what the OP exactly would consider an analog of the Zeeman effect on BH-magnetar merger. Such a merger is not characterized by discrete frequencies that could be shifted or split. However, at least in principle, the waveform of such a merger should carry the imprint of the magnetars magnetic field. (E.g. the orbital motion of the magnetar, ...


0

Nothing flows along magnetic field lines. They are just a mathematical construct to help visualize the field. At each point along a field line, it is parallel to the magnetic field. Most of the magnetism in a permanent magnet comes from electron spins, not the movement of electrons. Spin is a fundamental property of elementary particles, a purely quantum ...


1

If U and I are in antiphase, the system oscillates. This oscillation contains energy (which you previously put in). To arrive in an "in-phase"-state, it will dissipate the surplus of energy you previously put in. A mechanical analogy: You have two masses connected via a spring. Now you take one mass and push the object really fast to accelerate it forward. ...


2

No, here is what's happening. When a coil of wire is carrying a flow of electric current, it creates a magnetic field that loops through the center of the coil and out & around the exterior of the coil. The field is conveniently represented by field lines that trace out the direction a compass would point at various locations in the field. To build ...


0

I think nothing special happens as the outer ring rotates. If we use rings with real small thicknesses, the revolving of any of them around its center produces no tangible electric field circularly surrounding the ring. Even if there is any such electric field, it cannot set the inner ring magnet into motion. And, even if you slightly rotate the inner ring,...


0

The strength of an electromagnetic field scales as (number of turns) x (number of amps). The effectiveness of the electromagnet at lifting things has to do with the layout of the pole pieces that "focus" the field into the region of space in which you want the lifting effect to be concentrated. Both ampere-turns and the pole piece design are important.


0

A nice resource is GSU. Has a good pix illustration of the field lines as well. Note, the magnetic flux is a scalar quantity, while the magnetic field and area are bivectors. In electromagnetism, ‘flux’ is defined as a scalar (the surface integral of a vector field, i.e. a density function by unit area), with the term ‘flux density’ used for the bivector ...


1

This is a dichotomy of a discrete variable (the finite "number" of field lines) and a continuous variable (the B field smoothly changing values over all of space). While your question is specifically directed to magnetism, the intuition for the relationship between B-field strength and counting field lines might be more visible if we abstract the problem. ...


2

No, there is a field line passing through every point in space, so they are infinite in number. However, if you follow a finite number of field lines, they will be closer together when the magnetic flux density is greater. It may be better to think about a flux tube bounded by field lines. Gauss's law predicts that the product of the magnetic field and the ...


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