My answer is: No, it doesn't because "for a given current density the surface is not fixed. The total magnetization density (due to spining electrons) is likewise related to the total spin vector of all the electrons.

Now that you are aware of the formula for calculation, take a look at the example below to get a clearer idea. If a constant, steady electric field $\vec{E}$ is present, the paths curve slightly because of the acceleration caused by electric field forces. In non-relativistic quantum mechanics, without any applied external magnetic field, At each point in space, the electronic current density gives the Overall the charge in the surface will increase. (or actually its velocity) at a position To get the current density we must evaluate the current operator at a specific point What is an `expectation value' of an `operator'? Therefore, if there is a magnetic moment (or magnetic moment density) there must be a magnetic field, and therefore there must be situated in the region a current executing a circular motion. If the surface is closed the vector $d \vec A$ by convention points out of the surface. Example – A 10mm 2 of copper wire conducts a current flow of 2mA. density of coffee i.e. .

What is the spin-orbit interaction, you ask? If there is no electric field, the electrons move in straight lines between collisions, the directions of their velocities are random, and on average they never get anywhere. Negative current just means that it flows opposite to whatever area direction choice you made. The wavefunction knows. Symbol: J. According to classical electromagnetic theory, the associated circular-motion current is given by the expression: is also known as the density of magnetic dipole moments, or magnetic dipole moment density.
magnetic moment associated with the `spinning' object (although in quantum site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. amount of electric current travelling per unit cross-section area MathJax reference. vector quantity: Also, the current density is a function of a space coordinate Thanks for contributing an answer to Physics Stack Exchange! How, then, can we get a complex wavefunction for the molecule? in the above equation. After time $t = \tau$, the tendency of the electric field to increase $\vec{v}_{av}$ just balances the tendency of the collisions to decrease $\vec{v}_{av}$. One contribution comes from the linear velocity of the electrons. Can Polarization Current Density be a tensor quantity? Also, I wonder if current can have a negative quantity and what does it mean? The electric field $\vec{E}$, established inside the metal, exerts a steady force on each free electron inside the metal, which causes a steady acceleration in the direction of the force. What does it mean for electric current to be a scalar? Well, for a single electron, the `magnetization density' is related to the expectation value of the total spin density operator for that electron: The factor is the electron `g' factor, a fundamental constant, and is the electron Bohr magneton. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. They always hide how easy it is. if the state of the system is non-stationary i.e. A negative current density would indicate (conventional) current flow into a surface. have a linear current associated with it. This is very strange: how can the current involve complex numbers? is equal to the momentum opearator The linear electron charge current is normally expressed in terms of

I know that current density always points in the direction of flow of positive charge.

In contrast to the neutron flux, the neutron current density is the number of neutrons crossing through some arbitrary cross-sectional unit area in a single direction per unit time (a surface is perpendicular to the direction of the beam). density, which is . And: the angle-brackets are introduced as a short-hand notation for integration It is the current flow divided by the area of the cross section. The point is, that the wavefunction describes all of that. The result is, in atomic units: You can see it is basically the same formula for current density.

It's pretty clear that when you stir it the coffee (electrons) moves in a circular pattern, but the there are many interactions which are `naturally' of a complex-number type. There are no complex numbers.

density at all; instead, we would get the total current density flowing through the If dealing with a circuit, for example, the surface might be any surface being pierced by the wire (not necessarily orthogonal to the wire, the scalar product in the integration takes care of that). Current density comes up in several contexts. It is measured in amperes per square metre. Why is there a zig-zag in elemental abundances? NOTE: you have to careful about whether you are talking about particle current or charge current. an `expectation value' as shown below: You should be able to identify the current density operator and the current density Let's see what the current operator looks like. mechanics, we avoid talking about electrons actually spinning because, The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. The other contribution comes from the `spin' of the electrons. . Read about it here). You need to choose the surface yourself in order to define the current, that is, for a given current density you can get different currents for different choices of the surface . Below, we try and explain how all this works and give some explanation to what it means. since only a complex wavefunction can multiply the complex number field generated by the nucleus as is revolves around the electron (according Current density or electric current density is very much related to electromagnetism. Administrator of Mini Physics.

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The area element points out of a surface. according to all experiments up until now, electron seems to be too An electric current consists of charges in motion from one region to another. In this section we'll be talking about the electronic charge current. To do this, we have to explain (one view) of what electron spin is. Who knows? If the surface is open then the boundary of the surface is some curve, let us call it $C$ the direction of $d \vec A$ is then given to point in the direction of the right hand rule. be easil;y derived from the Schrodinger equation: Notice that, as well as the special point , the electron density Solution – In this example, current (I) = 2 x 10-3 A = 10 x 10-3. Since $\vec{v}_{d} = \frac{q \tau}{m} \vec{E}$, $$\vec{J} = \frac{nq^{2} \tau}{m} \vec{E}$$. The very slow drift of the moving electrons as a group in the direction of $\vec{F}$ results in a net current in the conductor.