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6

Electrostatic refers to the case where the fields are not time dependent. In that case the Maxwell's equations reduce to: $$\nabla \cdot E =\frac{\rho}{\epsilon_o} \\ \nabla \times E = 0 \implies E=-\nabla \phi \\ \text{then,} \nabla \cdot \nabla \phi = \nabla^2 \phi = -\frac{\rho}{\epsilon_o} $$ The solution to the last equation is: $$ \phi = ...


5

Multiplying by $e^{i\theta}$ is a rotation of $\theta$ in the complex plane. Physically it changes the phase of a plane wave by an angle $\theta$. This is a global symmetry because we arbitrarily choose a reference point for measuring the phase of plane waves. If we change the phase of all plane waves by an equal amount then this is equivalent to just moving ...


5

Either. It's context dependent. Chemists generally mean the whole atoms, nuclear physicists usually mean the nucleus, and people not in those categories could mean either. And there are exception to all those rules or thumb. And the distinctions is important when people start throwing masses around because the mass of an electron is almost on the same ...


4

In general, energy levels apply to the system1 (in your case the system of electron(s) and nucleus is the atom). So it is entirely appropriate to say that the atom is excited. It is only a few cases where it makes sense to factor the notion out and say that "this piece of the system" is excited. That works OK with hydrogen-like atoms because the nucleus is ...


3

I don't think there is an exact definition. The term is used as a means of referring to an array of observation times of some astronomical phenomenon. In common usage, the terms "long cadence", or less often "low cadence", means that there is generally a longer time interval between observations. On the other hand, a "short cadence" or "high cadence" means ...


3

Besides the electric field $\vec E$ and the $\vec B$ field there are two other macroscopic fields, the displacement field $\vec D$ and the magnetic field $\vec H$. In a vaccum, $\vec D= \vec E$ (up to a scaling constant) and $\vec H = \vec B$ (up to a scaling constant). The magnetic field $\vec{H}$ is often what you make with a permanent magnetic, and it ...


3

Cosmic Velocity has nothing to do with infinity. A cosmic velocity is the minimum speed directed in the necessary direction to escape the gravitational attraction of a cosmic body such as a planet, a star, or a galaxy. Here is a paper which a student wrote about the four cosmic velocities. I don't know if his exact classifications are in common usage, but ...


2

Basically, vectors are called contravariant because their components transform oppositely to the basis vectors: if our change of coordinates is such that $$ \frac{\partial}{\partial x^i} = \frac{\partial y^j}{\partial x^i} \frac{\partial}{\partial y^j}$$ then if we have a vector $\mathbf{V}$, its components $V^i_x$ in the $x$ coordinates are related to its ...


2

In the context of ion beams, space charge is the tendency of the beam to expand transversely (perpendicular to the direction of the beam's travel) due to the mutual repulsion of the ions in the beam. All the ions have the same sign charge, so they repel. The name "space charge" comes from plasma physics where is is often computationally easier to treat the ...


2

The notation is that of one specific isotope (isotopes are nuclides with the same number of protons) of the chemical element Pu. 94 is the number of its protons, which is also the total charge, 240 is the total number of nucleons (protons and neutrons). In a neutral Pu atom there will always be 94 electrons to offset the charge of the protons in the nucleus. ...


2

A ground state $^7\mathrm{Li}$ nucleus is stable, so this reaction is either direct or involves a unstable, intermediate, excited state of the lithium-7 nucleus. If you are studying that excited state1 then you consider this reaction as $$ ^6\mathrm{Li} + n \longrightarrow \, ^7\mathrm{Li}^* \longrightarrow \, ^4\mathrm{He} + ^3\!\mathrm{H} + \text{4.78 ...


1

In nuclear physics, an exited atom is exited due to its nuclei spins being aligned in a energetically not minimized constellation. This can happen due to external energy intake or as a part of a radioactive decay where the mother nucleus' spin constellation is carried over but then nearly instantaneous changes in its daugther nucleus. The freed energy of the ...


1

Mathematically speaking they are the same operator. Usually we reserve the d'Alembertian for 3+1 dimensional spacetime (so in absence of curvature it takes the form $\partial_0^2 - \nabla^2$), while the Laplace-Beltrami operator is defined for an aribtrary dimensional manifold with arbitrary signature. The only possible difference is that sometimes (not ...


1

I think you are mixing two things: gradient and divergence. The gradient is (normally) used when you have a scalar field, or function. A scalar field (or function) is when you associate a number to every point is space. The divergence is (again, normally) used when you have a vector field, or function. A vector field (or function) is when you associate a ...


1

The process by which the lithium becomes fissile due to neutron capture is called neutron activation. The subsequent decay is simply a fission reaction. There seems to be a precedent on various sites for such a process to be called a 'neutron capture induced fission reaction', although most of the Google results for the term refer to the more usual fission ...


1

Decays happen to individual nuclei ( particles). When more than one nucleus(particle) are involved it is called an "interaction". In this case neutron Li scattering Neutron capture by a nucleus is a possibility, in this case there is an intermediate nucleus formed , which can then decay.


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In the context of nuclear or particle physics the phrase "the strong interaction" means the same thing as "the strong force". In fact we rarely write a formula for the strong force in the sense that we write Coulombs law for the electrostatic force. Both terms are refering to the strong nuclear force. In the context of perturbation theory (or the lack of ...


1

In general, no you cannot. If you're told that the three source signals are all sinusoidal (for example), then Fourier analysis will give you the answer. But if, e.g., the three source signals are each a combination of various waveforms such as sawtooth or square, then there's no way to separate them unambiguously. I would like to warn you that there's no ...


1

A constraint condition can reduce the DOF of the system if it can be used to express a coordinate in terms of the others. This can always be done in case of holonomic constraints which are basically just algebraic functions of the coordinates and time. This means that you just have to manipulate the constraint equation in such a way that one of the ...


1

In fact, global gauge transformations are a subset of local gauge transformation: changing the same amount everywhere is a special case (ie, more restricting) of changing the phase of each point independently. In the Dirac Lagrangian $$\mathcal{L} = \bar{\psi}(i\gamma^\mu\partial_\mu - m)\psi$$ you have to derive $\psi$. If you make a global transformation ...


1

Joule heating is typically associated with increases in random kinetic energy (i.e., heat) due to $\mathbf{j} \cdot \mathbf{E}$. Ohmic dissipation and resistive heating are similar in a sense to Joule heating, as all three result from fluctuating electric fields acting as an effective drag force on an otherwise free flowing charged particle. Ion drag is ...


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In physics, escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero.[nb 1] It is the speed needed to "break free" from the gravitational attraction of a massive body, without further propulsion, i.e., without spending more fuel. For a spherically symmetric massive body such as a ...



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