# Tag Info

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Voltage and volume are not SI-units (Volt and $m^3$ are the SI units) Both can be abbreviated as V but this in not obligatory: one can choose any letter as long as it is clear what the meaning is. By the way,the letter "U" is quite frequently used for voltage instead of V, so you can avoid the problem.

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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 ...

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You calculate the gradient of a scalar field and get a vector field as a result. scalar field means for every point in space, the field has a value. vector field means for every point in space, the field has a vector, i.e. a value and a direction. To get an intuitive understanding, imagine the surface of the earth as a scalar field. On a map for example, ...

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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 ...

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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 ...

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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 ...

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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 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. 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 ... 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. ... 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 ... 1 The entire atom is referred to by Pu. 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 ... 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 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 ... 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 ... 0 In modern mathematical terminology, a functor is called covariant when it preserves the direction of the morphisms, contravariant if it reverses it. For a given differentiable map between manifolds (of which a special case would be open sets within the same manifold), the derivative is a map between the associated tangent bundles. This defines a covariant ... 0 The named after Lorentz force$$\vec F = q_e \vec v_e \times \vec B$$is part of the phenomenon of electromagnetic induction. According to the rules of vector products, the formula is changeable - for orthogonal vectors only - to the forms$$q_e \vec v_e = ( \vec B \times \vec F) / || \vec B|| ^2$$(induction of a current in a generator) and$$\vec B = ...

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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 ...

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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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p dot in d'Alembert's formula represents the derivative of the object's momentum with respect to time. delta * r represents what would have been the displacement of the object during the infinitesimal interval of p dot. So what d'Alembert is saying is that Force minus the effect of Force = zero. If you analyze a system this way, you can treat it as though ...

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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 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 ...

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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 ...

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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 ...

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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 ...

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It is possible to interpret D'Alembert's principle through the requirement that any particle is always in equilibrium in its own rest frame; it is, after all, at rest in this frame. However, as this frame is necessarily accelerating with respect to any inertial frame, there is an additional inertial force $-m\ddot{\mathbf x}$ on the particle. The requirement ...

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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: $$\phi = ... 1 A constraint condition can reduce the DOF of the system if it can be used to express a coordinate in terms of the others. This can always be done in case of holonomic constraints which are basically just algebraic functions of the coordinates and time. This means that you just have to manipulate the constraint equation in such a way that one of the ... 0 2nd law of thermodynamics has many almost equivalent formulations. The traditional ones always assume closed system, isolation is not needed - heat and work transfer are assumed to be allowed. One formulation: When thermodynamic system goes from equilibrium state 1 to equilibrium state 2, the entropies of these states obey the relation$$ S(2) - S(1) \geq ...

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