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It is really a matter of combinations. Potential energy is a feature of a system, so between two particles there is one potential energy. The summation however, will cadd the potential energy between two particles twice (e.g., $q_1\phi(\mathbf{r}_2)$ and $q_2\phi(\mathbf{r}_1)$). Hence, the one half term has to be introduced so that the potential energy of ...


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When you ask questions about things "in the limit", the answer is almost always "It depends". In this case, the answer is "it depends". The equation $Q=CV$ assumes linear behavior of the capacitor - in reality the dielectric of most capacitors has hysteresis as well as a nonlinear component, so as you increase the voltage, the capacitance will change. This ...


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If the shell and its charge distribution are spherically symmetric and static, and if electric field lines begin and end on charges, then we know that any electric field that might be present inside the shell must be directed radially (in or out). From there, a simple application of Gauss's law, using a spherical surface centered on the center of the shell ...


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you can draw feynman digrams and then calculate scattering amplitudes and it is in the non relativistic limit is proportinal to potential.so if the potential is positive it means they repel. this sort of claculation is done in peskin book and A.Zee book.in peskin book page no 125. this is the most rigorous work to prove gravity is always attractive. by ...


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(i) Roger Shawyer Shawyer's output seems to be mostly available on emdrive.com. Among the theoretical explanations he provides there are A Note on the Principles of EmDrive force measurement Principle of Operation Theory paper None of these appear to be peer-reviewed. (ii) NWPU group Applying Method of Reference 2 to Effectively Calculating ...


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Definition of potential difference is the amount of work per unit charge to move a charged particle from one place to the another place. The potential difference between point $a$ and point $b$ is as below, $$ V_a - V_b = - \int_{\mathbf{r}_b}^{\mathbf{r}_a} \mathbf{E}\cdot \mathrm{d}\mathbf{r}.$$ What we call as potential with $V=\frac{kQ}{r}$ is the amount ...


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You are right in stating that potential and hence potential differences are dependent on field. The relation in fact is $\mathbf{E} = -\nabla V$ Hence, as we can see, if $E$ = 0, then $\nabla V$ is in fact constant, not $V$. Now, to compute the potential, we can rely on coloumb's formula, taking $V$ at infinity t be zero, for a differential ...


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The inductance of a coaxial cable does depend on the number of coils. But in addition to that, a coaxial cable will have a nonzero inductance even if it is perfectly straight, because there is a magnetic field inside the cable whenever it is carrying current, and this takes energy to set up, so you cannot instantaneously increase the current from zero to $I$ ...


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Magnetic and electric fields can transform into each other under Lorentz transformations. One mans magnetic field can become other mans electric field. Like space-time coordinates transform under Lorentz transformations, so do the EM fields.


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Since this is not a homework, I want to add some thoughts about the limits for this calculations. First, every body, if accelerated, radiates and this happens on every curved path (if the path is not the geodesic gravitational line). Second, every charged particle has a magnetic dipole moment too and this moments get aligned under the each other influence. ...


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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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Although there are different types of "radiation," their common effect is to transfer some/most of their energy to the material they "hit," resulting in the breaking of the atomic bonds and or structures of the material. When "enough" bonds and/or structures are broken, the material will fail. Since the electrical characteristics of electronic components are ...


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Mainly cost. To achieve exclusion of magnetic flux for suspension requires not only expensive superconducting materials but also refrigeration systems to lower the superconductor temperature. The other reason is control. Electromagnetic suspension is inherently unstable when used open loop to suspend objects, but by using sensors and feedback controls can ...


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This will depend highly on temperature and the material. I could not find numbers quickly, but once heated above the Curie temperature a magnet will loose virtually all magnetization (as it will cease to be ferromagnetic). When heated close to the Curie temperature fluctuations will be strong enough to let the macroscopic magnetization decay. But I guess ...


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Short answer: plasma ball emits RF "noise". The touch screen is sensitive to noise (as it tries to detect the presence of your finger by detecting very tiny currents that appear between transparent electrodes as a result of the presence of your finger (which is dielectrically different than air ). Hoping someone else will elaborate for you.


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I will try to elaborate the self-action in the standard classical electrodynamic theory. An accelerated charge radiates electromagnetic waves-that is energy and momentum. The radiated energy is removed from the the kinetic energy of the point charged particle. So under the influence of a particular force, a charged particle seems to accelerates lesser than ...


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First of all, the substitution is not entirely correct, because $ds$ is not the same as $d\vec{s}$, for $ds$ is the modulus of $d\vec{s}$ and is hence a scalar. How to approach the problem is to convert the problem from one of vectors to one of scalars, and thus be able to manipulate the moduli of vectors. Let $v$ be the modulus of $\vec{v}$ to simplify ...



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