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If you have a system of independently oscillating point charges as radiators and they do not have a coherence among themselves. Then, If you take single dipole it radiate in a dumbbell shape. If you orient these radiators randomly oriented in space the radiation will propagate as a spherical wave. If you let this wave pass through a slit then you will see ...

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Without touching on electromagnetism, I'd like to bring up this construction from mechanics (it's in the Feynman lectures). Consider two equal particles approaching each other with equal speed. A----> <----B You can argue from first principles that if they stick together they will not be moving afterwards -- any argument you could make ...

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As the wiki article you quote states, momentum is defined as the product of the velocity times the mass of an object. Classical mechanics developed theoretically on the lines explained by WetSavanna in the other answer, the conservation of momentum and energy being cornerstones of the theory. Classical mechanics is a very successful theory, and ...

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Momentum / energy are the conserved Noether charges that correspond, by dint of Noether's Theorem to the invariance of the Lagrangian description of a system with respect to translation. Whenever a physical system's Lagrangian is invariant under a continuous transformation (e.g. shift of spatial / temporal origin, rotation of co-ordinates), there must be a ...

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Comments to the question (v3): OP is essentially asking about the Lagrangian field-theoretic formulation of a relativistic fluid in an external electromagnetic background $A_{\mu}$. Fluid dynamics have both a Lagrangian and an Eulerian picture. (Note that the word Lagrangian is used in two different meanings.) In the relativistic context, there is also ...

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I would intuitively expect that the positive particles will go one way, and the negative particles (electrons) will go the opposite way, as per Lorentz force. The Lorentz force is acting on the particles in the standard way you would expect, but the magnetic field close to the Earth (i.e., within ~2-4 $R_{E}$) near the geographic equator is roughly ...

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In general, $\frac{\partial L}{\partial \dot{q}}$ is the canonical (or generalized or conjugate*) momentum, and $m\dot x$, for $x$ the actual position, is kinetic momentum. Likewise, the cross product of the former with the generalized coordinate vector $q$ might be called "canonical angular momentum", and the cross product of the latter "kinetic angular ...

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The mistake you made was essentially transforming the force twice. In the frame in which the matter is stationary (I'll call this the primed frame), you correctly found: $F'=q\sigma'/2\epsilon_0$ and in the frame in which the matter is moving (unprimed) you correctly found: $F=q\sigma/2\epsilon_0 \gamma^2$ Since $\sigma'=\sigma/\gamma$ this is: $F'=\... 0 For the case of a charged hollow sphere the relationship is:$m_{em}=\frac{4}{3}m_0$because$m_{em}=\frac{4}{3}E_{em}/c^2\$ The electromagnetic mass depends on the shape you assume for the charged object. In the case above it is assumed the object is a charged, hollow sphere. In general the electromagnetic mass for a charged object producing electric and ...

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