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Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

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Proof that $\frac{1}{T}$ is the integrating factor for $dq$

The choise of the extensive quantities $(U,V)$ as state variables is appropriate, but of course $Q$ is not a state function. It is better to start from the equation of a reversible adiabatic transform …
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Prove $y=y',z=z'$ in Lorentz transformation

The transformation equations between cartesian coordinates of two inertial frames $\Sigma (x, y, z, t)$ and $\Sigma' (x ', y', z ', t')$ must be linear: $$ \left( \begin{split} x' = a_{11}x + a_{12}y …
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Simple derivation of the Maxwell's equations from the Electromagnetic Tensor

The question becomes more linear if we consider the genesis of the electromagnetic tensor. Homogeneous Maxwell's equations (written here in the Gauss system) $$ \nabla\cdot\boldsymbol{B}=0 \qquad \q …
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Why should angular momentum be conserved in this case?

For a system of bodies not subject to external forces the conservation of linear and angular momentum are incontestable theorems of Newtonian mechanics. but mechanical energy isn't usually conserved. …
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