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We see that all the natural systems aspire for minimum potential energy state and we also see that all the natural systems also aspire for maximum entropy state. Now from this understanding it seems that entropy is inversely proportional to potential energy. All the systems aspire for minimum pot...
In dimension $3$, we have the angular momentum $\omega = q \times v$, and since
$$\frac{d}{dt} \omega = v \times v + q \times (F/m)$$
from the fact the force is central (so $F$ is parallel to $q$) we obtain the conservation of $\omega$, so $q$ always lies in the plane perpendicular to $\omega$.
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The empty vacuum of space shouldn't offer any resistance to a travelling electron, and so a large collection of electrons should similarly travel through a vacuum without resistance.
As a result, the bottom line is that an empty vacuum should be an excellent conductor of electricity, since it of...
