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Molecules are not that large. The density of air at 1 Atm and 20°C is $2.5\times 10^{25}$ m$^{-3}$. So, the average spacing, using your teacher's method, is about $(2.5\times 10^{25})^{-1/3} = 3.4$ nm. The radius of molecular nitrogen is 0.2 nm. So, the diameter is about 0.4 nm. The means that only about $(0.4/3.4)^3 = 0.0016$ of the volume of air is ...

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The velocity vector is changing all the time. The magnitude is constant, but the direction is changing all the time (circular motion). So, the Lorentz force, which is perpendicular changes $\vec v$ without changing its magnitude $v$, which is prohibited as the energy increase is $\vec F . \vec v =0$.

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Then an electron moves non-parallel to a magnetic field it get deflected. But the curve the electron describes is not a circle. The electron moves on a spiral path and this time it slows down to zero velocity. To be precise the spirale path is a path made from "tangerine slices". How does this happens? The reason for the so called Lorentz force is based on ...

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The power (work per unit time) of a force $\vec F$ on a particle with velocity $v$ is given by: $$P = \vec F \cdot \vec v.$$ If this number is positive, then the force tends to speed the particle up. If it is negative, it tends to slow the particle down. You can see this in the Work-Energy theorem, the differential form of which consists of applying ...

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The smoke is a mixture of air and tiny 'dust' particles, which are much larger than the air molecules and undergo Brownian motion. Watching the dust particles under a microscope in a smoke cell (where the smoke is at rest), one can directly observe this Brownian motion.

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