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The factor δ(y) indicates that the charge distribtution is non-zero only for y=0, i.e. on the zx plane; likewise, δ(z) that it is non-zero only on the xy plane. Thefore, the product δ(y)δ(x) Indiactes that the charge distribution in non-zero on the intersection of zx and xy planes, i.e. the x-axis. Then, the function λ(x) defines the actual form of the ...

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$$\rho(\mathbf{r})=\lambda(x)\delta(y)\delta(z)$$ describes a charge density in the form of a (possibly infinite, depends on what your allowed x values are in the system) line in 3D space, where $\lambda(x)$ is the linear charge density as a function of x. The delta functions indicates the charge density is concentrated at one point in the yz plane, but ...

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In the standard model of particle physics which fits the data up to now elementary particles entering the lagrangian are point particles with mass. The electron, for example is one of the elementary particles, and it does have a mass and the fit gives it 0 volume. There are experiments which try to set limits to how small the volume of the electron is. ...

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Is it possible for an object to have mass but zero volume? No. Can there exist a particle/object in the universe having mass but no volume? No. Is it possible that mass can exist without volume and density? No. We think we know that matter is anything having mass and that it occupies space, but is it possible that this statement is ...

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Based on the latest breakthroughs in particle physics, the answer is a plain NO - it's not possible for a massive particle to have no volume. In fact, it is NOT possible for any particle, whether massive or massless, to have zero volume. ALL particles have a certain volume, no matter how small beyond observation. On the contrary, mass is an intrinsic ...

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Your question states that We think we know that matter is anything having mass and that it occupies space but in fact, we know better than that. We have good reason to believe that fundamental particles are point-like. In other words, they have no internal structure, size, or volume. And they indeed have mass. We have a theoretical understanding (in ...

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I'll address your question a little different, because talking about volumn and particles is problematic in many ways. Let's phrase your question "can there be two particles with mass be at the same place". The answer is yes. There are two types of particles:fermions and bosons. While fermions (electrons, protons) repel each other (not only because of the ...

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As @Goobs says, the pressure force is $0$ at the top of the water line and increases to $\rho~g~y~dA$ on a surface of area $dA$ at depth $y$. Since this pressure increases linearly from $0$ to $\rho~g~y$ the average force on the wall is the average of the start and end: so, it is half of this value, and the total pressure is $\frac 12 \rho g h (h \ell).$

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It turns out it has a special significance in terms of compressibility of information. For a state ${\rho}$ with an eigendecomposition, ${\rho=\sum_{i}\lambda_{i}|\psi_{i}\rangle\langle \psi_{i}|}$ the Von Neumann entropy ${S(\rho)}$is defined as, ${S(\rho)=-\mathrm{tr} \rho \log \rho=\sum_{i} \lambda_{i} \log \lambda_{i}}$ For any general pure state ...

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