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Sure, flash lights sent within the train cannot be observed by the observer on the platform. Nobody (or no device) can see light that is not sent directly to its eyes (receiver). Observer on the platform can see light sent within the train only if it is resent to him after it travelled locally (i.e. unseen directly from the platform). Therefore, there will ...


1

Well, the key difference here is that one is a vector quantity while the other is a scalar. If your angle is measured in radians then angular frequency $\omega$ is given by $$ \omega = 2 \pi f \space \mbox{(rad)} s^{-1} $$ while angular velocity is $$ \vec{\Omega} = \frac{d \vec{v}}{dt} \mbox{m} \space s^{-1} $$ What you have above is the magnitude of ...


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The difference between stress and pressure has to do with the difference between isotropic and anisotropic force. There's a Wikipedia section on the decomposition of the Cauchy stress $\boldsymbol{\sigma}$ into "hydrostatic" and "deviatoric" components, $$\boldsymbol{\sigma}=\mathbf{s}+p\mathbf{I}$$ where the pressure $p$ is ...


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Given a stress tensor $\mathbf{\sigma}$, which has 9 components in general, the pressure (in continuum mechanics at least) is defined as $P = 1/3 tr(\mathbf{\sigma})$. So the pressure at a point in the continuum is the average of the three normal stresses at the point. The off-diagonal terms manifest as shear stress. It's hard to say "stress" without ...


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Pressure is defined as force per unit area applied to an object in a direction perpendicular to the surface. And naturally pressure can cause stress inside an object. Whereas stress is the property of the body under load and is related to the internal forces. It is defined as a reaction produced by the molecules of the body under some action which may ...


1

In principle, $\mathcal{N}$ gives you the number of supercharges in your theory. There are, however, cases with more than one irreducible (pseudo-)real spinor representations. If you have $N$ charges in one and $N'$ charges in the other representation, you can denote the total number of charges as $\mathcal{N}=(N,N')$ in order to emphasize the difference. ...


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This was answered well in the comments but I'll write it up as a proper answer. There are two main questions here: Why is there an asymmetry between matter and antimatter? given that there's an asymmetry, why did matter win out? The second question is answered rather easily. The Big Bang produced more of one of the two types and everything, from ...


1

The work required to move a charge $q$ between two locations $a$ and $b$ with a voltage difference $V_{ab}$ is $$w=V_{ab}q.$$ Differentiating with respect to $q$, one obtains $$\frac{dw}{dq}=V_{ab},$$ which is how the book got the equation. Basically, the intuition is that voltage is "work per charge moved".


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Usually problems are framed with "before" and "after" states. A book was here, a force applied, and later the book was there. So there might be an implicit time interval, but that interval is not used in calculating the work. Also, frequently, the object starts at rest and ends at rest, also providing a time interval, which again is not used in ...


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Charge is a quantity which arises from Noether's theorem, due to continuuous global symmetries (up to a total derivative) of an action, and as such we have many types of charge, other than electric. For example, consider the Dirac Lagrangian, $$\mathcal{L} = \bar{\psi}(i\gamma^{\mu}\partial_{\mu}-m)\psi$$ which describes fermions. It is invariant by a ...


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Charge is a fundamental conserved property of particles. It is, if you like, a measure of how much a particle interacts with electromagnetic fields. A particle with charge can produce and be affected by electromagnetic fields. This is what we mean when we say a particle has charge. Its a simple quantised way to measure the coupling strength of particles with ...


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It is the amount of energy $E$ that must be transferred to an object through Force so that it can get displaced by some distance $s$. In completely layman's terms, the amount of energy someone must spend to do something.


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small and big is comparison and comparison is the common denominator. If we view the distant telephone wire with one normal eye and and the other with microscopic vision, this observational dimension conflict as well as an apparent new extra dimension will arise. Physics will have to accept observers consciousness as the canvas for extra spatial dimensions. ...


1

The dot product is missing. The integral must also be multiplied by a Cosine of the angle between the vectors. $dl$ and $dr$ are the same thing. It's just an infinitesimally small distance on the direction of the field.



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