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The simplest way to look at this is that energy can also reveal itself in negative forms. Don't think of it as something only positive, but also there's a negative part of it in the universe that's not directly visible. For example, we have good reasons to believe that the total energy in the universe adds up to zero. We also have experiments that show ...

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Well, if you want an answer at the 9-grader level, it's probably this: We don't know, and it's mostly irrelevant to how the universe behaves now. In particular, the Big Bang Theory doesn't care about what happened before the Big Bang. According to many interpretations of different branches of physics, the question doesn't even make sense, e.g. what happened ...

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Definitions First, let's start by defining some parameters: $\mu_{o}$ is the permeability of free space $\varepsilon_{o}$ is the permittivity of free space $\mathbf{E}$ is the 3-vector electric field $\mathbf{B}$ is the 3-vector magnetic field $\mathbf{S}$ is the 3-vector Poynting flux (also called the Poynting vector) $\mathbf{j}$ is the 3-vector ...

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It is a method that is generally used for conservative unidimensional problems (problems with only one degree of freedom, here your angle $\theta$ or cartesian coordinate $x$). You'll notice that it is equivalent to using Newton's second law in this case : let us write the total energy $E = \frac{1}{2} m v^2 + V(x)$, $V$ being potential energy. The problem ...

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