# Tag Info

12

The wording of the question suggests that the electrons were the first objects or particles whose charge required the people to establish the sign convention. But that's obviously not the case. The electron was discovered by J. J. Thomson in 1897 but for much more than a century before that moment, people had already been studying electric (and magnetic) ...

0

This is not necessarily incorrect I think, but not very clear either. Because one cannot automatically assume that everyone thinks that positive is right and negative is left, one could instead say "in the direction of motion" or "opposite the direction of motion" to denote the direction in a clear and non-biased way.

2

I wouldn't say it's necessarily incorrect, but it's certainly a bit confusing. If you have a coordinate system set up beforehand, you shouldn't need to reference "to the left" or "to the right" as well as specifying the components of the velocity. The information is all right there in the velocity components. It seems to just add confusion.

0

Lenz's law states that the electromotive force is equal to the negative time derivative of magnetic flux: $$\mathcal{E} = -\frac{\partial}{\partial t} \phi_B$$. The magnetic flux simply represents the surface integral of the magnetic field. This is important, as the area of this surface and the magnetic field at each point along this surface is now taken ...

2

The integral form of the Maxwell-Faraday law is $$\oint\limits_{\partial S} \mathbf{E} \cdot d\boldsymbol\ell = -\frac{d}{dt} \int\limits_S \mathbf{B} \cdot \hat{\mathbf{n}}\,da.$$ If you want to apply the time derivative to the integral on the RHS, you must account for two effects that can cause a change in the magnetic flux: the time derivative of the ...

0

Perhaps I can explain the difference. Consider a piston in a cylinder with the inside of the cylinder being the system. The surroundings are outside the cylinder. Assume there is a gas inside the cylinder exerting a pressure $p$ on the piston from the inside. Let there be a vacuum on the outside, but several weights sit on the outside of the piston. ...

1

The question to ask your self is "Work done on the system or work done by the system?" The sign convention (and not every book uses the same one), is all about which direction you measure as the positive displacement in the thermodynamic case. To keep it sorted out you just have to remember that the first law of thermodynamics is simply a ...

4

Yes. You are missing the fact that he is using the convention $$\nabla = (\partial_1, \partial_2, \partial_3)$$ as opposed to $$\nabla = (\partial^1, \partial^2, \partial^3)$$ The first convention is by far the most common in my experience.

2

In many books, the difference between $d$ and $\delta$ is that, in the first case, we have the differential of a function and, in the second case, we have the variation of a functional.

16

The symbol $\Delta$ refers to a finite variation or change of a quantity – by finite, I mean one that is not infinitely small. The symbols $d,\delta$ refer to infinitesimal variations or numerators and denominators of derivatives. The difference between $d$ and $\delta$ is that $dX$ is only used if $X$ without the $d$ is an actual quantity that may be ...

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