# Tag Info

1

Yes. These sentences describe the Maxwell equations. Nevertheless you should add the directions of the fields as they play an important role too, eg. at Ampere's circuital law: A changing electric field or current produces a current circulating in the orthogonal plane of the direction of change of field/current. [or something like that] You might even look ...

1

Maxwell's equations can be written in the form $$\partial_{\mu}F^{\mu\nu} = \frac{4\pi}{c} j^{\nu},\qquad \partial_{\lambda}F_{\mu\nu}+ \textrm{cyclic}(\lambda,\mu,\nu)=0$$ with $F_{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}$. Let us look at the first set: the right hand side is a vector (and this can be proven looking at the equation for the ...

0

The Lorentz force for the magnetic field $\vec F$=q$\vec v\times\vec B$ states that if you have a charge q moving in a region in which there is a magnetic field, then a force proportional to the speed of the charge acts on it. Correctly if $v=0$, then $F=0$. I don't understand what you mean with "the magnetic force is not moving" (how a force can move?), ...

2

He's just trying to discuss the most general case, as happens during all previous paragraphs (the third one also discusses a $\phi(v)$ that turns out must be 1 as well): In this paragraph, he assumes the non-prime and prime fields as already given both satisfying Maxwell equations (boxes 1 & 3). He then tries to connect them, similar to his reasoning ...

1

There's something wrong with your sign permutations in the Hodge star operator calculation. If $F = B + E \wedge dt$, then, in 2D, $F = B dx \wedge dy + E_x dx \wedge dt + E_y dy \wedge dt$, as you wrote yourself. Now, let us take our initial Hodge star as $\star dx \wedge dy = dt$. This means that $\star dt \wedge dx = dy$ and $\star dy \wedge dt = dx$, ...

2

You're missing the fact that your situation as you've defined it is physically impossible. Remember that one of Maxwell's equations is $\vec{\nabla}\cdot\vec{B} = 0$, but your magnetic field configuration $\vec{B} \propto (0, 0, -z)$ doesn't satisfy this. Given that, it's not surprising that Maxwell's other equations give inconsistent results. Incidentally, ...

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