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8 votes

From what equations is magnetic field uniquely determined for a given current distribution?

The domain is important. The solution is given by Biot-Savart if it is the entire $\mathbb R^3$ space, with some assumptions on the regularity and decay of $B$ (e.g. $L^2$). In this case, you can ...
LPZ's user avatar
  • 13.1k
3 votes

Ampere's law on solenoid, using a circular loop

So, you're just doing: $$ \epsilon \rightarrow 0 $$ but never getting there, and then asking: "Hey, why is $\epsilon \ne 0$" The field outside the solenoid is not zero, it is only zero if: ...
JEB's user avatar
  • 35.4k
3 votes

How to avoid the ordinary Coulomb solution in QCD?

First, I think your proposed current would break gauge invariance, but that's a relatively trivial problem in that I think you could reformulate your question getting around that issue. The bigger ...
Andrew's user avatar
  • 51.2k
2 votes

Can plasmas have eddy currents?

Yes. Induced currents in plasmas can be useful. The poloidal field in a tokamak is an eddy current induced by a magnetic field that threads the torus.
John Doty's user avatar
  • 21.8k
2 votes

Is First-Class Constraint Generator of matter Gauge Symmetry in EM example?

From @Andrew's comment, I know how to solve it. In scalar QED, EM field would couple to current $J^{\mu}(x) = \phi^{\star}(x)\partial^{\mu}\phi(x) - \phi(x)\partial^{\mu}\phi^{\star}(x)$, and the ...
Ting-Kai Hsu's user avatar
1 vote

Explanation between the potential energy of a charge and the electric force experienced by a charge

As that charge moves towards the other, the force that it experiences becomes stronger. Wouldn't that mean that the charge itself could do more "stuffs" Your issue is that "potential ...
BioPhysicist's user avatar
  • 57.2k
1 vote

Why is $(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F_{\alpha\beta}\partial_\mu(F^{\alpha\beta})$?

Having realized my error of thinking the multiplication was non-commutative, it becomes clear: $$(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F^{\alpha\beta}(\partial_\mu F_{\alpha\beta})=\eta_{\...
user410662's user avatar
1 vote

Why is $(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F_{\alpha\beta}\partial_\mu(F^{\alpha\beta})$?

Here the solution asserts that this is equal to simply equal to twice the first part of the term, implying $(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F_{\alpha\beta}\partial_\mu(F^{\alpha\beta})$. ...
hft's user avatar
  • 21.9k
1 vote

Is First-Class Constraint Generator of matter Gauge Symmetry in EM example?

The solution to OP's problem is to include a pertinent matter sector in the E&M Lagrangian (3) (in OP's case: a complex scalar $\phi$). This produces the source term in the first-class secondary ...
Qmechanic's user avatar
  • 207k

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