Timeline for Question on boundary condition for Maxwell's Equations and Coulomb's law
Current License: CC BY-SA 4.0
22 events
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| Apr 15, 2022 at 9:35 | comment | added | jensen paull | Coulombs law can be derived from maxwells equations using only gauss law and assumptions. It can also be directly derived from maxwells equations and a charge density of $Q\delta^3(r)$ | |
| Apr 15, 2022 at 9:33 | comment | added | jensen paull | In the context of electrodynamics, ( and technically electrostatics): We CAN also feel the fields from an electron in andromeda, otherwise we wouldn't be able to see the light from there. | |
| Apr 15, 2022 at 9:31 | comment | added | jensen paull | Please note $E = 0, R= \infty$ doesnt have to be the case when considering electrodynamics. Background EM solutions can exist that are non zero, that are not limited to constant solutions, but inherend wave like solutions "tagged onto" the fields 'produced' by charged. These fields are determined by initial conditions of the universe and not the location of charges and currents. | |
| Apr 15, 2022 at 9:14 | history | edited | Urb | CC BY-SA 4.0 |
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| Mar 12, 2015 at 16:24 | vote | accept | CommunityBot | ||
| Mar 12, 2015 at 3:50 | history | edited | Ali Moh | CC BY-SA 3.0 |
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| Mar 12, 2015 at 3:38 | comment | added | user70720 | Let us continue this discussion in chat. | |
| Mar 12, 2015 at 3:38 | comment | added | user70720 | Lets take this discussion to chat. Thank you very much for answering my inquiries. | |
| Mar 12, 2015 at 3:37 | comment | added | user70720 | Okay. So common sense has to be used along with Maxwell's equations to derive the Coloumb law. Does that mean that Coloumb's law isn't fully contained within Maxwell's equations and Lorentz's equation, but also with the fact that a small charge cannot produce an infinit energy? | |
| Mar 12, 2015 at 3:34 | comment | added | Ali Moh | No. It has to do with common sense and everyday experience, that a small charge cannot produce an infinite energy that permeates the entire universe. | |
| Mar 12, 2015 at 3:33 | comment | added | user70720 | So $E$ has to vanish at $r→∞$ because otherwise conservation of energy will be violated? In other word, is the boundary condition $E→0$ as $r→∞$ motivated by the physical principle of conservation of energy? | |
| Mar 12, 2015 at 3:26 | comment | added | Ali Moh | A situation where $E\neq 0$ at $r\rightarrow\infty$ is the hypothetical problem you see in electrostatics where you have an "infinite" uniformly charged wire. Or an "infinite" uniformly charged sheet. | |
| Mar 12, 2015 at 3:25 | comment | added | Ali Moh | To be precise it has to vanish at least as fast as $1/r$, because: 1- because otherwise this would imply that you can feel an electron in Andromeda. 2 - This would imply that the electric energy stored in the electromagnetic field of a small charge to be infinite (forgetting now about the energy exactly near the point charge). | |
| Mar 12, 2015 at 3:18 | comment | added | user70720 | Thanks for the re-edit. Why does $E→0$ as $r→∞$? Do there exist situations where $E$ is not zero at $r = ∞$, or am I missing something obvious? | |
| Mar 12, 2015 at 3:17 | comment | added | Ali Moh | The justification for spherical symmetry when deriving coulombs law using Gauss's law is inevitable, because if a spherically symmetric charge resulted in an asymmetric electric field this would be a very nontrivial statement about the electric permittivity of the vacuum. | |
| Mar 12, 2015 at 3:13 | history | edited | Ali Moh | CC BY-SA 3.0 |
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| Mar 12, 2015 at 3:01 | review | Low quality answers | |||
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| Mar 12, 2015 at 2:59 | history | edited | Ali Moh | CC BY-SA 3.0 |
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| Mar 12, 2015 at 2:59 | comment | added | Ali Moh | My answer was misleading, i'll edit it. | |
| Mar 12, 2015 at 2:55 | comment | added | user70720 | Also, would it make sense for a different boundary condition to be chosen such that $F(x)$ is a nonconstant function? | |
| Mar 12, 2015 at 2:46 | comment | added | user70720 | Thanks for the response. How can coloumb's law be derived from Maxwell's law and Lorentz's law without resorting to ambiguities or assumptions? Is there a link? Most texbooks include a proof using the integral form of Maxwell's equations, but the spherical symmetry of the electric field is assumed, without justification. | |
| Mar 12, 2015 at 2:42 | history | answered | Ali Moh | CC BY-SA 3.0 |