Timeline for What kind of quantity is $\int_{x_1}^{x_2} \vec B \cdot \text{d}\vec s$?
Current License: CC BY-SA 3.0
11 events
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| Jan 3, 2017 at 20:26 | comment | added | Ghosal_C | @ThePhoton: I have edited the statement. | |
| Jan 3, 2017 at 20:25 | history | edited | Ghosal_C | CC BY-SA 3.0 |
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| Jan 3, 2017 at 18:59 | comment | added | The Photon | It still seems to me that your 2nd sentence implies that $\int\vec{E}.\mathrm{d}\vec{l}$ is significant only in electrostatics. Could you improve the wording to clarify? Future readers who aren't clear on what's being discussed can refer to EMF in a loop confusion. | |
| Jan 3, 2017 at 17:26 | comment | added | Ghosal_C | No problem man. You're welcome. You could accept it as the right answer if you liked it. | |
| Jan 3, 2017 at 17:11 | comment | added | Marc | Yes, I think my picture of how things work is not really correct. Thanks for the last two comments. Unfortunately, it doesn't fit into my current thinking very well. Maybe I need to look for a good book because I feel like I need more elaboration. | |
| Jan 3, 2017 at 17:08 | comment | added | Ghosal_C | See, the line integral makes sense as a loop because it allows you to integrate the amount of current passing through it, but not as an energy since you do not have monopoles and the amount energy required to transfer a monopole in a non conservative field is path conscious and makes no concrete physical sense. So when you say from infinity to that point, you better make sure you specify which path you take because talking about the starting and ending points over a non conservative integral is absolutely pointless and half information | |
| Jan 3, 2017 at 17:02 | comment | added | Ghosal_C | And also in that case the closed circular integral of the field will not be zero. It is equal to the rate of change magnetic flux. The reason I was comparing to electrostatic fields is because you drew a comparison to Gauß's law and then went on to define potential which is the energy needed to transfer a unit charge from infinity to a certain point in presence of the charges field. In case of a field to changing magnetic flux, there ARE no charges. Hence no Gauß's law or potential the electric field then is similar to magnetic field with closed loops as lines force | |
| Jan 3, 2017 at 17:02 | comment | added | Marc | That is my point. If I understood you correctly you say that we cannot hope for a physical interpretation of $\int \vec B \cdot d \vec s$ analogous to the verrsion involving $\vec E$ because $\vec E$ can be derived from a potential and $\vec B$ can't. But the line integral still has physical interpretation in terms of energy even in situations where $\vec E$ cannot be derived from a potential. | |
| Jan 3, 2017 at 16:55 | comment | added | Ghosal_C | Yes but you cannot define a potential for the electric field that arises due to changing magnetic fields | |
| Jan 3, 2017 at 16:53 | comment | added | Marc | Hmm. $\int \vec E \cdot \text{d} \vec s$ still has the property of being the energy a unit charge needs to travel along the path even if $\vec E$ cannot be derived of a potential because a changing magnetic flux makes the electric field non-conservative. So I'm not sure if your chain of reasoning is correct. | |
| Jan 3, 2017 at 16:38 | history | answered | Ghosal_C | CC BY-SA 3.0 |