Using Ampere's Law to Calculate Magnetic Field at a Point

AI Thread Summary
Ampere's Law can be challenging to apply for calculating the magnetic field at a single point when no surface exists where the magnetic field is constant. To solve for the magnetic field symbolically, one must utilize Maxwell's equations, specifically the relationship between curl B and current density j. Depending on the configuration, the Biot-Savart law may provide a more effective approach for determining the magnetic field. The constant in the equation varies with different unit systems, which is crucial for accurate calculations. Overall, while direct application of Ampere's Law at a point is complex, alternative methods like the Biot-Savart law may yield better results.
swraman
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Is there any way to use Ampere's Law \oint_{C}\beta d\ell = \mu_{0}I to calculate teh magnetic field \beta at a single point if there are no surfaces C such that \beta is constant over the surface's perimeter?

Thanks

Raman

Edit: I mean solve symbolically, no estimation/splitting the integral up into discrete sums
 
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Ampere's law at a point is the Maxwell equation for curl B~j.
You then have to solve a differential equation for B.
 
what is B~j?
 
Depending on the set-up, you may be better off using the Biot-Savart law instead. There may or may not be a way to get an expression for current density J depending on how the question is given.
 
swraman said:
what is B~j?
Maxwell's equation is (Curl B)=k j. The constant k is different in different systems of units.
By ~ I meant that (Curl B) was proportional to j.
 
Oh ok Thanks
 
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