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

[swraman]

Is there any way to use Ampere's Law $$\oint_{C}\beta d\ell = \mu_{0}I$$ to calculate the 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

 

[Meir Achuz]

Ampere's law at a point is the Maxwell equation for curl B~j.
You then have to solve a differential equation for B.

 

[swraman]

what is B~j?

 

[Defennder]

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.

 

[Meir Achuz]

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.

 

[swraman]

Oh ok Thanks