- #1

kated

- 2

- 1

- Homework Statement
- I want to find the potential of a field at a point where the curl of the field is zero but there are regions(for example far away from the point that interest us) that have non zero curl.

- Relevant Equations
- E=-gradV

curl E = Ω ≠ 0

We know that in electrostatics, there is path independency for line integral of E, so E is a conservative field and thus we have E=-gradV. Integrating this from ro(reference point of our choice) to the point r we are studying, along a random path, we get the solution of the above equation, e.g. the potential V. But, there are some areas (possibly far away from

the point r that interests us) where the curl E is not zero, e.g., curl E = Ω ≠ 0 , with Ω

being a vector field perpendicular to the plane, which only exists in these areas, then

how would we solve again Α=gradΛ, to find the scalar function Λ at point r? (how will the previous (usual)

solution change/get corrected?) Consider the (unusual) case where Ω is a static

(time-independent) field.

the point r that interests us) where the curl E is not zero, e.g., curl E = Ω ≠ 0 , with Ω

being a vector field perpendicular to the plane, which only exists in these areas, then

how would we solve again Α=gradΛ, to find the scalar function Λ at point r? (how will the previous (usual)

solution change/get corrected?) Consider the (unusual) case where Ω is a static

(time-independent) field.