- #1

- 24

- 0

I have a general question ..

if i have for example...

curl F = B

F and B are vectors and B is constant vector ..

is there any way to extract vector F?

thanks

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- Thread starter M.M.M
- Start date

- #1

- 24

- 0

I have a general question ..

if i have for example...

curl F = B

F and B are vectors and B is constant vector ..

is there any way to extract vector F?

thanks

- #2

- 901

- 2

- #3

HallsofIvy

Science Advisor

Homework Helper

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- 964

[tex]\nabla\times F= \left(\frac{\partial F_y}{\partial z}- \frac{\partial F_z}{\partial y}\right)\vec{i}- \left(\frac{\partial F_x}{\partial z}- \frac{\partial F_z}{\partial x}\right)\vec{j}+ \left(\frac{\partial F_y}{\partial x}- \frac{\partial F_x}{\partial y}\right)\vec{k}[/tex]

so that would be essentially solving the system of equations

[tex]\frac{\partial F_y}{\partial z}- \frac{\partial F_z}{\partial y}= B_x[/tex]

[tex]\frac{\partial F_x}{\partial z}- \frac{\partial F_z}{\partial x}= B_y[/tex]

[tex]\frac{\partial F_y}{\partial x}- \frac{\partial F_x}{\partial y}= B_z[/tex]

Since we can think of the cross product of two vectors as giving a vector perpendicular to both, that system, and the original equation, has a solution only if B is "perpendicular" to the "vector" [itex]\nabla[/itex]", that is if [itex]div B= \nabla\cdot B= 0[/itex].

- #4

Dick

Science Advisor

Homework Helper

- 26,260

- 619

I have a general question ..

if i have for example...

curl F = B

F and B are vectors and B is constant vector ..

is there any way to extract vector F?

thanks

## Homework Statement

## Homework Equations

## The Attempt at a Solution

There's no unique solution since there are a lot of vector fields with curl zero. If you just want any one try messing around with linear functions of the coordinates, like F=(0,a*x,b*x+c*y).

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