- #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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- 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

- 41,833

- 963

[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).

Share: