- #1

- Thread starter KitchiRUs
- Start date

- #1

- #2

Khashishi

Science Advisor

- 2,815

- 493

If you were a "magnetic charge", pushed around by the magnetic field, you would trace out the path of the magnetic field line.

If you think of the magnetic field as an arrow at each point, then the line of force is what you get by connecting all these arrows together into a continuous trajectory.

- #3

- 6

- 0

I'm attempting to reproduce those plots, in 2D and in 3D, but I still don't fully understand what it means when I plot Bx vs By or Bx vs x vs y (in 3D).

Would Bx vs x vs y represent the gradient of the field in the xy plane?

- #4

Khashishi

Science Advisor

- 2,815

- 493

It doesn't really make sense to plot [itex]B_x(x,y,z) vs B_y(x,y,z)[/itex] without specifying what x, y, and z are.

Gradient is something different. It is the slope of a scalar field. The gradient of [itex]B_x[/itex] is a vector field, while the gradient of [itex]\mathbf{B}[/itex] is a rank 2 tensor because [itex]\mathbf{B}[/itex] is already a vector field

- #5

- 1,233

- 18

- #6

- 6

- 0

Also, I plotted [itex]\textsl{B}_{x}[/itex] vs [itex]\textsl{B}_{y}[/itex], and it looked like the dipole field plots that we see in textbooks... After reading what you guys have said I'm confused about why that happens.

- #7

- 1,233

- 18

Then your streamline equation is:

dx(t)/Bx = dy(t)/By = dz(t)/Bz,

Which can be cross-multiplied to give your equations (dx/dy = Bx/By, dy/dz = By/Bz, dz/dx = Bz/Bx), then integrated to find

The difficulty of solving these depends on the form of

- #8

- 6

- 0

I was looking at the differential equations I had... I just didn't make the connection between them and what I was plotting.

- Replies
- 5

- Views
- 821

- Replies
- 4

- Views
- 7K

- Replies
- 0

- Views
- 3K

- Last Post

- Replies
- 4

- Views
- 7K

- Last Post

- Replies
- 1

- Views
- 961

- Last Post

- Replies
- 0

- Views
- 1K

- Last Post

- Replies
- 7

- Views
- 626

- Last Post

- Replies
- 6

- Views
- 5K

- Last Post

- Replies
- 2

- Views
- 2K

- Replies
- 3

- Views
- 24K