I need a charged particle trajectory in crossed E and B that is a cycloid in the x-y plane. This part is simple enough, but I want the trajectory to be parabolic in the x-z plane. The images will help explain what I need.
The left image shows the shape I want to achieve, and the right image...
Ok, so my research is basically modeling self replicating cracks with analog E and B fields. This means that I need an analytical expression (not experimental method).
I am looking to find a combination of electric and magnetic fields that create something similar to the (d) crests
Currently, I have the cracks flipped clockwise 90deg, so that the crests are concave up. And each crest can be defined by a parabolic function (which are uniform with each new...
Ok, so I have attempted your method, but I just learned forward/backward difference methods last semester. I have reduced the problem significantly and felt an update was finally appropriate.
For the spiral-paraboloid shape $$(atcos(at),atsin(at),Rt^{2})$$
I can make 2 assumptions:
1.) The B...
Thanks, do you have any insight for the 3D example? Can it be done using the same algorithm you proposed for 2D? I am working in 3D because the delamination of the thin film cracks creates an upwards peeling effect along with the planar propagation of the crack.
So, the example I used for the...
Hi, Physics Forum. I have been frequenting this site's threads since high school, and finally needed to ask some questions of my own. I am a physics undergrad working on relating self replicating fracture mechanics and E+M.
I hope I can contribute to this great community! Thanks
So I am constructing an analogy between the self replicating fracturing effect on thin films and the path of a charged particle. (Qualitatively, several cracks have similar shapes to charged particle motion) I won't go into the details of the fracture mechanics, so I will only use E+M...