Applet: Particle on helix with magnet and tangent vector
The red helix is parametrized by $\dllp(t) = (\cos t, \sin t, t/(3\pi))$, for $0 \le t \le 6\pi$. For a given value of $t$ (changed by the blue point on the slider), the magenta point represents a magnetic bead at point $\dllp(t)$. The blue vector represents the tangent vector in the direction of the particle's movement for increasing $t$. The green rectangle represents a large magnet, which induces the constant magnetic field represented by the vector field $\dlvf(x,y,z) = (-1/2, 0, 0)$ and illustrated with the green vector. The work done by the magnetic field on the particle is determined by the component of $\dlvf$ in the direction of the tangent vector, which is shown by the cyan mark on the green slider.
Applet file: helix_particle_magnet_tangent_vector.m
This applet is found in the pages
General information about LiveGraphics3D applets
This applet was created using LiveGraphics3D. To manipulate it, you can
- click and drag to rotate in any direction,
- shift + click and drag up/down to zoom out/in,
- shift + click and drag left/right to rotate around an axis coming out of the screen, and
- press Home to reset to the original view.
Most of the LiveGraphics3D applets have parameters that you can change. In general, you can click and drag points or balls around to change the parameters.
Since these applets use Java, you must have Java installed and properly configured in your browser for the them to display. You can get Java here. If you have trouble getting them to display in your browser, you can visit the LiveGraphics3D troubleshooting page for information on how to get the Java applets to work.
On occasion, even when Java is configured correctly, the Java applets don't load the first time and one instead sees an error message. You can wait a few moments to see if the applet will eventually load itself anyway. You can also reload the page to see if the applet will properly load. Sometimes, one needs to do this multiple times.