Math Insight

Applet: Particle on helix with magnet

The blue 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 cyan point on the slider), the red point represents a magnetic bead at point $\dllp(t)$. 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 arrows. The magnetic field does work on the bead as it moves along the curve.