# Math Insight

### 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

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