A charged particle moving in a helical path generates a uniform magnetic field. A simple electromagnet is made of a helical electric coil (called a solenoid).
A helix is a curve in 3D space given by its parametric equation r(t) = (a cos t, a sin t, bt), where t is time, r is the position vector, a and b are positive constants.
(a) Compute its arc length between the points (a, 0, 0) and (a, 0, 2πb).
(b) Compute the work done by the force field F = (0, 0, 1) along the helical path from (a, 0, 0) to (a, 0, 2πb).