The world line of a particle is described by the parametric equations in some lorentz frame t(lambda) = a sinh (lambda/a), x(lambda) = a cosh(lambda/a) , where lambda is the parameter and a is a constant. describe the motion and compute the particle's four-velocity and acceleration components. show that lambda is proper time along the world line and that the acceleration is uniform. interpret a.

Certain bacteria (such as aquaspirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. if a transmission line carrying 100 a is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (assume that a field less than 5% of the earth’s field would have little effect on the bacteria. take the earth’s field to be 5.0 * 10-5 t, and ignore the effects of the seawater.)