Show that the vector potential given in cylindrical coördinates by ar 0 describes a uniform magnetic field b =-boz (b): find the lagrangian for a particle with mass m and charge q moving through this field and find the equations of motion. find the two conserved quantities po and p, associated with the fact that the lagrangian is independent of θ and z (c): show that if we choose the origin to be on the path of the particle, then e0 at all times. solve the equations of motion for this case and show that the particle moves in a helix.

During takeoff, the sound intensity level of a jet engine is 170db at a distance of 34 m. what's the sound intensity level at a distance of 1.0 km?

Aparticle's position is given by x = 3.00 - 9.00t + 3t2, in which x is in meters and t is in seconds. (a) what is its velocity at t = 1 s? (b) is it moving in the positive or negative direction of x just then? (c) what is its speed just then? (d) is the speed increasing or decreasing just then? (try answering the next two questions without further calculation.) (e) is there ever an instant when the velocity is zero? if so, give the time t; if not, answer "0". (f) is there a time after t = 3 s when the particle is moving in the negative direction of x? if so, give the time t; if not, answer "0".

Using the free-body diagram, calculate the net force acting on the sled. is the sled in a state of dynamic equilibrium?