You will modify a shell program to calculate the motion of a charged particle in a region of space where there is an electric field due to an electric dipole. Recall that a dipole is constructed from two equal magnitude, opposite sign charges (q) separated by a distance s. You will be given a shell program that contains the location and charge of the dipole. You will have to write a loop that does several things in order: 1) it computes the electric field caused by the dipole at the location of the moving particle, 2) it uses the momentum update formula (Newton's 2nd law) to find the change in momentum caused by the impulse from the electric force on the particle after a short time interval, 3) it uses the position update formula to determine how the particle will move in a short time step. Then the loop will repeat these calculations starting at the new particle location. After following the motion for some assigned time, you will input the final value of the particle location and velocity for credit.

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b