Assignment:
Computational Project: College physics
1. Suppose the total charge Q is distributed uniformly over a ring-shaped with radius R. Find the electric potential at distance z above the center. Use: Q=1μC,R=5 cm and ,z=20 cm.
2. The potential energy between two of neutral atoms or molecules is given by Lennard-Jones:
U(r)=4ε((σ/r)12-(σ/r)6 )
Where is the depth of the potential and σis the distance at which the potential energy is zero.
Based on a model the values of the parameters for water are: ε=15.32 kJ/mol and σ=0.302 nm. Plot the potential energy versus distance for water.
Calculate the electric force and plot it by using the finite difference method and compare it with the analytical function: F(r)=24ε(2 σ12/r13 -σ6/r7 )
3. A simple model of a long DNA is a long tiny cylinderwith radius of 1 nm and dielectric constant of κ and linear charge density of λ.
a. Find the electric field at distance r from DNA.
b. Plot electric field versus distance for λ=-2 |e|/nm and κ=80.
c. Find electric potentialby using finite deference method and compare it with analytical solution.