Physics 307 Homework
 RU Links   Radford University   Department of Physics   RU Planetarium   RUSMART pages (weather) Spring 2013 Classes & Info   PHYS 112   PHYS 307   PHYS/GEOL 406   My daily schedule   My C.V. Summer jobs/internships   NSF REU Program (list of REU sites) Other links   The Nucleus (resources for    physics/astronomy undergrads)   Pre-Health information   R.U.F.R.E.E.Z.I.N.G.    pics from the north pole trip    the picture from the trip   Simple 2-liter water rocket   American Institute of Physics Homework #4: Due Saturday, February 23 by 11:00am Here is an electric field: E={Kxx2y,Kyx3y2} where this only has x- and y-components, and Kx and Ky take care of all constants and units. Find the potential difference φ between the points (6,0) and (6,9). Here is an electric field: E=y K⋅y2x3, where the bold-faced y is the unit vector in the y-direction, and the constant K takes care of the magnitude and units.    a. Find the general expression for the electric potential φ associated with this field.    b. Find the general expression for the charge density ρ associated with this field. Here is a spherically symmetric charge distribution: ρ=K⋅r5 where K=1.00x10-10C/m8.    a. Find the general expressions (no numbers yet) for the electric field at an arbitrary distance 'r' from the origin. Note that both the charge density ρ and the electric field E will be spherically symmetric--include the appropriate unit vector for E.    b. If the magnitude of the electric field at a radial distance r=0.85m from the origin is 1.38N/C, determine the value of the constant that appeared in part (a). Here is a spherically symmetric charge distribution: ρ=K⋅r6 where K=1.20x10-10C/m9.    a. Find the general expression for the electric potential φ due to this charge distribution. Don't forget to include the correct number of integration constants!    b. Assuming the constants that appeared in part (a) are equal to zero, find the potential at r=1.20m from the origin. Using Mathematica, plot BOTH the electric field vectors and the electric field unit vectors due to two charges: (+)16μC charge located at the point (x,y)=(0.90m, 1.30m) and (-)7μC charge located at the point (x,y)=((-)1.2m, 0.45m). Both charges will be on the same plot. You are to plot this in the range x=-4.0m to 4.0m and y=4.0m to 4.0m. I would be glad to check your program before you turn it in. I'm assuming you can tell the theme of this homework is to exercise your ability to go back and forth between the electric potential φ, the electric field vector E, and the charge density ρ. There are only so many problems that I can assign and grade. Feel free to do soemthing radical like have others make up potentials, fields or charge densities for you--in both Cartesian and spherical coordinates--and go from one entity to the other.    That's all for homework #4.