1. Here is an electric field: E={K_xx²y,K_yx³y²} where this only has x- and y-components, and K_x and K_y take care of all constants and units. Find the potential difference φ between the points (6,0) and (6,9).
2. 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.
   
3. 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).
4. 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.
5. 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.

   That's all for homework #4.