DAY 4 -- Homework

----- The first four problems are PHY 232 (Calculus) only -----

1. 
   Determine g.

2. In the problem above, use the following JAVA programs to plot a surface plot of U(x,y), to plots the equipotential surfaces of U(x,y), and to plot the E-field in the chip.
   
   Surface Plotter for this problem
   Equipotential Surfaces Plotter for this problem
   
   NOTE – if these JAVA programs will not run, you can use this FLASH program
   (click here) but it is a little more complicated. There is a button for toggling between surface (3d grapher) and equipotent (contour) plots. Set xmin, ymin, and zmin to -10, and xmax, ymax, and zmax to +10. Also, you can use Wolfram Alpha (click here) and tell it to “plot <insert equation here> for -10<x<10, -10<y<10” but its free capabilities are limited.
   
   Vector Field Plotter for this problem (I have not found an alternative to this JAVA program)
   
   
   

3. A wafer of silicon in a microchip that measures 4.0 mm x 3.0 mm x 0.1 mm has a complex potential applied to it in order to channel the flow of current through the chip in a particular manner. The potential is given by
   U(x,y) = ((x+y)² + (y/20)*(1600-x²)*sin(x/4)²)/500
   where U is in mV if x & y are measured from the lower left corner of the chip in tenths of a millimeter (i.e. at the upper right corner, x = 40, y = 30, and U = 10 mV approximately). Find an equation for the E-field in this chip.
   
   
   
   

4. In the problem above, use the following JAVA programs to plot a surface plot of U(x,y), to plots the equipotential surfaces of U(x,y), and to plot the E-field in the chip.
   
   Surface Plotter for this problem
   Equipotential Surfaces Plotter for this problem
   
   NOTE – if these JAVA programs will not run, you can use this FLASH program
   (click here) or Wolfram Alpha (click here).
   
   Vector Field Plotter for this problem
   
   
   

5. An ionized Helium atom has two protons in its nucleus and one electron “orbiting” it. If the nucleus and the electron are separated by 0.1 x 10^-10 m, as shown, find all locations where the potential is zero.
   
   
   
   

6. A charge of –2 nC is located at the origin. Use the following JAVA program to plot a surface plot of U(x,y).
   
   Surface Plotter for this problem
   
   NOTE – if this JAVA program will not run, you can use this FLASH program
   (click here) but it is a little more complicated. Set xmin, ymin, and zmin to -10, and xmax, ymax, and zmax to +10. Also, you can use Wolfram Alpha (click here) and tell it to “plot <insert equation here> for -10<x<10, -10<y<10” but its free capabilities are limited.
   
   Note – in these programs the equation to be plotted must be entered in usual “computer notation”. This means multiplication is *, division is /, and powers are ^. So
   
   U(x,y) = 2x² + 4y/x³
   
   would mean the following is entered in the box that says “PLOT” or “U(x,y)”:
   
   (2*x^2)+(4*y/(x^3))
   
   

7. Three protons are located at the corners of a 1 mm square. Find the potential at the 4^th corner.