Field and wave

1) Write the potential for a dipole and use ezcontour to show its equipotential lines
2) Write the potential for a quadrupole and use ezcontour to show its equipotential lines
3) Write the potential for an octupole and use isosurface to who its equipotential surfaces
4) Write the potential for the isosurface shown in task #1 of the project and use polarplot3D to show its
equipotential surface. Where are the charges located in the isosurface?
5) Explain for the problem in task #2 of Project 1, what are the general solutions for R(r) and Ξ¦(Ο†) and
why inside a cylinder
𝑉(π‘Ÿ,πœ™) = οΏ½π΄π‘›π‘Ÿπ‘›π‘ π‘–π‘›(π‘›πœ™)
𝑛
6) Explain why
π΄π‘š = οΏ½
4𝑉0
πœ‹π‘π‘šπ‘š
π‘š π‘œπ‘‘π‘‘
0 π‘š 𝑒𝑣𝑒𝑛
7) Use results in questions 5 and 6 to write the potential in cylindrical coordinates for task #2 of Project
1.
8) Explain the Matlab script using polarplot3D and show what is the critical mode the Project referred
to.