3. Three point charges --q , +q, and +q are on the x-axis as shown. The negative charge is at position (x, y, z) = (-a, 0, 0). One of the positive charges is at the origin and the other positive charge is at position (+a, 0, 0).
b+
+q
A) Write down an exact expression for the voltage everywhere V = V(x, y, z). Give the answer in cartesian coordinates (x, y, z). Use your expression to compute the voltage on the x-axis at r = (5a, 0. 0). (Give your answer in terms of q, a, and known constants.)
B) What is the dipole moment of this system (magnitude and direction). Does the dipole moment depend on the choice of origin? Explain, briefly.
C) Write down an expression for the voltage using the first two non-zero terms of the multipole expansion. You cau use either spherical coordinates or cartesian coordinates (up to you) . Use your expression to compute the voltage on the x-axis at r = (5a, 0, 0)
D) Are your answers for the voltage at r = (5a, 0, 0) from parts (a) and (c) identical? Should they be? Explain, briefly.
