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Three charged particles with charges {-q, q, -q} are placed on the z axis at z =
{-d,0, d}. See the diagram
below.
d
d
a. (4 pts) List as many symmetries associated with this arrangement of charges as you can identify.
b. (6 pts) Calculate the electric field on the x axis: i.e. determine E(x, 0,0).
c. (6 pts) Evaluate the electric potential on the x axis. i.e. determine $(x,0,0).
d. (5 pts) Show that Ex
e. (3 pts) Why were we able to apply E = -Vø as we did in part d without having obtained the full
functional form for ø(x, y, z). Be explicit.
f. (3 pts) What is E(x,0,0) in the limit x >> d to zeroth order in d/x?
g. (3 pts) What is ø(x,0,0) in the limit x >> d to zeroth order in d/x?

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