# 3-a) Consider the following configuration of point charges: charge q at ~r1 = (a, 0, 0); charge −qat ~r2 = (−a, 0, 0); charge q at ~r3 = (0, a, 0); and finally charge −q at ~r4 = (0, −a, 0); so a total offour point charges. Determine the electric field E~ at a generic point on the z-axis. Discuss whathappens when |z|  a.b) Consider the following configuration of point charges: Charge q at ~r1 = (0, 0, a); charge q at~r2 = (0, 0, −a); and finally charge −2q at ~r3 = (0, 0, 0); so a total of three point charges. Determinethe electric field E~i) at a generic point on the x-axis. Discuss what happens when |x|  a,ii) at a generic point on the z-axis. Discuss what happens when |z|  a.

Question

3-a) Consider the following configuration of point charges: charge q at ~r1 = (a, 0, 0); charge −q
at ~r2 = (−a, 0, 0); charge q at ~r3 = (0, a, 0); and finally charge −q at ~r4 = (0, −a, 0); so a total of
four point charges. Determine the electric field E~ at a generic point on the z-axis. Discuss what
happens when |z|  a.
b) Consider the following configuration of point charges: Charge q at ~r1 = (0, 0, a); charge q at
~r2 = (0, 0, −a); and finally charge −2q at ~r3 = (0, 0, 0); so a total of three point charges. Determine
the electric field E~
i) at a generic point on the x-axis. Discuss what happens when |x|  a,
ii) at a generic point on the z-axis. Discuss what happens when |z|  a.

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