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.

Step 1

(a)

The figure 1 shows the generic point charges.

Step 2

The electric field at a generic point on the *z* axis is,

Substitute the point values from the given figure.

Step 3

According to the given condition,...

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