  # 1-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 electrostatic potential V (assuming that V = 0 as |~r| → ∞) ata generic point on the z-axis.b) Determine the electrostatic energy U stored in this configuration of charges.

Question

1-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 electrostatic potential V (assuming that V = 0 as |~r| → ∞) at
a generic point on the z-axis.
b) Determine the electrostatic energy U stored in this configuration of charges.

check_circleExpert Solution
Step 1
1. a) Potential due to discrete system of charges is given by,
Step 2

Here, Vr is the potential, q is the charge, r is the distance from ith charge to the point where potential is to be determined and k is constant and its value is 9×109 Nm2/C2.

Use the above equation and plug in the required values and find potential due to four charges at -axis.

Step 3

Hence, potential at each points on z-axis is zero.

b) Potential energy, U due to configuration of charges is the sum of the all wo...

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### Electrostatic Potential and Capacitance 