Four identical charges (+1.6 ìC each) are brought from infinity and fixed to a straight line. Each charge is 0.36 m from the next. Determine the electric potential energy of this group.

i placed the charges as follow
q1 q2 q 3 q4
and used q1 as the starting point so EPE = 0
then i used the equation V = Kq/r and multiple the V by (1.6 micro columb) to get the EPE. I did that for q2 q3 q4 and changing r as i get closer to q4. Then i added all the EPE together but i am missing something.

EPE of q1 = 0
EPE of q2
(q1)(k)/(.36m) = V
EPE2 = (V)(1.6 micro columb)

EPE of q3
(q)(k)/(.36m) + (q)(k)/(.36m x 2) = V
EPE3 = (V)(1.6 micro columb)

EPE of q4
(q)(k)/(.36m) + (q)(k)/(.36m x 2) + (q)(k)/(.36m x 4) = V
EPE4 = (V)(1.6 micro columb)

Add EPE (1 + 2 + 3 + 4) = Total EPE of the group

but i am doing something wrong, can someone help thanks

EPE of q4:
(q)k[1/(0.36 m)+ 1/(2x0.36 m) + 1/(3x0.36 m)]

To determine the electric potential energy (EPE) of the group of charges, you are on the right track by using the equation V = Kq/r, where V is the electric potential, K is the Coulomb constant (9 x 10^9 Nm^2/C^2), q is the magnitude of the charge, and r is the distance between the charges.

Here's the correct approach to calculating the EPE for each charge and the total EPE:

1. EPE of q1: Since it is the starting point, the EPE is considered zero.

2. EPE of q2: The electric potential (V) at q2 due to q1 is V = Kq1/0.36 m. Multiply V by the magnitude of the charge, q2 (1.6 x 10^-6 C), to obtain the EPE2 = (V)(q2).

3. EPE of q3: The electric potential (V) at q3 due to q1 and q2 can be calculated as V = Kq1/0.36 m + Kq2/(2x0.36 m). Add the electric potential due to each charge, and then multiply it by the magnitude of q3 to obtain EPE3 = (V)(q3).

4. EPE of q4: The electric potential (V) at q4 due to q1, q2, and q3 can be calculated as V = Kq1/0.36 m + Kq2/(2x0.36 m) + Kq3/(3x0.36 m). Add the electric potential due to each charge, and then multiply it by the magnitude of q4 to obtain EPE4 = (V)(q4).

5. Total EPE of the group: Add up all the individual EPEs (EPE2, EPE3, EPE4) to obtain the total EPE of the group.

To summarize, correct equations for EPE of each charge and the total EPE are as follows:

EPE2 = (Kq1/0.36 m)(q2)
EPE3 = (Kq1/0.36 m + Kq2/(2x0.36 m))(q3)
EPE4 = (Kq1/0.36 m + Kq2/(2x0.36 m) + Kq3/(3x0.36 m))(q4)

Total EPE of the group = EPE2 + EPE3 + EPE4

Remember to plug in the appropriate values for q1, q2, q3, q4, and K (Coulomb constant = 9 x 10^9 Nm^2/C^2) to get the final numerical result.