Find the electrical potential energy (EPE) of three point charges placed as follows on the x-axis: +2.0 μC at x = 0, +3.0 μC at x = 20 cm, and +6.0 μC at x = 50 cm. Take the (EPE) to be zero when the charges are far separated.

To find the electrical potential energy (EPE) of the three point charges, we can use the formula:

EPE = k * q1 * q2 / r

where EPE is the electrical potential energy, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

Let's calculate the EPE for each pair of charges and then sum them up to get the total EPE.

Pair 1: +2.0 μC at x = 0 and +3.0 μC at x = 20 cm

First, we need to convert the charges from micro-Coulombs to Coulombs.
q1 = +2.0 μC = 2.0 x 10^-6 C
q2 = +3.0 μC = 3.0 x 10^-6 C

The distance between these charges, r, is 20 cm = 0.2 m.

Now we can calculate the EPE for this pair:
EPE1 = k * q1 * q2 / r
EPE1 = (8.99 x 10^9 Nm^2/C^2) * (2.0 x 10^-6 C) * (3.0 x 10^-6 C) / 0.2 m

Pair 2: +2.0 μC at x = 0 and +6.0 μC at x = 50 cm

Similarly, convert the charges to Coulombs:
q1 = +2.0 μC = 2.0 x 10^-6 C
q2 = +6.0 μC = 6.0 x 10^-6 C

The distance between these charges, r, is 50 cm = 0.5 m.

Calculate the EPE for this pair:
EPE2 = k * q1 * q2 / r
EPE2 = (8.99 x 10^9 Nm^2/C^2) * (2.0 x 10^-6 C) * (6.0 x 10^-6 C) / 0.5 m

Pair 3: +3.0 μC at x = 20 cm and +6.0 μC at x = 50 cm

Converting charges to Coulombs:
q1 = +3.0 μC = 3.0 x 10^-6 C
q2 = +6.0 μC = 6.0 x 10^-6 C

Distance between the charges, r, is 30 cm = 0.3 m.

Calculate the EPE for this pair:
EPE3 = k * q1 * q2 / r
EPE3 = (8.99 x 10^9 Nm^2/C^2) * (3.0 x 10^-6 C) * (6.0 x 10^-6 C) / 0.3 m

Total EPE = EPE1 + EPE2 + EPE3

Summing up the EPE values will give you the total electrical potential energy of the system.

Hmmm. Total energy?

Putting the first there, no PE.
second one, PE2= kq1q2/distancebetween.

Adding the third one, PE3 adding third is kq3q1/distance13 + kq3q2/distanc12

compute the distances between 1-3, 2-3, 1-2, compute. Then add PE2 and PE3