We study the three point charges. They are held at the corners of an equilateral triangle with ℓ = 0.7 m. What is the electric potential energy of the system of three point charges? Use for the three charges

q1 = +2Q,
q2 = −3Q,
q3 = +Q,
where
Q = 120 nC

Do kq1q2/r for each pair. Sum the three.

To calculate the electric potential energy of the system, we need to consider the interaction between each pair of charges. The electric potential energy between two point charges is given by the equation:

U = k * (q1 * q2) / r

where U is the electric potential energy, k is Coulomb's constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

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

For q1 and q2:

U12 = k * (q1 * q2) / r12

where r12 is the distance between q1 and q2. In this case, q1 is +2Q and q2 is -3Q.

The distance between q1 and q2 can be found using the Pythagorean theorem in the equilateral triangle:

r12 = l * sqrt(3) / 2

where l is the length of one side of the equilateral triangle.

Substituting the values:

r12 = 0.7 m * sqrt(3) / 2

Now, we can calculate U12:

U12 = (8.99 x 10^9 N m^2/C^2) * (2Q * -3Q) / (0.7 m * sqrt(3) / 2)

Next, let's calculate U13 for q1 and q3:

U13 = k * (q1 * q3) / r13

where r13 is the distance between q1 and q3.

Using the same method as before, we can find:

r13 = l

Now, we can calculate U13:

U13 = (8.99 x 10^9 N m^2/C^2) * (2Q * Q) / (0.7 m)

Finally, let's calculate U23 for q2 and q3:

U23 = k * (q2 * q3) / r23

Similar to the previous calculations, we find:

r23 = l * sqrt(3)

U23 = (8.99 x 10^9 N m^2/C^2) * (-3Q * Q) / (0.7 m * sqrt(3))

Now, we can sum up the individual potential energies:

Total potential energy = U12 + U13 + U23

After substituting the given values and calculating the expressions, you will get the electric potential energy of the system of three point charges.