Kinetic Energy among a set of Point Charges

[Danneskjöld]

Homework Statement

A set of point charges is held in place at the vertices of an
equilateral triangle of side 10.0 cm, as shown in the figure (a) .
Find the maximum amount of total kinetic energy that will be
produced when the charges are released from rest in the
frictionless void of outer space.

Homework Equations

Unsure, but believe this one is paramount:

V = k*(q/r)

The Attempt at a Solution

I'm using the formula V = k(q1)/r1 and the example in my textbook on page 590,
which is for only 2 point charges within an isosceles triangle, simply adds the
V1 + V2 to get Vtotal, so I assumed (probably incorrectly) that I could use
this method with 3 charges within an equilateral triangle and simply added the
V1 + V2 + V3 = 809.1 N*m/C. However, they want the answer in joules,
so what if I was even correct in my method, what should be done to my
answer in order to convert it to joules? Are N*m/C = Volts? Wouldn't that
mean I would need to then multiply by the same charges I just multiplied by?
And would I use each individual charge added together, or... what do I do with
these Coulombs?

 

[anathema]

Hi there,

To calculate the maximum amount of total kinetic energy that will be produced when the charges are released, we need to first determine the total potential energy of the system. This can be done by using the formula V = k*q/r, where k is the Coulomb constant, q is the charge of each point charge, and r is the distance between the charges.

Since the charges are held in place at the vertices of an equilateral triangle, the distance between each charge will be equal to the side length of the triangle, which is 10 cm. So, we can rewrite the formula as V = k*q/10 cm.

Next, we need to determine the charge of each point charge. Since they are not given, we can assume them to be equal and represent them as q. This means that the total potential energy of the system can be written as:

Vtotal = k*q/10 cm + k*q/10 cm + k*q/10 cm

= 3*k*q/10 cm

= 3*(8.99*10^9 N*m^2/C^2)*(q/C)/10 cm

= 26.97*q N*m/C

Now, to convert this to joules, we need to multiply by the charge of each point charge again, which will give us the total potential energy in joules.

Therefore, the maximum amount of total potential energy that will be produced when the charges are released is 26.97*q^2 joules.

To find the maximum amount of total kinetic energy, we need to remember that energy is conserved in a system. This means that the total potential energy before the charges are released will be equal to the total kinetic energy after they are released. So, the maximum amount of total kinetic energy will also be 26.97*q^2 joules.

I hope this helps! Let me know if you have any other questions.