Electric Force and Work Question

[erisedk]

Homework Statement

Three identical particles, each possessing mass m and charge +q, are placed at the corners of an equilateral triangle with side r. The particles are simultaneously set free and start flying apart symmetrically due to coulomb's repulsion forces. The work performed by Coulomb's forces acting on each particle until the particles fly from one another to a very large distance is --

Homework Equations

The Attempt at a Solution

According to the work energy theorem,
ΔKE = W
Also ΔKE of one particle = 2kq^2/r
So, ΔKE of all three particles = 6kq^2/r
Hence, W = 6kq^2/r

However, the answer given is kq^2/r

What have I done wrong?

 

[haruspex]

Homework Statement

Three identical particles, each possessing mass m and charge +q, are placed at the corners of an equilateral triangle with side r. The particles are simultaneously set free and start flying apart symmetrically due to coulomb's repulsion forces. The work performed by Coulomb's forces acting on each particle until the particles fly from one another to a very large distance is --

Homework Equations

The Attempt at a Solution

According to the work energy theorem,
ΔKE = W
Also ΔKE of one particle = 2kq^2/r
So, ΔKE of all three particles = 6kq^2/r
Hence, W = 6kq^2/r

However, the answer given is kq^2/r

What have I done wrong?

Neither answer looks right to me.
Are you sure you have quoted the given answer correctly?
You quoted the work done as the first particle goes off a great distance. That having happened, what work is done on the next one?

 

[erisedk]

What about 3kq^2/r?
That's the potential energy of the system initially.
I have quoted it right, but sometimes those answers at the back can be wrong so it's not necessary to completely trust it.

 

[haruspex]

What about 3kq^2/r?

That's the answer I'd give.

 

[erisedk]

Ok thank you then, that's what I thought sometime after the original post.

 

[erisedk]

Maybe, they're asking work done on ONE particle, that's why it's 1/3rd?

 

[haruspex]

Maybe, they're asking work done on ONE particle, that's why it's 1/3rd?

Yes, it says 'each'.