Electric force calculate the separation

[Young wolf]

Homework Statement

two charges with the same charge q and mass m are moving with the same acceleration at each instant. calculate the separation between them.

Homework Equations

The Attempt at a Solution

F=kqq/r^2
so, F= k q^2/r^2
r^2=kq^2/F
let the acceleration be a, then F=ma.
r= q√k/F
=q/√4πε0ma
but the answer given is q/√4πε0m
where did I go wrong ? can someone explain please?

 

[mfb]

You should make brackets for square roots and denominators, otherwise it is unclear where the fraction ends.

The given answer has mismatching units, it cannot be correct.

 

[rude man]

Their separation is a function of time and initial displacement, not constant, yes?
They can't be co-orbital since they repel rather than attract each other.
?

 

[haruspex]

two charges with the same charge q and mass m are moving with the same acceleration at each instant. calculate the separation between them.

Is that an exact copy of the problem as given to you? As rude man points out, the separation cannot be constant. That being so, one would normally expect the answer to be as a function of time. You have found it as a function of the instantaneous acceleration.

More likely, they are supposed to be equal and opposite charges. In that case, the acceleration can be constant, and the answer you found is still valid. I suggest that the given answer has omitted the acceleration by mistake.