charges and electric forces?

Question

Two charges, Q1=3mC and Q2=4mC are initially held at 5metres apart. They are then released and move away from each other. Calculate the work done by the electric forces needed to separate them by 10 meters.

Please show the working for I really need to understand how to go through it.

Answer 1

This can be done by using
work=force*distance
or more generally
work = the integral of force over distance

if you use the coulomb force

F = constant * Q1*Q2/r^2

where r is the distance

then the potential is (integrating the force)

Potential = - constant * Q1*Q2/r

The work done is then the change in potential
Work done = Potential (r=5) - potential(r=10)

Then change this number to positive because you are intested in the absolute value.

The values of the constants are in the reference I have given. Don't forget to convert to coulombs beforehand.

Answer 2

This can be done without using integration.
This work is equal to the change in potential energy of the two charges. Let us assume charge Q1 is stationary. We are allowed to use this frame of reference, why not. Energy is still the same.
the potential energy is -k*Q1*Q2/r where k is a constant (equal to 1/(4*PI*epsilon0) and r is the difference. Before we release them, they have the energy E1= -kQ1Q2/5m , at 10 metres they have E2=-kQ1Q2/10m=(E1)/2
The change in energy is E2-E1= (E1)/2-E1=-(E1)/2=kQ1Q2/5m
This is the work you seek.
Just roll in the numbers and presto.
I prefer this solution asI don't very much like to integrate.