If the third charge (–| q 3 |) is placed at point P, but not held fixed, it will experience a force and accelerate away from the other two charges. If q3 = q = –1.0 nC, the mass of the third charge m3 is 5.0 x 10-12 kg, and s = 4.0 cm, what will the speed of charged particle #3 [in m/s] be after it has moved a very large distance away?

Complete Question

The complete question is shown on the first uploaded image

A

The potential of this system is  

B

The electric potential at point p is

C

The work required is  

D

The speed of the charge is  

Explanation:

A sketch to explain the question is shown on the second uploaded image

Generally the potential energy for a system of two charges is mathematically represented as

where k is the electrostatic constant with a value of  

           q is the charge with a value of  

           d is the distance given as  

Now we are given that   and   and

Now substituting values

The electric potential at point P is mathematically obtained with the formula

I.e the potential at plus the potential at  

Now potential at is mathematically represented as

and the potential at is mathematically represented as

Now substituting into formula for potential at  P

The Workdone to bring the third negative charge is mathematically evaluated as

From the Question are told that the charge would a force and an acceleration which implies that all its potential energy would be converted to kinetic energy.This can be mathematically  represented as

Where

Now making v the subject we have