Question

Three point charges q, -2q and -2q are placed at the vertices of an equilateral triangle of side a find the work done by external force to increase their separation to 2a(in joules).

Answer 1

Hint: Electric potential energy is the total energy possessed by unit charge placed in outer space at any point. Substituting the value of charge in the electric potential energy equation and finding out the resultant will give the answer.

Complete step by step answer:
We know that electric potential energy is the total energy possessed by unit charge placed in outer space at any point.
Here the initial electrostatic potential energy is given by,

$U_i=k{\displaystyle \frac{(q\times -2q)}{a}}+k{\displaystyle \frac{(-2q\times -2q)}{a}}+k{\displaystyle \frac{(-2q\times q)}{a}}$

$=-2k{\displaystyle \frac{q^2}{a}}+4k{\displaystyle \frac{q^2}{a}}-2k{\displaystyle \frac{q^2}{a}}$
$=0$
 Final electrostatic potential energy is given by ,
$U_f=k{\displaystyle \frac{q(-2q)}{2a}}+k{\displaystyle \frac{(-2q\times -2q)}{2a}}+k{\displaystyle \frac{(-2q\times -q)}{2a}}$
$=-2k{\displaystyle \frac{\left(q^2\right)}{2a}}+4k{\displaystyle \frac{\left(q^2\right)}{2a}}-2k{\displaystyle \frac{\left(q^2\right)}{2a}}$
$=0$
According to energy conservation theorem, energy can neither be created nor destroyed,
Therefore, we can write that
Change in potential energy is equal to the work done by an external force.
In short, work done by external force will be zero

Hence the answer for the question will be zero.


Note:
When solving this question, the sign of the charges should be taken care. Otherwise the answer will be faulty. The electric potential energy of any given charge or system of charges is defined as the total work done by any external force in bringing a charge q or a system of charges from infinity to the current position in space in uniform motion which means without undergoing any kind of acceleration. It is also defined as the energy needed to do some work against the opposing electric field. Electric potential energy is a scalar quantity as it is an energy itself that means it possesses magnitude only and no direction. It is generally measured in terms of Joules and is denoted by V.