Question

A point charge with charge q1 is held stationary at the origin. A second point charge with charge q2 moves from the point (x1, 0) to the point (x2, y2). Please use k for Coulomb's constant rather than writing it out as (1/4πϵ0).
How much work W is done by the electrostatic force on the moving point charge?

Answer 1

Answer:

$W=kq_1q_2(\dfrac{1}{x_1}-\dfrac{1}{\sqrt{x_2^2+y_2^2}})$

Explanation:

Position of charge q₁ is (0,0)

Position of charge q₂ is (x₁,0)

So, the electric potential energy between the charges is given by :

$U_1=k\dfrac{q_1q_2}{x_1}$

Now the position of charge q₂ has been changes from (x₁,0) to (x₂,y₂). Now, electric potential energy between the charges is :

$U_2=k\dfrac{q_1q_2}{\sqrt{x_2^2+y_2^2}}$

We know form the work energy theorem that, the change in potential energy is equal to the work done. Mathematically, it is given by :

$W=-\Delta U$

$W=-(U_2-U_1)$

$W=(U_1-U_2)$

$W=(k\dfrac{q_1q_2}{x_1}-k\dfrac{q_1q_2}{\sqrt{x_2^2+y_2^2}})$

$W=kq_1q_2(\dfrac{1}{x_1}-\dfrac{1}{\sqrt{x_2^2+y_2^2}})$

Hence, the work done by the electrostatic force on the moving point charge is $kq_1q_2(\dfrac{1}{x_1}-\dfrac{1}{\sqrt{x_2^2+y_2^2}})$. Hence, this is the required solution.