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

`W=kq_1q_2((1)/(x_1)-(1)/(√(x_2^2+y_2^2)))`

Step-by-step 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(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(q_1q_2)/(√(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(q_1q_2)/(x_1)-k(q_1q_2)/(√(x_2^2+y_2^2)))`

`W=kq_1q_2((1)/(x_1)-(1)/(√(x_2^2+y_2^2)))`

Hence, the work done by the electrostatic force on the moving point charge is
`kq_1q_2((1)/(x_1)-(1)/(√(x_2^2+y_2^2)))`. Hence, this is the required solution.