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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?

Respuesta :

Answer:

[tex]W=kq_1q_2(\dfrac{1}{x_1}-\dfrac{1}{\sqrt{x_2^2+y_2^2}})[/tex]

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 :

[tex]U_1=k\dfrac{q_1q_2}{x_1}[/tex]

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

[tex]U_2=k\dfrac{q_1q_2}{\sqrt{x_2^2+y_2^2}}[/tex]

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

[tex]W=-\Delta U[/tex]

[tex]W=-(U_2-U_1)[/tex]

[tex]W=(U_1-U_2)[/tex]

[tex]W=(k\dfrac{q_1q_2}{x_1}-k\dfrac{q_1q_2}{\sqrt{x_2^2+y_2^2}})[/tex]

[tex]W=kq_1q_2(\dfrac{1}{x_1}-\dfrac{1}{\sqrt{x_2^2+y_2^2}})[/tex]

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

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