Question

How much work w is done by the electrostatic force on the moving point charge?

Answer 1

As we know that electrostatic force is a conservative force

so we can say by the condition of conservative force

`F_c = -(dU)/(dr)`

here we can rearrange the above equation as

`dU = - F_c.dr`

now integrate both sides

`\int dU = - \int F_c . dr`

Now we know by the definition of work done by a force is given by

`W = \int F.dr`

now work done by conservative force is given as

`W_c = \int F_c . dr`

Now from above work done by electric field to move charge from one point to other is given as

`W_(EF) = \int F_(e).dr = - \int dU`

so here work done is given as

`W_(EF) = U_i - U_f`

so change in potential energy is given by work done