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

$F_c = -\frac{dU}{dr}$

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