Question

Work done by the field of fixed static charges on a 50mC charge is -20 J, as the charge moves from point A to point B slowly. The work done by the external agent is?

Answer 1

As the charge moves slowly we can assume that there is no kinetic energy gained by the charge in the process. So in accordance with the Work-Energy theorem work done by all the force on the charge must be zero.
There are only two forces acting on the charge, which implies
$W_{externalagent}+W_{electrostatic}=0$
$W_{externalagent}-20=0$
$W_{externalagent}=20J$