Suppose you have a very long line of charge with uniform charge per unit mass, λ, lying along the y -axis. (Only part of it is shown in the figure.)   Using Gauss's Law, it is fairly easy to show (Don't do it!) that the electric field vector (i.e. the electric force per unit charge) in the x-y plane due to this line charge is given by .   There is also a uniform gravitational field (i.e. the gravitational force per unit mass) given by .

If you release an object with a charge q and mass m from rest at x = 10 cm, y = 40 cm,   it will follow the curved path shown by the solid line.   The parameters of the problem are such that the object passes through the point x = 50 cm, y = 10 cm.  

(a) Starting with the fundamental definition of work, find the work done by the combined electric and gravitational forces on the object if it moves not along the curved path but along the path shown by the dotted lines.