An insulating sphere of radius 0.250 m has uniform charge density 7.40×10⁻⁹ C/m³. A small object that can be treated as a point charge is released from rest just outside the surface of the sphere. The small object has a positive charge 3.70×10⁻⁶ C.

How much work does the electric field of the sphere do on the object as the object moves to a point very far from the sphere?

 W = 1.611 10⁻⁵ (1 / 0.250 - 1 / R_max)

 If R_max is infinite,  W = 6.444 10⁻⁵-5 J

Explanation:

The work is defined as

          W = F.dr

In this case the outside is repulsive since the two bodies have the same charge signand the angle is zero

The force is given by Coulomb's law

           F = k Q q / r²

The charge can be found from the density

            ρ = Q / V

            ρ = Q / (4/3 π R³)

            Q = ρ 4/3 π R³

The work is

             W = k ρ 4/3 π R³ q ∫ 1 / r² dr

We integrate

             W = 8,988 10⁹ 7.40 10⁻⁹ 4/3 π 0.250³ 3.70 10⁻⁶ (-1 / r)

We evaluate between the lower limit r = R and the upper limit r = R_max

              W = 16.11 10⁻⁶ (-1 / R_max + 1 / R)

              W = 1.611 10⁻⁵ (1 / 0.250 - 1 / R_max)

If R_max is infinite, the work is

            W = 1.611 10⁻⁵ 1 / 0.250

            W = 6.444 10⁻⁵-5 J

a.   mass number from atomic number