In this scenario, two point charges q and -q are held stationary at separate d. We need to find out the work done by electric forces as the spacing changes to 2d.


The electric force between two point charges is given by Coulomb's law:
F = (kq1q2)/r^2
where
k is Coulomb's constant (9 x 10^9 N m^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges


Let's first calculate the electric force between the two charges when they are separated by a distance d.
F = (kq(-q))/d^2 [since charges are opposite in nature]
F = -kq^2/d^2


Now, let's calculate the electric force between the two charges when they are separated by a distance 2d.
F' = (kq(-q))/(2d)^2 [since charges are opposite in nature]
F' = -kq^2/(4d^2)


The work done by electric forces as the spacing changes from d to 2d is given by the difference in potential energy between the two configurations. The potential energy of a system of two point charges is given by:
U = (kq1q2)/r


The potential energy of the system when the charges are separated by a distance d is:
U = (kq(-q))/d
U = -kq^2/d


The potential energy of the system when the charges are separated by a distance 2d is:
U' = (kq(-q))/(2d)
U' = -kq^2/(2d)


The difference in potential energy between the two configurations is:
ΔU = U' - U
ΔU = (-kq^2/(2d)) - (-kq^2/d)
ΔU = -kq^2/(2d)


The work done by electric forces as the spacing changes from d to 2d is equal to the difference in potential energy:
W = ΔU
W = -kq^2/(2d)


Therefore, the work done by electric forces as the spacing changes from d to 2d is -kq^2/(2d). This represents the energy required to move the charges apart from each other.