Problem $8\mathrm{.}2.$Imagine two infinite parallel nonconducting planes, a distance d apart, carrying equal and opposite uniform surface charges $$$.$ A point charge q is at rest in the space between them, a distance zo above the $-$o surface. The electric field is E $=$ Eo $+$Eg$.$The total field energy is infinite, but the interaction energy $($subtracting off the portions due to o alone and q alone$)$ is finite.$($a$)$ Calculate the interaction energy of this configuration.$($b$)$ Compare the interaction energy to the potential energy of q $($take it to be zero at the center between the planes$).($c$)$ From the gradient of the interaction energy determine the force on g $($no surprise$)\mathrm{.}6$