Problem $8\mathrm{.}2.$ lmagine two infnite parallel nonconducting planes, a distance d apart, carry$-$ing equal and opposite uniform surface charges $$o$.$ A point charge q is at rest in the spacebetween them, a distance zo above the $-$o surface. The electric feld is E $=$ E$,+$ E $.$Thetota$/$ feld energy is infnite, but the interaction energy $($subtracting offthe portions due to oalone and g alone$)$ is finite.

$($a$)$Calculate the interaction energy of this confguration.$($b$)$ Compare the interaction energy to the potential energy ofg $($take it to be zero at the centerbetween the planes$).$

$($c$)$ From the gradient ofthe interaction energy determine the force on g $($no surprise$)\mathrm{.}6$