$1.$ A conductor at potential $\backslash ($ V$=0\backslash )$ has the shape of an infinite plane except for a hemispherical bulge of radius $\backslash ($ a $\backslash ).$ A charge $\backslash ($ q $\backslash )$ is placed above the center of the bulge, a distance $\backslash ($ p $\backslash )$ from the plane $($or $\backslash ($ p$-$a $\backslash )$ from the top of the bulge$).($See attached figure for a view from the plane.$)$ What is the force on the charge? $(35$ points$)$