(a) a consequence of the average potential theorem is that all extrema of the electric potential occur on the boundary surface s of a volume v. use this together with gauss' law to prove that for a charge-free region of space whose boundaries have well defined potentials, the solution to laplace's equation is unique 2. 5] (b) apply the uniqueness theorem in part (a) to calculate the surface charge density that is induced on a grounded conducting plate of infinite extent (of finite thickness) when a point charge q is placed at a distance d above the plate. the potential positionfdue to a point [9] [hint: you may need to use the result at charge q at position , v(r)= q/(4te- )] (c) what is displacement current and why is it a necessary modification to ampere's law in arriving at maxwell's equations