Question

(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 [6]

Answer 1

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