(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

Four objects are being tested to see how they are affected by fluid friction. object w has a surface area of 4.5 cm2, object x has a surface area of 2.5 cm2, object y has a surface area of 6.2 cm2, and object z has a surface area of 3 cm2. which object would experience the most fluid friction?

When a neutral charge, comes into contact with a positive charge they repel each other nothing happens the neutral charge becomes negative they attract each other

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.