(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

An experiment is designed to test the relationship between the initial height of a basketball before it is dropped to the height of its rebound bounce. the height of the rebound bounce is measured using a scale positioned behind the ball. in the above experiment, which condition would not be controlled? a). the starting height of the ballb). the surface the ball bounces on c). the type of ball d). the method to measure the rebound height of the ball

Athermometer is removed from a room where the temperature is 70° f and is taken outside, where the air temperature is 10° f. after one-half minute the thermometer reads 60° f. what is the reading of the thermometer at t = 1 min? (round your answer to two decimal places.) ° f how long will it take for the thermometer to reach 30° f? (round your answer to two decimal places.)

Classify the following soils according to the uscs classification system. provide appropriate uscs designations. a) this sample of well-graded gravel with sand was obtained from a large earthen dam in vancouver, canada. the sample has 73% fine to coarse sub-angular gravel, 25% fine to coarse sub-angular sand and 2% fines. the maximum size of the particles is 75 mm. the coefficient of curvature is 2.7, while the uniformity coefficient is 12.4. b) this dark brown and wet soil with a “strong organic odor” has 100% passing the no. 200 sieve. the liquid limit of the material is 32% when not dried and is 21% when oven-dried. the plastic index is 21% when not dried. c) this sand has 61% predominantly fine sand, 23% silty fines, and 16% fine sub-rounded gravel size. the maximum size is 20 mm. the liquid limit is 33% and the plastic limit is 27%. d) this soil has 74% fine to coarse sub-angular reddish sand and 26% organic and silty dark brown fines. the liquid limit is 37% when not dried and is 26% when oven dried. the plastic index is 6% when not dried.