Consider a point charge q in three-dimensional space. symmetry requires the electric field to point directly away from the charge in all directions. to find e(r), the magnitude of the field at distance r from the charge, the logical gaussian surface is a sphere centered at the charge. the electric field is normal to this surface, so the dot product of the electric field and an infinitesimal surface element involves cos(0)=1. the flux integral is therefore reduced to ∫e(r)da=e(r)a(r), where e(r) is the magnitude of the electric field on the gaussian surface, and a(r) is the area of the surface.

Imagine you work as a consultant, and your daily job involves listening to the constructive criticism of others. as part of your job, you must listen to opposing viewpoints to make important decisions. in this activity, you are a consulting dam engineer. you must make a decision about four different dams; should they be repaired, taken down, or left alone? you will listen to contrasting opinions about what should be done with the dams before you make the final decision. as the consulting dam engineer, what do you decide to do with this dam? explain your reasoning. by making your decision, did you support the opinions of the mayor and/or the dam safety official? why or why not? (site 1)

(a) calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. silver has 47 electrons per atom, and its molar mass is 107.87 g/mol. (b) imagine adding electrons to the pin until the negative charge has the very large value 1.00 mc. how many electrons are added for every 109 electrons already present

What is the increase in density of a medium due to wave travel?