CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ?(r) is given by Here a is a positive constant having units of C/m3. (a) Determine a in terms of Q and R. (b) Using Gauss’s law, derive an expression for the magnitude of the electric field as a function of r. Do this separately for all three regions. Express your answers in terms of Q. (c) What fraction of the total charge is contained within the region R/2 ? r ? R? (d) What is the magnitude of at r = R/2? (e) If an electron with charge q’ = -e is released from rest at any point in any of the three regions, the resulting motion will be oscillatory but not simple harmonic. Why?
Consideration of our ecological footprint allows us to measure our impact on Earth based on resource use. More considerate consumption choices need to include aspects of economics and social costs as well as environmental costs. TERMS TO KNOW: Sustainable - capable of being continued without degrading the environment Economics - the social science that deals with how we allocate scarce resources Ecosystem services - essential ecological processes that make life on Earth possible Ecological footprint - the land needed to provide the resources for and assimilate the waste of a person or population Natural capital - consumable resources like air, water, trees, fish, and the systems that produce them Natural Interest - what is produced by the capital over time - more trees, fish, and oxyge
