Reference no: EM131004001
P1. Use the method of Green function to find an integral expression for the electrostatic potential in the half-space defined by z ≥ 0. The electrostatic potential Φ on the plane z = 0 is zero everywhere except inside a circle of radius R. In this area, the electrostatic potential is given by Φ(ρ, Φ, 0)= V0 (R-ρ)2/R2, where ρ is the distance to the origin.
(a) Find the potential along the axis of the circles (the z axis).
(b) Find the potential at large distance from the origin.
(c) Discuss what happens to these potentials when a point charge q is placed at (x0, y0, z0), where z0 is positive, and the potential on the plane z = 0 remains the same.
P2 Consider the region bounded by two concentric spherical surfaces. On the inner boundary (r = a) of this region, the electrostatic potential is specified by Φ (a, θ, Φ) = V0 cos2(θ) in spherical coordinates, and on the outer boundary (r = b), the electrostatic potential is specified by Φ (b, θ, Φ) = 2V0. Find the electrostatic potential in this region (a < r < b).
P3 A system consists of 4 point charges and a localized distribution of charge centered at the origin. The point charges are q, 2q, -q and -2q, located at (a, 0, 0), (-a, 0, 0), (0, a, 0) and (0, -a, 0), respectively. The charge density of the localized distribution of charge is given by
ρ(r) = q/a5.r2e-r cos2(θ)sinΦ
Find the multipole moments of the system and make a multipole expansion of the potential at large distances (r >> a), up to the term (a/r)3.
|
Derive the corresponding odes
: Prove that in polar coordinates, Laplace equation is (∂2u / ∂r2) + (∂u / r ∂r) + (∂2u / r2∂θ2) = 0, Let u(r, θ) = R(r) - Θ(θ) and derive the corresponding ODEs for R(r) and Θ(θ). Assume the boundary conditions on u.
|
|
Illustrate how these choices will affect economic growth
: Two economies, the United States and country G, cur- rently have identical production possibilities frontiers, CI, but have chosen differing combinations of capital and consumer goods as indicated. Illustrate how these choices will affect economic..
|
|
How innovation affect us production possibilities frontier
: Technological change is an important driver of economic growth. Refer to the "Technology" column in the Marketplace section of a recent Wall Street Journal. Find a story about a technological innovation that seems interesting to you. How will this..
|
|
What are the functions of the components of mental status
: What are the functions of the components of mental status and an interview in determining the competence of clients? Explain with examples and rationales
|
|
Find the multipole moments of the system
: Find the multipole moments of the system and make a multipole expansion and Find the potential along the axis of the circles
|
|
Has productivity actually declined anywhere
: (Labor Productivity) Go to the Bureau of Labor Statistics (BLS) page on Quarterly Labor Productivity at http://www. bls.gov/lpc/ and get the latest news release on productivity and costs. Rank the various sectors of the U.S. economy from highest t..
|
|
Improve the behavior and attitudes of organizational members
: Describe methods used to assess the behaviors and attitudes of organizational members, and apply 1 model in an analysis of your organization.
|
|
Discuss the shared experiences of members of your cohort
: Tasks: Write a 2- to 3-page reflection paper and discuss the shared experiences of members of your cohort. Your paper should be based on your personal experiences as well as research on your generational cohort
|
|
How should a globally-dispersed supply chain be managed
: What should be the long-term strategic role of foreign productions sites? Should the firm abandon a foreign site if factor costs change, or is there value to maintaining an operation at a given location even if economic conditions change?
|