Problem 2: The potential energy for a particular two-dimensional force field is given by V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency. (a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or the equivalent to plot contours of constant potential energy for various energy levels, over a region of the plane centered on the origin. (b) Show that an infinitesimal displacement along an equipotential line has the form dx dr = dz x + ŷ. kx (c) Find the expression for the force field, and plot this vector field over the same region of the plane (and with the same choice of constants) as in part (a).

Problem 2: The potential energy for a particular two-dimensional force field is given by V(x, y) = Axe-ky, where the constants A and k are chosen for dimensional consistency. (a) Choose specific (and reasonable) values for A and k, and use Mathematica, Desmos, or the equivalent to plot contours of constant potential energy for various energy levels, over a region of the plane centered on the origin. (b) Show that an infinitesimal displacement along an equipotential line has the form dx dr = dz x + ŷ. kx (c) Find the expression for the force field, and plot this vector field over the same region of the plane (and with the same choice of constants) as in part (a).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Don't use chat gpt are any ai, plz i vill upvote u for right answer... Needs Complete typed solution with 100 % accuracy.
1. Find the dimensions of K, knowing that P: Pressure, V: volume and that the following equation is dimensionally correct K = PV + Q Subsequently, convert the dimensional formula to terms of units of the International System of Units and the English System of Units.
If the following equation is dimensionally homogeneous, find the dimensions of the physical quantity K indicated in the system of fundamental physical quantities: Length, Mass and Time. Ep -G Mm K where Ep is the gravitational potential energy (same units as the kinetic energy E mv²/2), M and m are the mass of the earth and the mass of the body, respectively, and G is the universal gravitation constant G~ 6,67 x 10-11 N m² kg²
For the section shown below, composed of a semicircle together with a ¼ circle, we are asked to determine the polar moment of inertia about O in cm^4. Tip: use the geometric property tables of the sections to solve the problem. Source: Porto (2014, p. 51). PORTO, M. A. Exercises for vector mechanics. Sao Paulo: University of Sao Paulo, 2014. 4 question options: a) The moment of inertia is 8654.21 cm^4. B) The moment of inertia is 3926.99 cm^4. c) The moment of inertia is 10865.98 cm^4. d) The moment of inertia is 7853.98 cm^4. e) The moment of inertia is 11708.97 cm^4.
Q1 Determine the dimensions of a and b so that the following equation is a dimensional homogencous equation. P = a u + 17.03 x 106 b2 p Where, P is the partial pressure u is the velocity, S is thc specific gravity and p is density of the fluid
2. The apparatus shown below is designed to measure the density of an unknown fluid (p2₂). The two sides of the device are separated by a movable, frictionless partition. The partition is attached to the immobile sidewalls of the device via springs (different spring constants) on either side. Before pouring fluid into the device, both springs are unstretched. The device has a rectangular cross-section and extends a width w into the page. Derive an expression for the unknown density p2 = f(p1, h₁, h₂, k₁, k2, Ax, g), where Ar is the displacement of the partition relative to its equilibrium location before the fluids are poured into the apparatus. h₁ P1 k₁ 5 P2 ли Ax k₂ h₂
X2 = 5x1 + 5x2 - 7x3
For a venturi meter given below, the volumetric flow rate is defined in terms of the geometrical parameters, the density of working fluid (p), and density of the manometer liquid (pm) as 4. Q = f(D, D2, A2, g, h, Pmv Pr) %3D Write down the balance equations and show your work to end up with an expression for the volumetric flow rate in terms of the variables defined above.
I need answer within 20 minutes please please with my best wishes
3. One model of the glomerular membrane is a microporous membrane in which right cylindrical porespenetrate all the way through the membrane. Assume that the pores have a length of 50 nm and aradius of 3.5 nm. The viscosity of plasma is 0.002 Pa s. The average hydrostatic pressure in theglomerulus is 60 mm Hg, hydrostatic pressure in Bowman’s space is 20 mm Hg and the averageoncotic pressure of glomerular capillary blood is 28 mm Hg.A. Calculate the flow through a single pore assuming laminar flow (use the Poiseuille flowequation).B. How many pores would there have to be to produce a normal GFR?C. If the total aggregate area of the kidneys for filtration is 1.5 m2, what is the density of thepores (number of pores per unit area)D. What fraction of the area is present as pores
Engineers are worried about the wind forces on a sculpture in Queen Mary campus. The sculpture has a height Ha = 5 m and a diameter, Da = 2 m, as shown in Figure Q3. The engineers decide to investigate making a smaller scale model testing in a water tunnel. They need to match the Reynolds number and the aspect ratio, AR = H/D. The characteristic length scale in the Reynolds number can be the diameter. Water has a density and viscosity of pw = 1000 kg/m3 and μw = 1 mPa. s, while air has a density and viscosity of pa = 1.2 kg/m3 and μa = 18 x 10-6 Pa. s. The average wind speed by the sculpture is Ua = 6 m/s. 1. The maximum height of the model that the engineers can place in the water tunnel is 1.5 m. Find the diameter of the model needed. 2. Find the average speed of water needed for the experiments to match the average wind speed past the sculpture. 3. It is known that at a wind speed of Ua = 4 m/s, the flow past the sculpture becomes turbulent. To visualise the flow in the experiments,…
Consider the following equation: 1 dollar bill ≈ 6 in. Is thisrelation dimensionally inconsistent? Does it satisfy thePDH? Why?