3. A particular scalar field a is given by a. a=20 ex sin(πy/3) in Cartesian b. a=10psin() in cylindrical c. a=30cos(e)/r² in spherical find its Laplacian at P(-2,4,-6) for Cartesian, P(√2,π/2,7) for cylindrical and P(5, 30°, 60°) for spherical coordinate systems.
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- Just a follow up question, did you insert them into the quadratic equation? and if so, how can we know the point connnections?The spherical harmonics are the eigenfunctions of ?̂2 and ?̂ ? for the rigid rotor and thehydrogen atom (and other spherically symmetric problems). In this problem, we willexamine the nature of the angular nodes for these systems.Since the spherical harmonics include a factor of eim, which never has magnitude zero, forthis exercise we will construct some linear combinations of the spherical harmonics so weare working with real-valued functions. Two of the real-valued spherical harmonics are:12 (?1−1 + ?11) = 12 √ 32? sin ? cos ? 12? (?32 − ?3−2) = 14 √1052? sin2 ? cos ? sin 2?(a) Determine the angles at which nodal surfaces will occur for each of these functions, anddescribe the nature of the nodal surfaces that they represent. In other words, identifythe locations of nodal planes and other surfaces in the Cartesian axis system.(b) What atomic orbitals (e.g. 1s, 2p, etc.) are represented by these functions and what isthe total number of distinct angular nodal surfaces?How many angular nodes are there for the spherical harmonic Y3,0 and at which values of θ do they occur?
- Let f(x)= 4xex - sin(5x). Find the third derivative of this function. Note ex is denoted as e^x below. Select one: (12+4x^3)e^x + 125sin(5x) 12e^x + 125cos(5x) not in the list (12+4x)e^x + 125cos(5x) (8+4x)e^x + 25sin(5x)I think my problem with this question is the algebra. I think everything was under the square root at some point in the problem due to the pythagorian theorem. I'm confused about how it went from all being under the square root to only the top portion being under the square root.Consider a uniformly charged ring in the xy plane, centered at the origin. The ring has radius a and positive charge q distributed evenly along its circumference. Imagine a small metal ball of mass m and negative charge −q0. The ball is released from rest at the point (0,0,d) and constrained to move along the z axis, with no damping. If 0<d≪a, what will be the ball's subsequent trajectory? repelled from the origin attracted toward the origin and coming to rest oscillating along the z axis between z=d and z=−d circling around the z axis at z=d
- Hello, I understand that to calculate the net charge in the shell, I need to integrate the equation from 4 cm to 6 cm with volume charge density times 2 * pi * r * dr. However, since the problem here provides me with a novel expression of p = b/r, I am a bit lost... Could you please tell me how I can solve such problem?Determine the electric field at a distance `d` to the right of a thin-walled cylindrical shell with uniform distributed charge (See attached image). Provided are: the total charge `Q`, radius `R`, and shell length `h`. I can compute most of the solution, however, I don't understand the integration limits (See attached image). Given that the point on which I'm calculating the electric field is on the right side of the shell, shouldn't I be integrating from `d + h` to `d` instead of the other way around? If not, why?Find the shape of the free surface under constant ?? and ?? = −?.
- I'm a little confused here. Why is E = (1/e0) *integral row dx? Isn't Integral(E dA) = Qenc/e0 = integral (row dV)/e0. I'm not sure if what you wrote follows from Gauss' Law. Where did you expression from for the junction potentional? I don't see it my book or anywhere else.1. What would be the period of the pendulum if it is on the moon, where the acceleration due to gravity is one-sixth that on earth? 2. An airplane performs a loop-the-loop maintaining a constant speed of 180 mi/hr. (a.) What is the maximum radius of the loop? (b.) If the pilot weighs 150 lb, what will his apparent weight be at the bottom of the loop? 3. According to Rutherford and Bohr, what kind of force is necessary to keep atomic electrons in orbit and what provides this force? 4.Why is it more difficult to charge an object by rubbing on a humid day than on a dry day? 5. A battery having a voltage of 3.00 V is connected through a rheostat to a uniform wire 100 cm long. The wire has a resistance of the rheostat be in order that the voltage per millimeter of the wire shall be exactly 1 mV? 6. The sides of a right triangle are BC=3, AC=4, and AB=5 cm. if +10 statC charges are placed at the corners B and C, what is the magnitude and direction of the electric intensity at A?Consider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.