1) Given that ρ_{v} = 12ρ nC/m^{3} for 1 < ρ < 2 (and zero otherwise), prove that:
a) D = 0 for ρ < 1, and
b) D_{ρ} = 8 (ρ^{3}-1) / 2ρ for 1 < ρ < 2
c) D_{ρ} = 28/ρ for ρ > 2.
Figure 23-51 shows a spherical shell with uniform volume charge density ρ = 1.76 nC/m3, inner radius a = 11.0 cm, and outer radius b = 2.10a. What is the magnitude of the electric field at the following radial distances: (a) r = 0: 0 N/C (b) r = a/2.00: 0 N/C (c) r = a: 0 N/C (d) r = 1.50a: ______ N/C (e) r = b: ______ N/C (f) r = 3.00b: _______N/C Figure 23-51
The figure below shows a spherical shell with uniform volume charge density ρ = 2.00 nC/m3, inner radius a = 5.0 cm, and outer radius b = 2.60a.What is the magnitude of the electric field at the following radial distances:(a) r = 0:(b) r = a/2.00:(c) r = a:(d) r = 1.50a:(e) r = b:(f) r = 3.00b:
In the ground state of the H atom, n = 1,l=0 R_1,0 (r)=2/(a^(3/2) ) e^(-ρ/2), Y_0,0=1/√4π Write down ψ_(n,l,m) (r,θ,ϕ) What is the expectation value of the radial momentum, which you may evaluate in the reduced ρ coordinate, i.e., obtain the expectation value of the p =ℏ/i d/dρ. Does the answer seem to contradict with the Bohr model?
In 2-dimensional flow not rubbing, not compressed (ρ = 1100 kg / m3 ), has a component velocity fields in m / sec as follows, u = Ay - Bx and v = Ax + By, ⃗g =g ^ k. Coordinates are expressed in meters, and A = 2 s-1 and B = 4s-1. The pressure p0 = 150 kPa at the point (x, y) = (0, 0). (a) Does this school fulfill the law of conservation of mass?...
Qi (8 pts) Tank in fig below is used to pressurize fertilizer solution (ρ 1000 kg/m3, g-10 m/g2) for spraying. The tank pressure above liquid surface (1) is 30 kPa gage. Height of liquid h 0.8 m. The velocity (m/s) at the outlet (2) (exposed to atmosphere) is closest to: (a) 5.5 (b) 7 (c) 8.7 (d) 15
Question 1: a) For any linear phase filter, prove that if zo is a zero, then so must zobe. Hint: Using the properties of the z-transform, write h[n] = Eh[N - n) in the z-domain, and substitute 2 = 20. b) For any Type III or Type IV filter, prove that z = 1 is a zero. c) For any Type II filter, prove that z = -1 is a zero. d) In light of the above, find the zeros...
Question 5 15 marks] Let X be a random variable with pdf -{ fx(z) = - 0<r<1 (1) 0 :otherwise, Xa, n>2, be iid. random variables with pdf where 0> 0. Let X. X2.... given by (1) (a) Let Ylog X, where X has pdf given by (1). Show that the pdf of Y is Be- otherwise, (b) Show that the log-likelihood given the X, is = n log0+ (0- 1)log X (0 X) Hence show that the maximum likelihood...
Chapter 23, Problem 052 The figure shows a spherical shell with uniform volume charge density ρ = 2.01 nC/m3, inner radius a = 9.50 cm, and outer radius b = 3.4a, what is the magnitude of the electric field at radial distances (a) r = 0; (b) r-a/2.00, (c) r = a, (d) r = 1.50a, (e) r = b, and (f) r-3.00b?
A charge distribution is given by pv=6x2y2 nC/m3. Determine the total charge enclosed by a cube of side 2 m centered at the origin and whose edges are parallel to the axis.
(2) Suppose the random variables Yi and Yg have joint probability density function (n 2)-10 The marginal distributions are fi (y) = y/2 for 0 yIS 2 (zero otherwise) and fn (Y2)-2-2y2 for 0 Y2 1 (zero otherwise). (a) Calculate E(Y) and E(Y2) (b) Calculate the conditional densities of YilY2-/2 and Y2Y- (c) Derive ElYalyǐ-m] and EMM-Y21 (d) Calculate EIE(Y1Yİ)] and E [E(YĪ½j. and confirm your answers in (a). (e) Calculate E(YiYo) and compare it with E(Y)E(5). (2) Suppose the...