please solve it as soon as possible
Y1o(0 ) where an is the elp 2 Calculate the multipole moments of this charge 3) The n = 2, 1 = 1,...
2. Suppose Xi,X2,..., Xn are i.i.d. random variables such that a e [0, 1] and has the following density function: r (2a) (1a-1 where ? > 0 is the parameter for the distribution. It is known that E(X) = 2 Compute the method of moments estimator for a
PROBLEM 2 Calculate the total charge of a spherical shell with an inner radius a and an outer radius b. The volume charge density (the charge per unit volume) of the shell is given by the following function: a(r,θ, φ)-Por cos"(0) where Po is a positive constant.
5. Charge distributed on a spherical surface of radius a produces the potential φ(a, 0) φ.cos) on that surface, with θ the polar angle and φ, constant. Expressing answers in terms of the givens only, (a) Find φ(r,0), inside the surface and outside (both charge-free). Use zonal harmonics: Eq (3.65), pg 143. (b) Find the surface-charge density function σ(0). (Recall o-e,AE,ORMAL.) (c) Evaluate the dipole moment of the charge distribution, by comparing your exterior solution in (a) to the standard...
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?
3) In a vacuum diode electrons are emitted from a hot grounded cathode (V-0) and they are accelerated towards the anode at potential Vo (see Griffiths, prob.2.48). The clouds of emitted electrons build up until they reduce the electric field at the cathode to zero. From then on a steady current I flows between the plates. Let the anode and cathode be much larger than the distance d between them, so that the potential φ, electron density ρ and electron...
1. In the ground state of the H-atom the nuclear charge can be treated in first approxi- mation as a point charge centered at the origin and an electron density of A(r) =-교exp (-5) πα3 Here a is the Bohr radius, r-|ศ, and e is the elelnentary charge. (a) Determine the electric field strength E and the potential as a function of r. (b) Discuss the two limiting cases r < a and a Hint: you may find the following...
Problem 2. Being good sports let us consider the familiar (although mysterious!) hydrogen atom. The excited state wavefunction corresponding to a hydrogenic 2s orbital is given by where the Bohr radius ao 52.9 pm -1 (a) Find the normalized wavefunction. (b) Estimate the probability that an electron is in a volume t1.0 pm at the nucleus (r 0). (c) Estimate the probability that an electron is in a volume t -10 pm3 in an arbitrary direction at the Bohr radius...
The expression Φ(x, h)-(1-2xh + h2)-1/2 where |hl < 1 is the generating function for Legendre polynomials. φ(x, h) can be expressed as a sum of Legendre polynomials The function (x, h) = Po(x) + hA(x) + h2Pg(x) + hn (x) The generating function of the Legendre polynomials has some applications in Physics, such as expressing the electric potential at point P due to a charge q. The location of the charge is r with respect to the origin O...
dq Given a continuous charge distribution consisting of: A line charge of length L with linear charge density X A semicircular disc of radius R with surface charge density σ 11. The charge distribution is placed along the x-axis as shown in the figure. The linear charge density is uniform, λ Λο where Λ01s a constant, and the surface charge density varies as σ-00*sin (9) where .00 1s a constant over_charge dq Assume the potential of this distribution is zero...
4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate E(r) B. Use your answer to A to calculate V(r). C. Use your answer to B to calculate the energy of this charge configuration, via the expression U pV d where the integral must be evaluated over the bounded charge distribution. D. Use your answer to A to calculate the energy of this charge configuration, via the expression 2 2 space