1) A 2μC point charge is located at A(4, 3, 5) in free space. Find the electric field intensity components Ep, E, and E₂ of the at P(8, 12, 2). (The answer should be written in the simplest form).
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- !) given a line charge distribution of (102 C/m) on z axis, find VAB where A(3, 1/2,1) and B(4, z, 6).QI) given a line charge distribution of where A(3 , π2,1) and B(4, π, 6) . 10 -12 C/m) on z axis, find VABLall space Jall space 6. Self energy of a sphere of radius R and and uniform charge density with total charge Q is[Assume energy is given by U = where dt is elemental volume] 3 Q? Q r)² (4=r²dr) + /, o -)² (4#r² dr) = 1 R 1 Q 2 (True, False) = Lll space 2 €0 E²dr U = 4περτ2 5 4T€0 R 2 4περ R3
- A hydrogen atom (with the Bohr radius of half an angstrom) is situated between two metal plates 1 mm apart, which are connected to opposite terminals of a 500 V battery. What fraction of the atomic radius does the separation distance d amount to, roughly? Estimate the voltage you would need with this apparatus to ionize the atom.Consider the simple model of the hydrogen atom with the single electron that can only exist in allowed circular orbits around the proton. The radius of each orbit is r= (0.0529 nm)n?, with n = 1, 2, 3, .... Calculate the electric potential energy when the electron (a) is in the second orbit, with n = 2, and (b) has escaped from the atom, with n→ .Sketch the potential energy function of an electron in a hydrogen atom, (a) What is the value of this function at r=0 ? in the limit that r=? (b) What is unreasonable or inconsistent with the former result?
- A point charge with 10 nC is located at (-2,1,0) and an infinite length line charge distribution with uniform 1 nC/m charge density located at y=1, z=1 A) If V = 0 V at O(0,0,0) point, calculate V at A(3, –1,1) point. B) If V = 50 V at B(1,3,2), calculate V at (-1,2,2).Find the bound charges of a uniformly polarized P = -0ý + Po infinite slab with 2d thickness. Calculate boundary charge densities. Calculate the E, D and . X=-d x=dIs the total system energy of a dipole a positive potential or a negative potential? Explain your reasoning. HINT: consider the total energy of a bound state atom, where there is a positive nucleus and an electron in orbit/orbitals. Is the electron energy positive or negative energy?
- Find phonon density of states D(w) in 1D and 2D . Can phonon DOS be expressed as a function of energy? (I mean D(E)). I am asking this because I need to compare DOS of free electron and DOS of a phonon, and the DOS of a free electron is a function of energy D(E). If phonon DOS can be expressed as D(E) please find it in 1D and 2D.To obtain the value of an unknown electrical charge, a group performed an experiment. From the graph of the electric potential (voltage) V in volts, as a function of the inverse distance (1/r) in m^-1, the group obtained an angular coefficient 6838 Nm^2/C by the linear equation of the best straight line. Knowing that V=(kq)/r, calculate the value of the electric charge, in nC (nanocoulomb), from the slope provided by the best line. Round the answer to a whole number. Use: k = 8.9876 x 10^9 N⋅m^2⋅C^−2A particle of charge e and mass m is located at the midpoint ofthe line joining two mixed collinear dipoles with unit charges as shown in the figure. (The particle is constrained to move only along the line joining the dipoles). Assuming that the length ofthe dipoles is much shorter than their separation, the natural fre- quency ofoscillation of the particle is e,m 2d 2d 6e?R? (a) V negmd³ 6e?R 6e?d? (c) V TEgmRS 6e?d (b) | TIEgmd (d) |TEgMR