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3) i) Binary collisions: Define the terms "reverse...

3) i) Binary collisions: Define the terms "reverse collisions", "inverse collisions". and the assumption of "molecular chaos". How is this assumption expressed mathematically? When is it valid? ii) If a source gu is present, the continuity equ...

6) i) From the Langevin equation mdv/dt = -a. + F' '(t), 0,...

6) i) From the Langevin equation mdv/dt = -a. + F' '(t), 0, one can derive the equation (v=x) <xi> = C exp(-yt) + kT/a, Y = a/m, for the random displacement x of a particle. Assuming x=0 at t = 0. derive, from <x.i>. the result for <x>. as a function of t...

15.14 (a) We will denote the Fourier coefficient of F (t) b...

15.14 (a) We will denote the Fourier coefficient of F (t) by F "(co) and that of V (t) by V (). . That is = e int F de and = e dw (1) Substitution in the Langevin equation gives = or Denoting the spectral V (15.15.11) v(w) 12 = or = (2) (b) By (15.10.9) (3) Thus ds - (-iat...

L Graph: On Graph Sheet B, using a ruler and a protractor, ...

L Graph: On Graph Sheet B, using a ruler and a protractor, draw the two vectors A and B using the following data: (Ax = -4 cm, Ay = +3 cm) and (Bx = +6 cm, By = - -5 cm). Graphically add the two vectors to get the vector sum C = A + B, by using the tail-to-tip method. Use the ruler and protracto...

1.4 Limitations to Spherical Lenses In class we mentioned t...

1.4 Limitations to Spherical Lenses In class we mentioned that a sphere is a good - but not perfect approximation of an ideal lens. a) Suppose we make a single refractive surface with index of refraction n = 1.6 (immersed in air, n a 1 and a radius of curvature of 50 cm. What will the back focal ...

9. Static magnetoconducticity tensor. For the drift velocity...

9. Static magnetoconducticity tensor. For the drift velocity theory of (51), show that the static current density can be written in matrix form as Jx 1 -WeT Ex x To Jy WcT 1 1 + (WCT) 2 Ey . (64) 1 + (WcT) 2 E2 In the high magnetic field limit of WcT 1, show that Tyx = nec/B = Fo...

5. (a) When you are given the vector ü = - -...

5. (a) When you are given the vector ü = - -5Nx + 3Ny, in the unprimed coordinate system, determine the components of the vector in a primed coordinate system that is rotated counterclockwise 75° relative to the unprimed system. (b) Verify that the magnitude of the gi...

2. Using the technique of multiple an integral by itself wit...

2. Using the technique of multiple an integral by itself with a new variable and then changing to the polar coordinate system, determine the integral of where a is a known constant. 3. Using the results of problem 2 above, determine the integral of So dx Hint: Recall that one can differential t...

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