By Snieder R.

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3) ; Compute the ux of the magnetic eld through the surface of the Earth, take a sphere with radius R for this. e. Cartesian or spherical coordinates), but also choose the direction of the axes of your coordinate system with care. 1) for the de nition of the geometric variables. 1: De nition of the geometric variables in the calculation of the ux of a vector eld through an in nitesimal rectangular volume. outward ux through the right surface perpendicular through the x-axis is given by vx (x + dx y z)dydz, because vx(x + dx y z ) is the component of the ow perpendicular to that surface and dydz is the area of the surface.

13) i @t 2m ; ; r CHAPTER 6. THE THEOREM OF GAUSS 56 In this expression, h is Planck's constant h divided by 2 . Problem a: Check that Planck's constant has the dimension of angular momentum. Planck's constant has the numerical value h = 6:626 10;34 kg m2 =s. Suppose we are willing to accept that the motion of an electron is described by the Schrodinger equation, then the following question arises: What is the position of the electron as a function of time? According to the Copenhagen interpretation of quantum mechanics this is a meaningless question because the electron behaves like a wave and does not have a de nite location.

4). 4) Problem d: Compute v for this ow eld and verify that both the curl and the rotation vector of the paddle wheels are aligned with the z -axis. Show that the vorticity is positive where the paddle-wheels rotate in the counterclockwise direction and that the vorticity is negative where the paddle-wheels rotate in the clockwise direction. 3) that both rotation and shear cause a nonzero vorticity. Both phenomena lead to the rotation of imaginary paddle-wheels embedded in the vector eld. Therefore, the curl of a 46 CHAPTER 5.

### A guided tour of mathematical physics by Snieder R.

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