By Roel Snieder

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**Extra resources for A Guided Tour of Mathematical Physics **

**Sample text**

Gauss’s theorem can then be used to compute the integral of the divergence of the gravitational field. For the curl the situation is similar. 5) we computed the magnetic field generated by a current in a straight infinite wire. 12) again was used to compute the field away from the wire. 13) contained an unknown constant A. 12) was only used outside the wire, where J = 0. 5) therefore did not provide us with the relation between the field B and its source J. The only way to obtain this relation is to integrate the field equation.

Problem h: Use this expression and the result of problem f to compute your own wavelength while you are riding your bicycle. Are quantum-mechanical phenomena important when you ride you bicycle? Use your wavelength as an argument. Did you know you possessed a wavelength? 58 CHAPTER 6. 17) over the mass. Gauss’s theorem can then be used to compute the integral of the divergence of the gravitational field. For the curl the situation is similar. 5) we computed the magnetic field generated by a current in a straight infinite wire.

This relation was proposed by de Broglie in 1924 using completely different arguments than we have used here[13]. Its discovery was a major step in the development of quantum mechanics. Problem h: Use this expression and the result of problem f to compute your own wavelength while you are riding your bicycle. Are quantum-mechanical phenomena important when you ride you bicycle? Use your wavelength as an argument. Did you know you possessed a wavelength? 58 CHAPTER 6. 17) over the mass. Gauss’s theorem can then be used to compute the integral of the divergence of the gravitational field.

### A Guided Tour of Mathematical Physics by Roel Snieder

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