Chapter 41: Problem 5

Question: What inductance is rquired with a $17~{\rm pf}$ capacitor in order to construct an oscillator capable of generating $550~{\rm nm}$ (i.e. visible) electromagnetic waves? (Comment on your answer).

Solution: Recall, that for an LC-circuit, the angular frequency of current oscillations in the circuit is

$$\omega~=~\sqrt{1\over CL} \ \ \ .$$ (1)

The frequency of the radiation we are required to produce is

$$\omega~=~2\pi \nu~=~ {2\pi c\over \lambda}~=~ {2\pi 2.998\times 10^8\over 5.50\times 10^{-7}}~=~3.4\times 10^{15}~{\rm rad/s} \ \ \ .$$ (2)

Therefore,

$$L~=~{1\over\omega^2 C}~=~5.1\times 10^{-21}~{\rm H} \ \ \ .$$ (3)