# Does a charging capacitor emit an electromagnetic wave?

Assume you charge a (parallel plate) capacitor. This establishes an electric field (the $\mathbf E$ vector points from one plate to the other) and a circular magnetic field (the $\mathbf B$ vector points tangential to circles centered at the capacitors main axis) while the Poynting vector points inwards.

Would this generate a "visible" electromagnetic wave (assuming we could see all wavelengths)? How about the situation where the capacitor is connected to an AC source?

Bonus question: If the above questions can be answered positively, would it be (theoretically) possible to generate actual visible light, by choosing the right frequency of the AC?

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Charging and discharging a capacitor periodically surely creates electromagnetic waves, much like any oscillating electromagnetic system. The frequency of these electromagnetic waves is equal to the frequency at which the capacitors get charged and discharged. That means that if you have just DC, the frequency is de facto zero and the resulting electromagnetic waves will be pretty invisible. For the frequency to be that of the visible light, the circuit would have to be as small as an atom. Ideally, it would have to be an atom because atoms are the "circuits" that naturally emit visible light.

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Thanks for that comprehensive answer (especially the last part). However, regarding the DC thing: I was referring to the brief moment after flipping the switch and generating the electric field, shouldn't this correspond to a very brief "flash" (invisible for humans)? – bitmask Jan 28 '12 at 17:05
Yup! If there is a discontinuity, the function of time may be decomposed into all frequencies - pretty much all frequencies are represented, including the high ones. In practice, it may be hard to observe this flash but it's there. – Luboš Motl Jan 29 '12 at 6:39

You can generate electric field and (eventually) light with capacitor.

But required frequency for visible light is extremely high - c/650nm = 461Thz, way out of reach of current electronics.

But if you can live with very far IR (100um and more) - it can practically be generated that way with current state of electronics.

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