When ac current is passed through a wire, the electrons in the wire oscillate to and fro in the wire (due to change in polarity of current in the wire). If the ac current is of frequency, say 50Hz, then will the wire emit electromagnetic waves of the same frequency?
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Yes. they do produce an electric field, if we're working with $50$Hz a rough estimate is that the $\lambda$ would be $\frac{c}{f}=\frac{3\cdot 10^8}{50}\approx6000000$m which is a wavelength that's hard to make use of, but yes, em waves are produced.
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$\begingroup$ How much energy is lost like this? Is this a big part of the cable's resistance? $\endgroup$ Commented Jul 13, 2018 at 5:39
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$\begingroup$ What type of cable are you talking about ? Small wire for a circuit or power transmission cables? I am not all about electrical circuit theory, my field of study is electromagnetic field theory and photonics. $\endgroup$ Commented Jul 13, 2018 at 5:53
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2$\begingroup$ An efficient, resonant antenna would have to be of the size of half the wavelength of 6000 km. Any realistic cable is very far off resonance indeed. $\endgroup$– my2ctsCommented Jul 13, 2018 at 8:26