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We know that electrical devices don't work in magical environments like Hogwarts or Hogsmeade, so how are wizards using such Muggle technology in areas usually saturated with magic?
Do we know anything about wizard radios? Do they even use electricity in the way we do? Is it even electricity?
...many radios have been legally modified by the wizarding community for their own use, which broadcast regular wizarding programmes. The Ministry conceded that Muggles frequently catch snippets of advice on, for instance, how to prune a Venomous Tentacula, or how best to remove gnomes from a cabbage bed, but argued that the radio-listening Muggle population seems altogether more tolerant, gullible, or less convinced of their own good sense, than Muggle TV viewers. Reasons for this anomaly are examined at length in Professor Mordicus Egg’s The Philosophy of the Mundane: Why the Muggles Prefer Not to Know. Professor Egg argues cogently that Muggles are much more likely to believe they have misheard something than that they are hallucinating.
(Pottermore, "Technology").
So the Wizarding Wireless Network runs with magic, not electricity.
This is further shown when Mrs Weasley controls her wireless by magic rather than by using an electric remote control or something of that ilk.
They were all supposed to be listening to a Christmas broadcast by Mrs Weasley's favourite singer, Celestina Warbeck, whose voice was warbling out of the large wooden wireless. Fleur, who seemed to find Celestina very dull, was talking so loudly in the corner that a scowling Mrs Weasley kept pointing her wand at the volume control, so that Celestina grew louder and louder.
(Half-Blood Prince, Chapter 16, A Very Frosty Christmas).
Nevertheless, the restriction on using electricity around magic doesn't apply to all magical locations. It's mentioned solely in regard to Hogwarts. Presumably Hogwarts has more "magic in the air" than most other places because of the sheer number of people doing magic there.
"All those substitutes for magic Muggles use - electricity, and computers and radar, and all those things - they all go haywire around Hogwarts, there's too much magic in the air."
(Goblet of Fire, Chapter 28, The Madness of Mr Crouch).
It may well be that domestic homes like the Burrow aren't affected by this restriction.
J.K. Rowling covered this in the F.A.Q. of her old website. Wizards don’t need magic to make their versions of Muggle technology work, so the Wizarding Wireless Network (radios are specifically referred to as devices that would work this way) would run solely on magic and not use electricity.
Cameras, like radios (or, as the wizards call them 'wirelesses' – they're always a bit behind the times when it comes to Muggle technology) do exist in the wizarding world (there's a radio in the Weasleys' kitchen and we know there are cameras because of the moving photographs you see everywhere). Wizards do not need electricity to make these things work; they function by magic, but in the case of such objects the wizards liked the Muggle invention enough to appropriate the idea without adding cumbersome plugs/batteries.
- Why did Colin Creevey’s camera work etc? (F.A.Q. on J.K. Rowling’s old website)
Because they run on magic instead of electricity, there would be no trouble getting them to work in even areas like Hogwarts where there’s lots of magic in the air and Muggle devices won’t work.
