## Oh Larmor! Energy in Electromagnetic Waves

Posted in Cute Problems, The Universe and Stuff with tags , , , on April 16, 2021 by telescoper

This week I started the bit of my Advanced Electromagnetism module that deals with electromagnetic radiation, including deriving the famous Larmor Formula. It reminded me of this little physics riddle, which I thought I’d share again here.

As you all know, electromagnetic radiation consists of oscillating electric and magnetic fields rather like this:

(Graphic stolen from here.) The polarization state of the wave is defined by the direction of the Electric field, in this case vertically upwards.

Now the energy carried by an electromagnetic wave of a given wavelength is proportional to the square of its amplitude, denoted in the Figure by A, so the energy is of the form kA2 in this case with k constant. Two separate electromagnetic waves with the same amplitude and wavelength would thus carry an energy = 2kA2.

But now consider what happens if you superpose two waves in phase, each having the same wavelength, polarization and amplitude to generate a single wave with amplitude 2A. The energy carried now is k(2A)2 = 4kA2, which is twice the value obtained for two separate waves.

Where does the extra energy come from?

## Amplitude & Energy in Electromagnetic Waves

Posted in Cute Problems, The Universe and Stuff with tags , , , on September 22, 2015 by telescoper

Here’s a little physics riddle. As you all know, electromagnetic radiation consists of oscillating electric and magnetic fields rather like this:

(Graphic stolen from here.) The polarization state of the wave is defined by the direction of the Electric field, in this case vertically upwards.

Now the energy carried by an electromagnetic wave of a given wavelength is proportional to the square of its amplitude, denoted in the Figure by A, so the energy is of the form kA2 in this case with k constant. Two separate electromagnetic waves with the same amplitude and wavelength would thus carry an energy = 2kA2.

But now consider what happens if you superpose two waves in phase, each having the same wavelength, polarization and amplitude to generate a single wave with amplitude 2A. The energy carried now is k(2A)2 = 4kA2, which is twice the value obtained for two separate waves.

Where does the extra energy come from?

## Wind versus Nuclear: The real story in pictures

Posted in Science Politics, The Universe and Stuff with tags , , , on November 5, 2014 by telescoper

Here’s an interesting, balanced analysis of the statistics of wind power versus nuclear power in the UK over the past couple of months. There’s obviously room for more growth in renewable energy generation, but I still think we’ll need to increase nuclear capacity to provide a counter to the intermittent variability of wind power if we are to reduce our dependency on fossil fuels, which still produce most of the UK’s energy…

Graph showing the electricity generated by nuclear and wind power (in gigawatts) every 5 minutes for the months of September and October 2014. The grey area shows the period when wind power exceeded nuclear power. (Click Graph to enlarge)

For a few days in October 2014,  wind energy consistently generated more electricity in the UK than nuclear power. Wow!

You may have become aware of this through several news outlets. The event was reported on the BBC, but curiously the Daily Mail seems not to have noticed .

Alternatively, you may like me, have been watching live on Gridwatch – a web site that finally makes the data on electricity generation easily accessible.

I was curious about the context of this achievement and so I downloaded the historically archived data on electricity generation derived from coal, gas, nuclear and wind generation in the UK for the last three years. (Download Page)

And graphing the…

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## Beyond Entropy

Posted in Art, The Universe and Stuff with tags , , , , , on February 26, 2010 by telescoper

It’s a cold and rainy morning here in Geneva, but I’m really looking forward to the next few days here. I arrived yesterday evening after a flight that was longer than it should have been. It seems the French air traffic controllers went on some sort of strike so my flight from Heathrow wasn’t allowed to cross French air space. For a flight between London and Geneva that is a bit of a problem. In the end we flew west over Belgium and then down into Switzerland from the North, the whole thing taking about an hour longer than expected. Still, when I did get to where I was going I found the hotel nice and comfortable and, better still, had a very enjoyable dinner at a swish Italian restaurant. It was nice to leave the chaos of French airspace behind.

I’m here as part of an unusual research project called (ironically, in the light of the aforementioned travel problems) Beyond Entropy. Organized by the Architectural Association School of Architecture, this experiment will bring together a group of artists, architects and scientists to investigate the notion of Energy. The way this is being done is by setting up a series of groups (one artist, one architect and one scientist) to look at each of a number of different forms of energy: potential, electric, thermal, mechanical, and so on; my own focus is gravitational energy. Each group will work together over the following few days to generate ideas a collaboration intended to create a work of some sort that gives form to the specific concept of energy they’re looking at. The subtitle of the project is “When Energy becomes Form”.

After we go back home, we’ll continue to work over the following months to produce prototypes of whatever emerges from the collaboration. The results will be exhibited at the Venice Architecture Biennale and the Architectural Association in August 2010. It is hoped that next year these prototypes will be developed into full-scale installations for the Venice Art Biennale in 2011.

I have no idea at this stage how the collaboration will work out or what is going to come out at the other end. The canvas is completely blank. I don’t really know the artist (Carlos Garaicoa) or the architect (Eyal Weizman) that I’ll be working with either. That makes it strangely exciting. At any rate it’s certainly different from the sort of scientific workshop I usually attend.

Anyway, to kick things off we’re going to be spending most of today at CERN, where I’ll be heading by bus just about as soon as I’ve finished this blog post. Later on today I’ll be giving a short presentation about how gravitational energy relates to my own research in the hope that this will stimulate a few ideas for my collaborators. Arts-science collaborations like this have been tried before and they have a chequered history, but we’ll just have to see how it goes. It feels more like research than most research workshops I’ve been to, in fact, because I really haven’t a clue what is going to happen!

P.S. Fellow blogger Andrew Jaffe is here too, but I think I might have beaten him in the competitive blogging stakes.