A while ago, we had a ton of lightning. As a bonus, it always happened in the middle of the night. I love sleeping where it sounds like I am on the front line in WWI – no, I don’t. But, while lying awake waiting for the next BOOM I thought of something. Instead of just counting the time between flash and boom, maybe I could make a lightning detector.
For mere mortals, the first step might be to google “lightning detector”. I don’t want to do that. What fun would that be? I did look up something. The current in a typical lightning strike is on the order of 30,000 amps. How could I detect this.
I can think of two things. Could I detect the magnetic field from this current more than 10 miles away? Or maybe I could detect the change in magnetic flux through a loop of wire. For the second method it depends on the time rate of change of the magnetic field and the electric potential it would generate around a loop.
Let me pretend that lighting is a current that flows in a straight line (a huge wire in the sky). A single current creates magnetic fields that makes a circular vector field around the current. Here is a picture. (I will just use this lovely picture from wikipedia)
The magnitude of this magnetic field (for a long straight wire) changes with distance from the wire as:
Here μ0 is a constant and r is the distance from the “wire” to the location of interest. So, if I am 10 miles from a lightning strike, what kind of magnetic field could I even detect? This would be a magnetic field of 4 x 10-7 Tesla. Is that a large magnetic field? How about another example. What if I am 10 cm away from a wire with 1 amp of current? That would create a magnetic field of 2 x 10-6 Tesla. So, maybe it would be possible to detect this magnetic field (I will have to play with some detectors to try this).
The other question to address is time. How long does this current last? If it is super quick, I might not be able to even detect the magnetic field. This is directly tied to the other detection method – detecting an electric potential that goes with a changing magnetic field. I am not going to go into all the details (for now), but if you have a changing magnetic field and a loop of wire then the change in potential around that loop would be:
- N is the number of turns in the coil that makes up the loop
- B is the magnetic field vector
- n-hat is the unit vector that shows the orientation of the loop – it points perpendicular to the area of the loop
- A is the area of the loop
Suppose the area does not change. Also suppose that the magnetic field makes an angle θ with respect to the n-hat vector. This means that:
I honestly have no idea how long this lightning takes to happen. Also, this would give me the average change in electric potential – there are could be a spike depending on how quickly the magnetic field changes. Let me just suppose that Δt is around 0.1 seconds (just a guess) and my loop is a circle with a radius of 10 cm with 100 loops. What would the change in potential in the loop due to the lightning strike be? (assume best orientation of coil to lightning)
Ok, that is pretty low. Granted, my value for the change in time might be way off. But if it is not, even increasing the area and the number of loops both by a factor of 10 would still give a potential of around 10-3 volts.
There is another way to detect lightning – by the electromagnetic signal given off during the strike. If you google for “build a lightning detector”, you will find lots of info on these. Ok, but there is a problem. These all detect lightning, but I want to know where the lightning happens. I guess you could build two EM style lightning. If I want to know WHERE, I will need two detectors no matter which way I detect the lightning.
Enough rambling. I guess I should set up some small scale experiments.