In a recent episode of MacGyver, Angus (that's what his REALLY close friends call him) builds a Leyden jar with some very simple components. Of course there is some awesome physics here, so I will obviously go over this. Full disclosure---I'm currently the Technical Consult for the MacGyver show.
A long time ago, humans were just starting to figure out this whole electricity thing---in particular the study of electrostatics. The Leyden jar was originally used to store electric charge after some rubbed object is charged (like your socks in the dryer). There were two common variations of the Leyden jar, let me illustrate both.
For version 1, there are two pieces of metal around a glass cup. One piece of metal sits inside the cup and one is on the outside. However, for version 2 the inside metal is replaced with water. Yes, you can replace the metal with water as long as the water is an electrical conductor. Most water conducts electricity, but you could add a little salt just to make sure.
But how does it work? Really, the Leyden jar is just a capacitor---that's all. The simplest capacitor contains two parallel metal plates with nothing in between them. If you add charge to one side of the plates, this will pull the opposite charge onto the other plate (assuming there is a path for the charge to get on there). This is what it would look like.
In this example, there is a charge of +Q on one plate (and -Q on the other) with an electric potential difference of ΔV. The ratio of charge (on just one plate) to the potential difference is defined as the capacitance such that. The units for capacitance is the Farad.
However, it turns out that the value of the capacitance only depends on the physical configuration of the device. In this case that means the size of the plates, their seperation distance and the material that is in between them. For a parallel plate capacitor (like above) the capacitance can be calculated as:
The area of the capacitor is A and d is the distance between plates. The variable ε (epsilon) is called the permittivity and it depends on the type of material between the plates.
Even though the Leyden jar is in a different configuration, it basically works the same way. The outside metal can be grounded simply by holding it with your hand or running a wire to a metal water pipe. When you bring an charged object (like a plastic pen that your rub in your hair) near the metal in the middle, this will add charge to the water and draw the opposite charge to the outside metal. It's possible to get this up to fairly high voltage since the glass in between the water and metal acts as an insulator.
I guess you can figure this out by how it works---but still, let me show you how to make one. Here is a video I made to go along with this episode of MacGyver that walks you through this build.
Let me point out that making videos like this is one of the best parts of working with the MacGyver writers as the Technical Consultant for the show. Most of the hacks in MacGyver is at least scientifically plausible but many of them you shouldn't try at home (like jumping out of a three story window with a fire extinguisher and a body bag). Other hacks could have a home-version---that's what you get here. Everyone should play with stuff at some point.
What can you do with this Leyden jar? How about making a spark? First, ground it (either hold it or connect it to ground) and then rub something to get a charge (plastic on wool works). Touch this plastic to the metal in the middle and repeat this until you get tired. Now bring a wire from the outer foil to the metal nail in the middle and you should get a nice spark. Here's a small spark on a humid day (if it's dry it works better).
If you prefer to shock someone, ok---but it kind of hurts.
It might seem like you could just measure the value of a capacitor as easily as you could find the resistance of a resistor. Well, it's not quite that simple. Most of the multimeters that you will see do not directly measure capacitance---but there are some that do. How does it work? I'm not going to explain that right now, but I will come back with another post that looks at finding the value of a capacitor. For now, I'm just going to use one of the better multimeters.
Here is my actual Leyden jar. In this case I used a water bottle instead of a plastic cup as seen in the video.
The multimeter gives a capacitance value of 1.17 nF (nano Farads) or 1.17 x 10-9 Farads. Is this value even legit? What if I assume that the foil wrapped around the bottle is like a parallel plate capacitor---it kind of is if you unwrap it. In that case, I can estimate the capacitance value and compare the to the meter's value.
This particular water bottle has a height of about 10 cm and a diameter of 5.5 cm. That means that if I rolled out the foil, it would have an area of 0.1 m by 0.055 m or 0.0055 m2. The inside water in the bottle has approximately the same area. Now, what about the separation between plates? I'm just going to roughly estimate this with a value of 2 mm (0.002 meters). I will guess that plastic has a relative permittivity of 2.0. Using these values, I get a capacitance of 0.049 nFarads. Ok, so either my bottle thickness is way off or this meter isn't giving a very accurate value (or both).
The energy stored in a capacitor can be found by:
I have a value for the capacitance (I am going to use the value from the multimeter). But what about the voltage? Here's where I can use a great trick. Air has an electric field breakdown value of around 3 x 106 Volts per meter. This is the value of the electric field in air at which it switches from an insulator to a conductor. If I can estimate the length of the spark, I can use that to get the value of the capacitor voltage. Let's say the spark was 3 mm, this would give a voltage of 9,000 volts.
Now I just have to plug this into the energy equation and I get a stored energy of 0.05 Joules. That's not much, but it is something. I'm pretty sure you can charge up a Leyden to get a much bigger spark (probably over a centimeter) with much higher energy.
There are too many questions left unanswered. Here is a list of questions for you (or me).
- Build a Leyden jar and measure the capacitance. Don't use a multimeter.
- What if you take a Leyden jar and measure the capacitance. Now remove half of the aluminum foil. What should happen to the value of the capacitance? Now measure it and see what happens.
- Build two Leyden jars. Put them in series, does the expected value of capacitor come close to the measured value? What about two jars in parallel?
- Can you use one Leyden jar to charge another one?
- Use a spring scale or force probe to estimate the force need to rub a plastic rod with wool. Now estimate the energy a human puts into charging this rod. How does the human energy compare to the energy stored in the Leyden jar?
- Derive the expression for the energy stored in a capacitor.
- Calculate the capacitance of a cylindrical capacitor (instead of a parallel plate).
