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Name: Paige G.
Status: student
Age: 17
Location: N/A
Country: N/A
Date: 10/15/2004

What is the mass of an average lightning bolt? I am trying to determine the kinetic energy of the average bolt of lightning.

===================================================== NOTE: NOVEMBER 2014 - bELOW THE ORIGINAL RESPONSES, THERE ARE UP-DATED RESPONSE DUE TO A CHALLENGE TO THE ORIGINAL ANSWERS. ===================================================== Hello Paige- says the average lightning bolt measures 30,000 Amps, 5 Coulombs, 10^8 volts, and roughly 0.003 seconds. I'll guess the altitude it comes from is 10,000 feet.

The energy released would be the charge times the voltage: 5 Coul. x 10^8 Volts = 5e8 Joules. Before the lightning discharge, this energy is more or less evenly distributed over a large volume (1 cubic mile or so), being the square of the electric field from cloud to ground. This energy all suddenly converges horizontally to the middle and, I do not think it "shoots to ground", I think it just slams into the center axis, dissipating itself in the hot plasma of the lightning column. One could calculate a pressure pulse due to that mass flow suddenly converging in the middle.

The mass corresponding to this energy is (reversing E=mc2): m=E/c2, which always works provided it's all expressed in genuine, official MKS units. m= 5e8 Joules / (3e8 meter/sec)^2 = 5.5e-9 kg, roughly 1/2 micro-gram. Disappointingly small, I feel...

How hard would this moving mass punch the ground if it was travelling downwards?

I would assume it's travelling not at the speed of light, but at speed = distance / duration = 10,000 feet x 0.003 seconds = 3km * 3msec = 10 meter/second.

Momentum = 1/2 microgram * 10 meter/second; could not quite squash a mosquito if it was all in one spot. And it might be spread out over many square meters. Maybe a sensitive seismometer could pick it up.

Now that you know the mass and velocity, I will let you do the kinetic energy. Maybe that could kill my hypothetical mosquito.

It is not clear that all this mass/energy travels down right inside the visible lightning bolt. There is another point of view that says the energy flow is proportional to the electric field times the magnetic field, (assuming they are perpendicular) at each point in space. After all, we know that Voltage x Current = Power. Electric field always adds up to a voltage, and Magnetic field indicates a current.

It is called the Poynting vector. It is a person's name, not a redundancy pun. It is direction is perpendicular to both electric and magnetic lines. In this point of view, the energy flow is something free space always happens to do, in the vicinity of wherever you build a wire with a current in it. Kind of spooky. But the energy is not in the wire, just our handle on the energy. Has a lot to do with loop- and area- integrals of fields, complex calculus you may do in college.

Almost all the current of the lightning discharge is in the visible column, but it is surrounded by circling lines of magnetic field, which diminish in proportion to distance from the column. All this is immersed in a uniform vertical electric field from cloud to ground, which decreases continuously with time during the current flow.

So all this energy flow has the mass and momentum and K.E. you think it has, But it is borderless and much broader than the lightning column. And it surges not from top to bottom, but from outside to the center.

The reference above mentioned the rarer and stronger "Positive lightning", which may have roughly 100 times the energy of the usual negative lightning strike.

Perhaps you want to recalculate for that.

Then look up lightning strikes on Jupiter, probably stronger still.

Jim Swenson

PS- I regret not giving you this answer sooner, but I wanted to get it all straight.

=================================================================== NOVEMBER 2014 =================================================================== First off, from what little I know, E=mc^2 doesn't only work only for reactions where mass converts to energy on the atomic level? Secondly, lightening first travels up from ground to cloud and the "return stroke" is what we see as the bolt.

Robert Avakian

The information on the energy of an average lightning flash is basically correct.

The altitude of the initiation point of a lightning flash from a thunderstorm is from somewhat within the thunderstorm, so it could be anywhere from 10,000 to 50,000 feet.

The calculations of energy released are also basically correct.

The problem comes in trying to convert the energy into mass, which is not appropriate.

Lightning does not have mass and does not transfer mass; lightning is the result of energy transferred through and dissipated by air.

Lightning energy is conveyed through an ionized path produced by the stepped leader from the cloud and the conjoining leader that propagates up from the ground to meet it, thereby completing an electrical circuit between the cloud and the ground. Energy flows from the ground upwards to the cloud through the preferred path of ionized air (this is for a negative lightning flash; the opposite occurs for a positive flash). Mass is not transferred in this process.

The discussion about magnetic field and electric field in the Poynting Vector is not relevant to Paige's question and might have caused her to be further confused.

David R. Cook Meteorologist / Team Lead Atmospheric and Climate Research Program Environmental Science Division Argonne National Laboratory

We are scratching our heads as to the exact challenge. Our physicists and chemists have considered the article. Most seems within scientific limits. Perhaps we are missing something.

The force should be very small, the temperature very high and quite dispersed(thermodynamics 101).

There are factual considerations supporting the findings of Mr. Swenson.

1. Trees split and people turn to mush because of instantaneous water boiling. Water boiling and expansion produces a force. They do not split because of electron or photon induced force. 2. Sand forms fulgurites because of temperature, not force. 3. Photons have no(or very little) mass component to them. 4. The fulgurites and the trees are in situ, they did not move because of a momentum of photons

On the other hand, quantum phenomena can be "quirky", we just do not understand it all.

We can visualize the answer of Mr. Swenson as being substantially accurate within the confines of the original question. We also may add that we applaud Mr. Swenson with his attempt at this answer. He questions himself during the narrative, as we would, at multiple ambiguities in the question.

Science is a search for truth, not a certainty. It is an honest search and prone to self-questioning. It would appear to us that Mr. Swenson answered an ambiquous question as a scientist. His estimation should be valued.

Peter E. Hughes, Ph.D., Monadnock Radio Observatory, Milford, NH.

The question asks two things. First, what the mass of a lightning bolt is. The second is what the kinetic energy of a lightning bolt is. We first need to determine whether the questions are answerable. That is, whether the quantities “mass” and “kinetic energy” are measurable and assessable properties when applied to a lightning bolt.

Let us look at lightning to see how it operates to see if mass and kinetic energy make sense.

Although the parameters of a lightning bolt have been measured (duration, current, and so on), lightning is actually not understood well at all. One problem is that lightning is a multi-step process that sends out leaders (through poorly-understood ionized air) that ends with a large electrostatic discharge through a plasma channel. Presumably, the “bolt” is the large final discharge. The method by which the charges collect and go to the plasma channel is not known. Adding to the complication, a magnetic field forms around the plasma channel and electromagnetic waves are emitted from the bolt. The lightning can occur with positive or with negative polarity up in the cloud.

In a lightning bolt, static charges move to neutralize themselves. The bright plasma channel itself would consist of ionized air molecules and atoms. Ionization occurs when the molecules are dissociated from one or more of their electrons. An ionized plasma will conduct electricity. Because the temperature in a lightning bold is high, the molecules themselves may become dissociated too.

Electricity should not be thought of individual charges that travel long distances. Instead, most dynamic (e.g., electric current in a wire) and static electricity phenomena should be thought of like a long pipe that is used to move a fluid like oil. When some oil is pumped into the pipe on one end, the same amount of oil comes out of the pipe at the other end.

It is important to realize that most things ( including the plasma in a plasma channel) contain an enormous number of charges, and during an electrical event, like a lightning strike, the charges themselves (negative electrons or positive ions) move only a tiny distance.

The student has read in the encyclopedia that a lightning bolt transfers about 5 coulombs of charge. This is a very small amount of charge. If instead of a plasma column a copper wire were used to transfer the charge, then the electrons would move a distance that is much less than the thickness of a sheet of paper.

But the charge travels through a plasma column instead of copper. The charges would move farther because the number of charges available in ionized air is much smaller (and so the charged need to move farther. The transfer of charge could be accomplished by moving electrons (the lightweight negative particles) or by moving ionized molecules/atoms (the larger positive particles) or a combination.

Because of this complexity, it does not seem that a lightning bolt can have a usefully definable mass or kinetic energy. The plasma channel contains a “soup” of ionized molecules, ionized atoms, and electrons. A bolt isn’t a “thing,” but instead is a complicated electrical phenomenon which in which ions and electrons travel short distances for short period of time in a plasma channel that heats, expands, and cools, and at the same time generates magnetic and electromagnetic waves, and light as well as thunder. A complicated process!

Robert Eck

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