Ask A Scientist Physics Archive

name         Paige G.
status       student
age          17

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

http://encyclopedia.thefreedictionary.com/lightning
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.
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