Death by Electric Universe: Current vs. Voltage

I've often noted that various pseudo-scientific beliefs tote along other scientific misconceptions, some of which can be very harmful to the advocate or others.  There is even an entire web site chronicling the stories of the consequences of scientific misconceptions (What's the Harm.net).

I recently encountered another such misconception that warranted a more detailed explanation.  When a human body is exposed to charged particles, what is more fatal, the voltage or the current?

An electric universe supporter claimed that high current is needed to make exposure to charged particles fatal and that high voltages cannot be fatal. 

More specifically, I was making the point that in a space plasma in a region across an electric potential of 600 million volts (specifically in reference to the heliophysics environment claimed by Michael Mozina), the resulting radiation exposure will be quickly fatal.  Some Electric Universe supporters want to get around this problem with their model by claiming that only a high current can kill.

So what kills a person in an encounter with charged particles - high voltage or high current? 

The true answer is - both.  For what kills is determined by how much power is injected into the body by the charged particles and how those particles disrupt the body tissues.  This is dependent on current AND voltage.  At household voltages of tens to thousands of volts, a high current, at least 0.1 amps, is needed.  At 600 million volts, much less current needed.

So let's do the calculation that any radiation safety engineer should be able to do...

Doin' the Math…

We start with the technical definition of the unit of radiation exposure, the rad (Wikipedia: Rad (unit)):

1 rad = 0.01 Joules absorbed by 1 kg of mass

A fatal dose is 300 rads in one hour = 3 sieverts.  This is the low-end, whole-body dose, where a large portion of those exposed (but still less than 50%) can expect to die.  Above this threshold, the chance of fatality rises.

If it takes a minimum of 300 rads in one hour (3600 seconds) to be fatal, just how many electrons does it take with energies of 600 MeV?  How much current?

Consider electrons accelerated through a potential of 600 million volts.  For convenience, physicists define a unit of energy called the electron volt (eV), which is the kinetic energy of an electron moving through an electric potential of 1 volt (Wikipedia).  At 600 million volts, the electron has an energy of 600,000,000 eV or 600 MeV.  Converted to MKS units, this is an energy per electron of

600 MeV = 600e6 V * 1.609e-19 Coulombs = 9.7e-11 Joules

so we'll need a lot of electrons to inject a significant amount of energy into the human body.  Next, let's examine the radiation levels where we should be concerned.  The equation for the total accumulated dose is

dosage = energy flux * (target area/target mass)* time

As in the earlier exercises (see Death by Electric Universe.  Radiation Exposure Revisited), we'll assume the irradiated area of the human body is about 1 square meter (area = 1 m^2) with a mass of about 70 kilograms (mass = 7e4 gm).

600 MeV electrons are extremely relativistic, so their speed can be assumed to be essentially the speed of light.  However, if we're clever and do the algebra first, we won't need this information.  For simplicity, we'll let the particles be mono-energetic (all particles have exactly the same energy).  If we want to use a distribution of particles, we'd replace many of the simple multiplicative products with integrals (Wikipedia).  With this simplification, the energy flux becomes the product of the particle energy times the density of particles times their speed, so the dosage can also be written as:

dosage = (energy per particle * particle density * particle speed) 
               * (target area / target mass) * time

So let's be clever, and recognize that many of the components in this equation also exist in the definition of an electric current.

current = particle density * particle speed * target area 
               * charge per particle

which yields the amount of charge passing through a surface per unit of time.  We can re-write this to solve for:

particle density * particle speed * target area 
       = (current / charge per particle )

With this information, we can re-write the equation for dosage as:

dosage = energy per particle * (current / charge per particle) 
              * time / target mass

which we can then solve for the current:

current = dosage * target mass 
        * charge per particle / energy per particle / exposure time

To convert to rads, a unit of radiation dosage (Wikipedia), we divide MeV/gm by 62.4e6. 

current = dosage (rads) * mass * charge / energy  / time
        =  (300 rads) * (62.4e6 MeV/gm/rad) * (7e4 gm) * (1.6e-19 C) / (600 MeV) / (3600 s)
        = 9.7e-11 C/s
        = 9.7e-11 amps

which corresponds to (9.7e-11 C/s) / 1.6e-19 C = 6e8 electrons/s - about 60 million electrons per second.  This is an incredibly low current, yet it corresponds to a radiation dosage that can be fatal.

Using the definition of rad, we could also approach the problem from a slightly different direction by first computing the total energy deposition required for a fata dose.

300 rads * (0.01 J/kg/rad) * 70 kg = 210 J

Then the current can be derived from the same power = current * voltage of standard electromagnetism:

current = energy / time / voltage
        = 210 Joules / 3600s / 600e6 volts
        = 9.7e-11 amps

So if at 600 million volts, it takes such a tiny amount of current to kill, the next obvious question is, Why or How?

Kill Differently…

The two different extremes of particle energy kill differently.  

An electrical jolt direct to vital organ, say the heart, can kill instantly (or resuscitate).  On medical shows, you commonly hear defibrillators being charged to 400 watt-seconds = 400 Joules of power.  Amazingly small.  Most home coffeemakers use more in one second.

But if not directed at vital organ...

Currents of about 0.1 amp can kill at household voltage levels (a few tens to a few thousand volts).  Current at low voltage kills by disrupting the signal transfers of chemical ions in the nervous system to vital organs such as the heart.  At higher voltages, tissue damage can occur by resistive heating of tissue, such as boiling the water in tissue cells.  Under these conditions, death can occur quickly.

In the case of high-voltage particles, even at low current, death results from direct ionization of atoms in the body, which disrupts cell division and other biochemical processes.  Many of the atoms in the human body ionize at energies less than 20 electron volts.  An electron coming in with a total energy of 600 million electron volts can ionize a LOT of atoms before it is slowed to a safe energy.  This type of radiation exposure doesn't kill instantly, but damages cellular mechanisms to the point they cannot recover. The human body is always regenerating - incorporating ingested food into energy or new cells (fat?).  If that process is corrupted, illness or death results.

The Next Round of Electric Universe Excuses?

Perhaps the Electric Universe supporters and other cranks who advocate this notion think the electron current in a wire is composed of different 'stuff' than the electrons that pervade the space environment? 

These questions were actually asked, and answered, in the early part of the 1900s.  Numerous experiments have demonstrated that the electrons that carry the current in a wire are the exact same type of particle as the 'beta rays' emitted from atomic nuclei as part of a decay process and the electrons in the atom.  The only difference between them is how they get their energy, and how much energy they get.  This conceptual disconnect seems to be part of the pre-1900 science mentality prevalent among many pseudo-sciences.

Another popular evasion used in the pseudo-science community is that the mainstream workers are lying or part of a conspiracy to cover-up the facts.  So EU supporters might claim that reactor and radiation engineers are lying when they report these values as fatal radiation doses.  Hopefully, if an Electric Universe supporter wants to test this, they will put their own lives on the line, not like so many other pseudoscientists who readily let others take the risk for their ignorance… (see Fake bomb detector conman jailed for 10 years)

Electric Universe.  A dangerous ignorance…

Exercises for the Reader

1. At an electron energy of 600 MeV, how many rads would correspond to an electron current of 0.1 amps?
2. Using the definition of the rad above, derive the 62.4MeV/gm/rad conversion factor using dimensional analysis (I actually get a slightly different value).

References

• The Fatal Current 
• Measures Relative to the Biological Effect of Radiation Exposure   
• Roentgens, RADs, REMs, and other Units 
• Biological Effectiveness of High-Speed Electron Beam in Man
• INTRODUCTION TO IONIZING RADIATION
• CDC: Acute Radiation Syndrome: A Fact Sheet for Clinicians
• Wikipedia: Electric Shock,  Electrocution,  Electromagnetic Radiation & Health, Radioactivity, Roentgen Equivalent Man (REM), Ionizing Radiation
 

Update September 2, 2013:  Fixed minor typo in last equation.  Should be 'energy', not 'power'