In an article concerning ElectroMagnetic exposure limits, a quantity was expressed as 10mA mˉ². I understood this expression to mean 10mA per square root of 1 square meter which would equal, by my calcs, 10 square decimeters. I am not adamant about my conclusion. Another person looking at this valve is convinced it means 10mA per square meter. I am inclined to believe that is the value intended. I also think this expression could be read 10mA per square meter to the negative 2. 1 square meter to ˉ¹ could mean 0.1 square meter and 1 square meter to ˉ² would be 0.01 square meter. I have now confused myself to a point that I can not grasp the use of exponents with values of area or volume. Is there such a value as (m³)² ? Going from memory 5ˉ³ = 1/5x5x5 = 1/125 = .008. I think that is correct. I am having difficulty in how negative exponents are handled when applied to values of area and volume. Also I have become confused as to the effect an exponent has on a integer. Is m² a valid expression for a square meter or is it "slang." I generally would interpret m² to represent 10 meters assuming we are in base 10. So I am twisting in the wind not being able to explain exponent results. However, the primary question of this thread is, what is the area related to 10mA in the expression 10mA mˉ²?
EXPONENT CONFUSION
- Thread starter MDHASMDH
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10 mA per square meter is the correct interpretation.
Dr.Peterson
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Negative exponents mean reciprocals, as you say: [imath]m^{-2} = \frac{1}{m^2}[/imath]. That's why it means "per square meter". And, yes, [imath]m^2[/imath] is the proper notation for "square meters"; a square meter is the area of a square, 1 meter on a side.
You are in part confusing this with fractional exponents, which are roots: [imath]m^{1/2} = \sqrt{m}[/imath]. But if it had been that, it would not be per square root of a meter, but times square root of a meter. None of that would make any sense, though.
Another confusion you have is when you say, "1 square meter to ˉ¹ could mean 0.1 square meter"; you're thinking of [imath]10^{-1} m^2[/imath], which would be 0.1 square meter.
I very much enjoyed CANDIDE (THE OPTIMIST) by Voltaire
So 10mA mˉ² = 10mA/m² ?
Yes, you nailed it. I absolutely was doing my calculations in the form of n x 10ª . Problem was I have gotten into the habit thinking only of the exponent. If I have a value 12000nf (nano farads) my thinking says change the exponent from -9 to -6. That's abbreviated thinking for change the units from nano farads, 12000.0 x 10 to the -9th to 12 x 10 to the -6th then the value is 12µf (micro farads). I would see a value 2ˉ² and do a knee jerk calc and come up with a bogus result of 0.02. When my results were an obvious train wreck I was dumbfounded and just didn't see the trees for the forest. For a few years out of high school I worked construction and regularly calculated cubic yards of concrete and board feet of lumber. I entered the electronics field and don't recall dealing with values of area or volume since. I think there may be a unit for a volume of electrons but that work is above my pay scale. Thank you for the help.
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Electrical resistance of metallic wire is proportional to its length and inversely proportional to its cross-sectional area. So depending on the problem those units will come back to haunt you at your pay scale - yet!!! Keep up the good work!!!!