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what's your favorite equation?

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Tiamat

Lifer
Nov 25, 2003
14,068
5
71
Simplified Fowler-Nordheim Equation, the backbone of my thesis.

ln (I/V²) = ln ? - ?(1/V)

where:
? =1.56E-6 * (Aß²)/(d²F)
? = 6.87E9 * (d*F^1.5)/ß


I = Measured Current (mA)
V = Applied voltage (V)
A = Emitting area (cm²)
ß = Field Enhancement Factor = E*d/V
E = Electrical Field (V/cm)
d = Distance (m) between anode and cathode
F = Work function of the emitter

If the plot I/V² vs. 1/V yields a straight line with negative slope, the electrons traverse the vacuum between anode and cathode by quantum tunneling; also known as Fowler-Nordheim emission.
 

eLiu

Diamond Member
Jun 4, 2001
6,407
1
0
Navier-Stokes Equation YEAH! :D

Also, exp(i*pi) = -1 comes in a very close second.
 

Tiamat

Lifer
Nov 25, 2003
14,068
5
71
Originally posted by: eLiu
Navier-Stokes Equation YEAH! :D

Also, exp(i*pi) = -1 comes in a very close second.

The undergrad version of NS or the real version? :p
 

JohnCU

Banned
Dec 9, 2000
16,528
4
0
Originally posted by: Tiamat
Simplified Fowler-Nordheim Equation, the backbone of my thesis.

ln (I/V²) = ln ? - ?(1/V)

where:
? =1.56E-6 * (Aß²)/(d²F)
? = 6.87E9 * (d*F^1.5)/ß


I = Measured Current (mA)
V = Applied voltage (V)
A = Emitting area (cm²)
ß = Field Enhancement Factor = E*d/V
E = Electrical Field (V/cm)
d = Distance (m) between anode and cathode
F = Work function of the emitter

If the plot I/V² vs. 1/V yields a straight line with negative slope, the electrons traverse the vacuum between anode and cathode by quantum tunneling; also known as Fowler-Nordheim emission.

holy fuck that's awesome!
 

bobsmith1492

Diamond Member
Feb 21, 2004
3,875
3
81
I1 = I2 + I3 + ... (KCL)

(Va-Vb)/Ra + (Vb-Vc)/Rb + ... = 0 (KVL)

You can describe just about any system with these. Kirchoff was a genius. :)
 

us3rnotfound

Diamond Member
Jun 7, 2003
5,334
3
81
Originally posted by: bobsmith1492
I1 = I2 + I3 + ... (KCL)

(Va-Vb)/Ra + (Vb-Vc)/Rb + ... = 0 (KVL)

You can describe just about any system with these. Kirchoff was a genius. :)

And all of that stuff goes back to Ohm.
 

Shadow Conception

Golden Member
Mar 19, 2006
1,539
1
81
I never understood Kirchoff's voltage stuff. I ended up screwing the stuff up completely on the end of year exams for our Digital Electronics course, but I still averaged an A for the year. Having a teacher that pretty much took the course over the summer a year beforehand didn't help, either.