Show that the equation is homogeneous

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Discussion Overview

The discussion revolves around proving that the equation I = nAQv is homogeneous with respect to units. Participants explore the dimensional analysis of the variables involved in the equation.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant requests assistance in proving the homogeneity of the equation I = nAQv.
  • Another participant provides the units for each variable: I is in C/s, n in /m^3, A in m^2, Q in C, and v in m/s.
  • A participant realizes that n should not be ignored as it is not a constant and performs a dimensional analysis, concluding that the units simplify to I = A.
  • One participant clarifies that n represents the number of free charge carriers per unit volume, emphasizing its dimensional significance.
  • A later reply questions the interpretation of n, suggesting that it should refer specifically to free charge carriers to avoid dimensional inconsistencies.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of n in the equation, with some clarifying its role while others question the initial assumptions about its constancy and dimensionality. The discussion remains unresolved regarding the complete proof of homogeneity.

Contextual Notes

There are unresolved assumptions regarding the interpretation of n and its implications for the dimensional analysis. The discussion does not fully address all mathematical steps involved in proving homogeneity.

Gughanath
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Show that the equation is homogeneous with respect to units:
I = nAQv

I can't prove it, please help
 
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the unit of I is C/s
unit of n is /m^3
unit of A is m^2
unit of Q is C
unit of v is m/s
 
ooops i thought I could ignore n because its a constant, well now i know its not a constant. SO: I = (m^-3)(m^2)(As)(ms^-1), this cancels down nciely to give I = A!
 
n represents number of free charge per unit voloume, and it has a dimension of one over volume, don't forget next time
 
vincentchan said:
n represents number of free charge per unit voloume, and it has a dimension of one over volume, don't forget next time
You DID mean free charge CARRIERS per unit volume?
(Otherwise, you'd ebd up with charge squared..)
 

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