Show that the equation is homogeneous

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SUMMARY

The equation I = nAQv is homogeneous with respect to units, as demonstrated by the dimensional analysis. The unit of I is Coulombs per second (C/s), n is in inverse cubic meters (/m³), A is in square meters (m²), Q is in Coulombs (C), and v is in meters per second (m/s). When substituting these units into the equation, the dimensions simplify correctly to yield I = A, confirming the homogeneity of the equation. It is crucial to recognize that n represents the number of free charge carriers per unit volume, which has a dimension of one over volume.

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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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