Show that the equation is homogeneous

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The equation I = nAQv is demonstrated to be homogeneous with respect to units. The unit of I is C/s, while n has the unit /m^3, A is m^2, Q is C, and v is m/s. By substituting these units into the equation, it simplifies to I = (m^-3)(m^2)(C)(m/s), which ultimately reduces to A (C/s). The discussion emphasizes that n represents the number of free charge carriers per unit volume, which is crucial for maintaining dimensional consistency. This clarification helps avoid confusion regarding the units involved in the equation.
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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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