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# Show that the equation is homogeneous with respect to units

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1. Show that the equation is homogeneous with respect to units
Show that the equation I= nAvq is homogeneous with respect to units

I = nAvq
C/s = (n/m^3)(m^2)(m/s)(C)

(m^-3) x (m^-2) x m = m^0 = 1

so m's cancel

C/s = (n)C/s

How do you proceed from here?
2. Re: Show that the equation is homogeneous with respect to units
(Original post by sabre2th1)
Show that the equation I= nAvq is homogeneous with respect to units

I = nAvq
C/s = (n/m^3)(m^2)(m/s)(C)

(m^-3) x (m^-2) x m = m^0 = 1

so m's cancel

C/s = (n)C/s

How do you proceed from here?
What's n?
Does it have any units?
3. Re: Show that the equation is homogeneous with respect to units
(Original post by Stonebridge)
What's n?
Does it have any units?
N represents the number of charge carriers per unit volume, so in this case the number of charge carriers per m^3.

so units are n/m^3 ?
4. Re: Show that the equation is homogeneous with respect to units
(Original post by sabre2th1)
Show that the equation I= nAvq is homogeneous with respect to units

I = nAvq
C/s = (n/m^3)(m^2)(m/s)(C)

(m^-3) x (m^-2) x m = m^0 = 1

so m's cancel

C/s = (n)C/s

How do you proceed from here?
Being just a number of objects, n (as in, n/m^3 - you should really avoid using the same lowercase letter for two different things, as you have here) can be safely ignored when discussing units as it doesn't really have any. If you want it to make a bit more sense and include it, you also have to clarify that q is the charge per charge carrier (C/n, in your notation).

When you actually write up this answer though, fix your notation. Using n for two different things (number of electrons per unit volume in I = nAvq and just number of electrons later in your answer) makes your working unnecessarily confusing, and is generally a very bad idea.
Last edited by Concept186; 18-04-2012 at 15:45.
5. Re: Show that the equation is homogeneous with respect to units
(Original post by sabre2th1)
N represents the number of charge carriers per unit volume, so in this case the number of charge carriers per m^3.

so units are n/m^3 ?
"Number of" has no units, it's a pure number.ignore it when considering units.
So you have actually shown the equation to be homogenous.
6. Re: Show that the equation is homogeneous with respect to units
(Original post by Stonebridge)
"Number of" has no units, it's a pure number.ignore it when considering units.
So you have actually shown the equation to be homogenous.
Oh thanks !

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Last updated: April 18, 2012
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