Show that the equation is homogeneous

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In summary, the equation I = nAQv is homogeneous with respect to units, meaning that the units on both sides of the equation cancel out to give a dimensionless result. This is shown by breaking down the units of each term in the equation and simplifying them to give only the unit of A, which represents the number of free charge carriers per unit volume. It is important to remember to include this unit when working with this equation.
  • #1
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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  • #2
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
 
  • #3
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!
 
  • #4
n represents number of free charge per unit voloume, and it has a dimension of one over volume, don't forget next time
 
  • #5
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..)
 

What is a homogeneous equation?

A homogeneous equation is a type of mathematical equation where all the terms have the same degree. This means that each term has the same number of variables raised to the same power. For example, x^2 + 2xy + y^2 = 0 is a homogeneous equation because each term has two variables raised to the second power.

How do you know if an equation is homogeneous?

To determine if an equation is homogeneous, you must check if all the terms have the same degree. This can be done by looking at the exponents of the variables in each term. If they are all the same, then the equation is homogeneous.

Why is it important to show that an equation is homogeneous?

If an equation is homogeneous, it can be solved using certain techniques and methods that are specific to homogeneous equations. This can make solving the equation easier and more efficient.

What is the process for showing that an equation is homogeneous?

To show that an equation is homogeneous, you must first rearrange the equation so that all the terms are on one side and the constant is on the other side. Then, you must check if all the terms have the same degree. If they do, then the equation is homogeneous.

Can an equation be both homogeneous and non-homogeneous?

No, an equation can only be either homogeneous or non-homogeneous. If an equation has terms with different degrees, then it is considered non-homogeneous. However, it is possible for a system of equations to have both homogeneous and non-homogeneous equations.

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