- #1
tsoits
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1) Analogy in F = ma
2) In the definition of ampere, it is in terms of the force per unit length between two straight parallel conductors having equal current.
3) What's bad about this new definition?
From experiment, we find that
[itex]F = k m a[/itex]
and we deliberately choose [itex]k = 1[/itex] (dimensionaless) and thus we define the unit Newton, a derived unit.
[itex]F = k m a[/itex]
and we deliberately choose [itex]k = 1[/itex] (dimensionaless) and thus we define the unit Newton, a derived unit.
2) In the definition of ampere, it is in terms of the force per unit length between two straight parallel conductors having equal current.
[itex]f = K I^2 / r[/itex]
One ampere is defined for
[itex]I = K' \sqrt{f r}[/itex]
As we know today, the constant [itex]K'[/itex], has dimensions ([itex]A/ \sqrt{N}[/itex]).
What if we instead take K' as dimensionless, just like the constant in Newton's 1st law?
In this case, the new Ampere 1 A would have the same dimension as [itex]\sqrt{N}[/itex].
In other words, this new ampere is a derived unit instead?
One ampere is defined for
[itex]I = K' \sqrt{f r}[/itex]
As we know today, the constant [itex]K'[/itex], has dimensions ([itex]A/ \sqrt{N}[/itex]).
What if we instead take K' as dimensionless, just like the constant in Newton's 1st law?
In this case, the new Ampere 1 A would have the same dimension as [itex]\sqrt{N}[/itex].
In other words, this new ampere is a derived unit instead?
3) What's bad about this new definition?
I'm quite sure someone must have thought about this, or I must have made some terrible mistake. But as I can't find any references, here's what I can come up with so far:
a) [itex]\mu_0[/itex] becomes dimensionless. So the unit of [itex]\epsilon_0[/itex] has to be changed too (related to speed of light).
b) can't think of it yet..
Shouldn't there be a more fundamental reason for this?
a) [itex]\mu_0[/itex] becomes dimensionless. So the unit of [itex]\epsilon_0[/itex] has to be changed too (related to speed of light).
b) can't think of it yet..
Shouldn't there be a more fundamental reason for this?