Forces between two parallel charged rods (2 Viewers)
- Thread starter NexusRich
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There are usually reasons why these constants are interrelated but the reasons may be beyond HSC level. Things also changed in 2018 / 2019 with the SI redefinitions. Prior to the redefinition, 
had an exact value:
This arose from the definition of the ampere as the constant current that, when maintained between two straight parallel conductors (of infinite length and negligible circular cross section) placed 1 meter apart in vacuum, produces a force per unit length between them of equal to
. Applying this definition to Ampère's force law gives in exact terms. Having this as exact was necessary for the definition of the amp as the unit for current.
However, with the redefinitions came many subtle changes and the reasons for these are really not worth exploring at HSC level. The ampere is now defined in terms of the elementary charge and the second (both now fixed in value). As a consequence, is no longer a fixed constant, it now has an experimentally derived value with a measurement uncertainty. One recent report gave it as
 \times 10^{-7} = 1.256\ 637\ 062\ 12... \times 10^{-6}\ \text{H m}^{-1})
Note that the value has remained unchanged for the first nine significant figures and so the difference is irrelevant for many applications.
Units and constants are often interrelated, with being related to the fine-structure constant 
by the equation
with
being the Planck constant, 
being the speed of light, and 
being the elementary charge. Since these three now have fixed / defined values, it is only and that are variable and experimentally derived, and hence the uncertainty in is determined by the uncertainty in our measurements of the fine-structure constant.
The changes that accompanied the 2019 redefinitions touched on all our fundamental units and are covered unevenly in textbooks. The definitions are not necessarily intuitive for a non-specialist. For example, the kilogram is no longer defined by a prototype object against which comparisons can be made. It is now (effectively) that mass that, when combined with the definitions of the metre and the second, gives the Planck constant the exact value
.
This arose from the definition of the ampere as the constant current that, when maintained between two straight parallel conductors (of infinite length and negligible circular cross section) placed 1 meter apart in vacuum, produces a force per unit length between them of equal to
However, with the redefinitions came many subtle changes and the reasons for these are really not worth exploring at HSC level. The ampere is now defined in terms of the elementary charge and the second (both now fixed in value). As a consequence,
Note that the value has remained unchanged for the first nine significant figures and so the difference is irrelevant for many applications.
Units and constants are often interrelated, with
with
The changes that accompanied the 2019 redefinitions touched on all our fundamental units and are covered unevenly in textbooks. The definitions are not necessarily intuitive for a non-specialist. For example, the kilogram is no longer defined by a prototype object against which comparisons can be made. It is now (effectively) that mass that, when combined with the definitions of the metre and the second, gives the Planck constant the exact value