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Magnetic field and π 
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#1
Mar812, 11:33 AM

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Hi
as you know according to ampere's law ∫B.dl=μ_{0}I but why μ_{0} that appears in Maxwell's equations is exactly 4π *10^{7} ? for example in electric field ε_{0} is 8.85 *10^{12} and μ_{0} like ε_{0} is a constant that is related to material properties and why this constant is a special number as π that B is special ? 


#2
Mar812, 12:46 PM

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Hi Amir! Welcome to PF!
From the PF Library on magnetic field …What is µ_{0}? µ_{o} is the conversion factor between tesla ([itex]T\ =\ N/A.m[/itex]) and ampturns per metre ([itex]A/m[/itex]): so it has units of [itex]N/A^2[/itex]. Why isn't µ_{o} = 1 N/A^{2} (so that it needn't be mentioned)?(And the electric constant (permittivity of free space), [itex]\varepsilon_o[/itex], is defined as 1/µ_{0}c², = 10^{7}/4πc² C²/Nm² (or F/m).) 


#3
Mar812, 02:57 PM

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yes, your sentences is true ,but my query is that π is a number that related to sphere.but µo is a constant that related to environment.and why is a special number that has π ?
µo is exactly 4π 10^7 but if it is a constant about environment , why it is exactly a special number ? I think it should related to microscopic vacuum properties ,if isn't it ,why for other environments µ is not 4π *10^7 ? and is a other number? but for free space is a special number like π ! sorry for my english is not good. 


#4
Mar812, 03:06 PM

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Magnetic field and π
µ_{o} is simply the conversion factor between tesla and ampturns per metre. (of course, µ (for a material) is related to the material) The 4π is a standard factor in SI units, since it naturally relates the strength of a source to its flux (because the field from the source spread out over an area 4πr^{2} instead of r^{2}). 


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