What is Ampere circuital law

Ampere circuital law – After the discovery of Oersted and Biot-Savart, Ampere found a useful relation between magnetic field and electric current.     [ In the case of all basic laws of physics , Ampere’s law can’t be derived , its validity is based on the correctness of the result.] . According to Ampere circuital law that the linear integral of magnetic field (B) along a imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium µ0 . for a  long straight current carrying conductor  , magnetic field

                                                                    B= µ0 I/2ΠR

                                         So,  

                                  ∫B.dl =   ( µ0 I/2Πr) ∫dl    ( integrate with limit 0 to 2Πr )                                                      = ( µ0 I/2ΠR) × 2Πr = µ0I          

 

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