(Heres an excellent exercise to test your understanding. Let your thumb point into the direction of the current flow. The best way to find the direction of magnetic field due to a current carrying conductor is by using Fleming's right hand thumb rule. This page titled 7.5: Magnetic Field of an Infinitely-Long Straight Current-Bearing Wire is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Steven W. Ellingson (Virginia Tech Libraries' Open Education Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. I 2 That vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the A-B (Aharonov-Bohm) effect. . Making the elements very (infinitely) short, we proceed from summation to integration of the contributions to the magnetic field from inidividual parts of the conductor. ), Ampere's law becomes: The equation says that the integral of the magnetic field \end{aligned}. ) Too, a north pole feels a force in the direction of the H -field while the force on the south pole is opposite to the H -field. ^ The magnetic vector potential gets modified to A ( r, t) = 0 4 J ( r , t r ) | r r | d 3 r where t r = t 1 c | r r | is the retarded time. In this section, we use the magnetostatic form of Amperes Circuital Law (ACL) to determine the magnetic field due to a steady current \(I\) (units of A) in an infinitely-long straight wire. With this choice we have, \[I_{encl}=I ~~ \mbox{for}~\rho\ge a \nonumber \], For \(\rho
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