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www.GOALias.blogspot.comPhysicsANDRE AMPERE (1775 –1836)148Andre Ampere (1775 –1836) Andre Marie Amperewas a French physicist,mathematician andchemist who founded thescience of electrodynamics.Ampere was a child prodigywho mastered advancedmathematics by the age of12. Ampere grasped thesignificance of Oersted’sdiscovery. He carried out alarge series of experimentsto explore the relationshipbetween current electricityand magnetism. Theseinvestigations culminatedin 1827 with thepublication of the‘Mathematical Theory ofElectrodynamic PhenomenaDeduced Solely fromExperiments’. He hypothesisedthat all magneticphenomena are due tocirculating electriccurrents. Ampere washumble and absentminded.He once forgot aninvitation to dine with theEmperor Napoleon. He diedof pneumonia at the age of61. His gravestone bearsthe epitaph: Tandem Felix(Happy at last).(i)(ii)B is tangential to the loop and is a non-zero constantB, orB is normal to the loop, or(iii) B vanishes.Now, let L be the length (part) of the loop for which Bis tangential. Let I ebe the current enclosed by the loop.Then, Eq. (4.17) reduces to,BL =µ 0I e[4.17(b)]When there is a system with a symmetry such as fora straight infinite current-carrying wire in Fig. 4.15, theAmpere’s law enables an easy evaluation of the magneticfield, much the same way Gauss’ law helps indetermination of the electric field. This is exhibited in theExample 4.8 below. The boundary of the loop chosen isa circle and magnetic field is tangential to thecircumference of the circle. The law gives, for the left handside of Eq. [4.17 (b)], B. 2πr. We find that the magneticfield at a distance r outside the wire is tangential andgiven byB × 2πr = µ 0I,B = µ 0I/ (2πr) (4.18)The above result for the infinite wire is interestingfrom several points of view.(i) It implies that the field at every point on a circle ofradius r, (with the wire along the axis), is same inmagnitude. In other words, the magnetic fieldpossesses what is called a cylindrical symmetry. Thefield that normally can depend on three coordinatesdepends only on one: r. Whenever there is symmetry,the solutions simplify.(ii) The field direction at any point on this circle istangential to it. Thus, the lines of constant magnitudeof magnetic field form concentric circles. Notice now,in Fig. 4.1(c), the iron filings form concentric circles.These lines called magnetic field lines form closedloops. This is unlike the electrostatic field lines whichoriginate from positive charges and end at negativecharges. The expression for the magnetic field of astraight wire provides a theoretical justification toOersted’s experiments.(iii) Another interesting point to note is that even thoughthe wire is infinite, the field due to it at a nonzerodistance is not infinite. It tends to blow up only whenwe come very close to the wire. The field is directlyproportional to the current and inversely proportionalto the distance from the (infinitely long) currentsource.