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www.GOALias.blogspot.comMoving Charges andMagnetismF ba= I bL B aµ0IaI=2 π dbL(4.23)It is of course possible to compute the force on ‘a’ due to ‘b’. Fromconsiderations similar to above we can find the force F ab, on a segment oflength L of ‘a’ due to the current in ‘b’. It is equal in magnitude to F ba,and directed towards ‘b’. Thus,F ba= –F ab(4.24)Note that this is consistent with Newton’s third Law. Thus, at least forparallel conductors and steady currents, we have shown that theBiot-Savart law and the Lorentz force yield results in accordance withNewton’s third Law*.We have seen from above that currents flowing in the same directionattract each other. One can show that oppositely directed currents repeleach other. Thus,Parallel currents attract, and antiparallel currents repel.This rule is the opposite of what we find in electrostatics. Like (samesign) charges repel each other, but like (parallel) currents attract eachother.Let f barepresent the magnitude of the force F baper unit length. Then,from Eq. (4.23),µ0IaIbfba=2 ð d(4.25)The above expression is used to define the ampere (A), which is oneof the seven SI base units.The ampere is the value of that steady current which, when maintainedin each of the two very long, straight, parallel conductors of negligiblecross-section, and placed one metre apart in vacuum, would produceon each of these conductors a force equal to 2 × 10 –7 newtons per metreof length.This definition of the ampere was adopted in 1946. It is a theoreticaldefinition. In practice one must eliminate the effect of the earth’s magneticfield and substitute very long wires by multiturn coils of appropriategeometries. An instrument called the current balance is used to measurethis mechanical force.The SI unit of charge, namely, the coulomb, can now be defined interms of the ampere.When a steady current of 1A is set up in a conductor, the quantity ofcharge that flows through its cross-section in 1s is one coulomb (1C).* It turns out that when we have time-dependent currents and/or charges inmotion, Newton’s third law may not hold for forces between charges and/orconductors. An essential consequence of the Newton’s third law in mechanicsis conservation of momentum of an isolated system. This, however, holds evenfor the case of time-dependent situations with electromagnetic fields, providedthe momentum carried by fields is also taken into account.155