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Unformatted text preview: Physics 54 Steady Currents Ive had a lovely evening but this wasnt it. Groucho Marx Electric current One might think the discussion of charges in motion would begin with a description of the Felds of a single moving point charge. But those Felds are quite complicated even if the charge is moving with constant velocity, but especially if it is accelerating. However, when we consider the average Felds produced by a large number of identical charges moving (on average) relatively slowly the situation is much simpler . Especially simple is the case where the charges move with constant average velocity. In that case, called direct current (DC), the ow of charge is much like that of mass in a perfect uid. To describe the ow we introduce the electric current density : Current density Electric current density j is a vector Feld. Its direction is that of the ow of positive charge; its magnitude is equal to the amount of charge passing in unit time through unit area normal to the ow. To relate the net ow described by j to the average motion of the individual microscopic charges (such as electrons), consider a small cylinder of cross-section area A and length v t , where v is the average speed of the moving charges. This cylinder has volume Av t . We assume the moving charges are identical and have charge q , and that there are n charges per unit volume. The amount of charge that passes through area A in time t is equal to the amount in this cylinder at t = 0, which is nq ( Av t ) . It follows that the amount owing per unit area per unit time is nqv , so we have j = nq v . If q is positive, j is parallel to the velocity v . (or electron ow, j is opposite to v .) The total ux of j across a particular surface is of great practical importance. It is called the electric current , denoted by I . v A v t PHY 54 1 Steady Currents Electric current as fux oF current density I = j d A In our applications the conductors will usually be in the Form oF wires, For which the area in question is the cross-section oF the wire. The current I is then the total amount oF charge passing a particular point on the wire per unit time, which one oFten writes as Electric current as charge passing by per unit time I = dQ dt Electric current is measured in amperes (A). A current oF 1 A means that 1 C oF charge passes a point on the wire per second. This is a moderate size current. The SI system oF electrical units is in Fact based on the ampere, with one Coulomb oF charge dened as the amount fowing in one second past a point in a wire carrying a current oF one ampere. Resistance We have seen that charges in a conductor, leFt to themselves, quickly rearrange and come to rest in electrostatic equilibrium. To keep them moving requires continuous application oF an external E-eld. We will discuss below some possible sources oF this external eld. or now we will just assume such a eld exists....
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