CURRENT DRIFT VELOCITY AND CURRENT DENSITY
express current in terms of the drift velocity of the moving charges. Let’s con the situation of Fig. 26-3, a conductor with cross-section area A and an E directed from left to right. To begin with, we’ll assume that the free the conductor are positive; then the drift velocity is in the same direction as there are n charged particles per unit volume. We call n the concentration ; its SI unit is m-J. Assume that all the particles move with the same drift magnitude vd• In a time interval dt, each particle moves a distance Vd dt. that flow out of the right end of the shaded cylinder with length particles that were within this cylinder at the beginning of the interval dt. cylinder is AVd dt, and the number of particles within it is nAvd dt. If has a charge q, the charge dQ that flows out of the end of the cylinder.
There are no absolute value signs in Eq. (26-4). If q is positive, Vd is in the same tion as E, and if q is negative, vd is opposite to E; in either case, j is in the same . as E. Equation (26-3) gives the magnitude J of the vector current density i. In general, a conductor may contain several different moving charged having charges ql’ q2′ … , concentrations nl, ~, … , and drift velocities magnitudes An example is current flow in an ionic solution. In a chloride solution, current can be carried by both positive sodium ions and negative tine ions; the total current I is found by adding up the currents due to each . charged particle, using Eq. (26-2). Likewise, the total vector current density j is by using Eq. (26-4) for each charged particle and adding up the results. We will see in Section 26-5 that it is possible to have a current that is stead) is, one that is constant in time) only if the conducting material forms a closed called a complete circuit. In such a steady situation, the total charge in every se the conductor is constant. Hence the rate of flow of charge out at one end of a _ at any instant equals the rate of flow of charge in at the other end of the segment, current is the same at all cross sections of the circuit. We’ll make use of this when we analyze electric circuits later in this chapter. In many simple circuits, such as flashlights or electric drills, the direction of the rent is always the same; this is called direct current. But home appliances toasters, refrigerators, and televisions use alternating current, in which the changes direction. In this chapter we’ll consider direct current Alternating current has many special features worthy of detailed study, which examine in Chapter 32.