Current is flowing through the thick wire connected to the thin wire, as shown. Because the current can't pile up in a conductor, the current in the thick wire must be the same as the current in the thin wire. This brings up the concept of current density. If the current density, j, in a conductor is constant across the conductor, its magnitude is equal to the current, I, divided by the cross sectional area, A, of the wire. Given this definition of current density, and the fact that the current, I, is the same in both the thin and the thick parts of the wire, which part of the wire has a higher current density? ... The current density is current divided by area. ... The current is the same in both parts of the wire, but the current density is different. ... A wire with a diameter of 0.1 centimeters carries a 5 ampere current. What is the current density in the wire? ... Make sure you haven't confused diameter with radius. ... Check the conversion from centimeters to meters. ... How fast do electrons actually move in a current through a metal? Consider a metal conductor of length L with a cross sectional area A. The volume V of this section of wire is equal to A times L. The number of current-carrying electrons per unit volume is n. The magnitude of the total charge, Q, moving in the volume, V, is n e V, where e is the magnitude of the charge on a single electron. The current is the charge in this volume divided by the time it takes to for the charge to move through the length of wire. The drift speed v sub d is the magnitude of the average velocity of the electrons that comprise the current. The electrons also have random thermal motion that does not contribute to the current. The electrons move through the volume with the speed v sub d, which is equal to L divided by t. Now we have an equation relating current and drift speed. The result is that the current, I, is equal to the number of electrons per unit volume, n, times the charge on an electron, e, times the cross sectional area of the wire, A, times the drift speed, v sub d. By dividing both sides by A, we reach an equation that relates drift velocity and current density. This can be rearranged to solve for the drift speed. Let's plug in some typical numbers. For copper, n is about 11 times ten to the 22nd electrons per centimeter cubed. We obtained a value of 640 amps per centimeter squared for the current density in a previous example. The drift velocity is only about 3 hundredths of a centimeter per second. Why doesn't it take hours for the lights to come on when you flip the switch? Even though the electrons drift along fairly slowly, they begin drifting throughout the wire almost immediately when the switch is turned on. Current density, unlike current itself, is actually a vector, even though so far we have considered only its magnitude. We can put the equation we previously derived into vector form to relate the drift velocity to the current density vector. The negative sign is present here because the charge carrying electrons are negatively charged.

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