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20.1 Current  (Page 3/10)

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In part a, positive charges move toward the right through a conducting wire. The direction of movement of charge is indicated by arrows along the length of the wire. The area of a cross section of the wire is labeled as A. The direction of the electric field E is toward the right, in the same direction as movement of positive charge. The current direction is also toward the right, shown by an arrow. In part b, negative charges move toward the left through a conducting wire. The direction of movement of charge is indicated by arrows along the length of the wire. The area of a cross section of the wire is labeled as A. The direction of the electric field E is toward the right, opposite the direction of movement of negative charge. The current direction is also toward the right, shown by an arrow.
Current I size 12{I } {} is the rate at which charge moves through an area A , such as the cross-section of a wire. Conventional current is defined to move in the direction of the electric field. (a) Positive charges move in the direction of the electric field and the same direction as conventional current. (b) Negative charges move in the direction opposite to the electric field. Conventional current is in the direction opposite to the movement of negative charge. The flow of electrons is sometimes referred to as electronic flow.

Calculating the number of electrons that move through a calculator

If the 0.300-mA current through the calculator mentioned in the [link] example is carried by electrons, how many electrons per second pass through it?

Strategy

The current calculated in the previous example was defined for the flow of positive charge. For electrons, the magnitude is the same, but the sign is opposite, I electrons = − 0.300 × 10 −3 C/s .Since each electron ( e − ) has a charge of –1 . 60 × 10 − 19 C , we can convert the current in coulombs per second to electrons per second.

Solution

Starting with the definition of current, we have

I electrons = Δ Q electrons Δ t = –0 . 300 × 10 − 3 C s . size 12{I = { {ΔQ} over {Δt} } = { {0 "." "300 " times " 10" rSup { size 8{ - 3} } " C"} over {"s"} } "."} {}

We divide this by the charge per electron, so that

e – s = –0 . 300 × 10 – 3 C s × 1 e – –1 .60 × 10 − 19 C = 1.88 × 10 15 e – s .

Discussion

There are so many charged particles moving, even in small currents, that individual charges are not noticed, just as individual water molecules are not noticed in water flow. Even more amazing is that they do not always keep moving forward like soldiers in a parade. Rather they are like a crowd of people with movement in different directions but a general trend to move forward. There are lots of collisions with atoms in the metal wire and, of course, with other electrons.

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Drift velocity

Electrical signals are known to move very rapidly. Telephone conversations carried by currents in wires cover large distances without noticeable delays. Lights come on as soon as a switch is flicked. Most electrical signals carried by currents travel at speeds on the order of 10 8 m/s size 12{"10" rSup { size 8{8} } `"m/s"} {} , a significant fraction of the speed of light. Interestingly, the individual charges that make up the current move much more slowly on average, typically drifting at speeds on the order of 10 − 4 m/s size 12{"10" rSup { size 8{ - 4} } `"m/s"} {} . How do we reconcile these two speeds, and what does it tell us about standard conductors?

The high speed of electrical signals results from the fact that the force between charges acts rapidly at a distance. Thus, when a free charge is forced into a wire, as in [link] , the incoming charge pushes other charges ahead of it, which in turn push on charges farther down the line. The density of charge in a system cannot easily be increased, and so the signal is passed on rapidly. The resulting electrical shock wave moves through the system at nearly the speed of light. To be precise, this rapidly moving signal or shock wave is a rapidly propagating change in electric field.

Negatively charged electrons move through a conducting wire. Two electrons are shown entering the wire from one end, and two electrons are shown leaving the wire at the other end. The direction of movement of charge is indicated by arrows along the length of the wire toward the right. Some electrons are shown inside the wire.
When charged particles are forced into this volume of a conductor, an equal number are quickly forced to leave. The repulsion between like charges makes it difficult to increase the number of charges in a volume. Thus, as one charge enters, another leaves almost immediately, carrying the signal rapidly forward.

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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