Ia reminds us, an isolated conducting loop-regardless of whether it has an excess charge-is all at the same potential. No electric field can exist within. it or along its surface. Although conduction electrons are available, no net electric
force acts on them and thus th re is no current. If, as in , we insert a battery in he loop, the conducting loop is no longer at a single potential. Electric fields act inside the material making up the loop, exerting forces on the conduction electrons, causing them to move, and thus establishing a current. After a very short time, the electron flow reaches a constant value and the current is in its steady state (it does not vary with time). shows a section of a conductor, part of a conducting loop in which current has been established. If charge dq passes through a hypothetical plane (suchas aa’) in time dr, then the current j through that plane is defined as.
in which the current i may vary with time. Under steady-state conditions, the current is the same for planes aa’, bb’, and c’ and indeed for all planes that pass completely through the conductor, no matter what their location or orientation. This follows from the fact that charge is conserved. Under the steady-state conditions assumed here, an electron must pass through plane aa’ .for every electron that passes through plane ee’. In the same way, if we have a
steady flow of water through a garden hose, a drop of water must leave the nozzle for every drop that enters the house at the other end. The amount of water in the hose is a conserved quantity ..]lIe .SI unit ~or current is the coulomb per second, also called the ampere (A): 1 ampere = 1 A = 1 coulomb per second = 1 Cis. The ampere is an SI base unit; the coulomb is defined in terms of the ampere, as we discussed in Chapter 22. The formal definition of the ampere is discussed in Chapter 30. . r Current, as d fined by Eq. 27-1, is a scalar because bath charge and time in that equation are scalars. Yet, as in 1 b, we often represent a current with an arrow to indicate that charge is moving. Such arrows are not vectors, however, and they do not require vector addition. F shows a conductor with current io splitting at a junction into two branches. Because charge is conserved, the magnitudes of the currents in the branches must add to yield the magnitude of the current in the original conductor, so that