Chapter 18: Electric Field and Circuits

What is the most important general difference between a system in steady state and a system in equilibrium?

What is the most important general difference between a system in steady state and a system in equilibrium?

The drift speed in a copper wire is $7\times {10}^{-5}\frac{m}{s}$for a typical electron current. Calculate the magnitude of the electric field inside the copper wire. The mobility of mobile electrons in copper is $4.5\times {10}^{-3}\left(\frac{m}{s}\right)/\left(\frac{N}{C}\right)$. (Note that though the electric field in the wire is very small, it is adequate to push a sizable electron current through the copper wire.)

Suppose that a wire leads into another, thinner wire of the same material that has only a third the cross-sectional area. In the steady state, the number of electrons per second flowing through the thick wire must be equal to the number of electrons per second flowing through the thin wire. If the drift speed$\overline{{\mathbf{V}}_{\mathbf{1}}}$in the thick wire is $\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\frac{\mathbf{m}}{\mathbf{s}}$, what is the drift speed ${\overline{\mathbf{V}}}_{\mathbf{2}}$in the thinner wire?

Describe the following attributes of a metal wire in steady

state vs. equilibrium:

Suppose that a wire leads into another, thinner wire of the same material that has only half the cross-sectional area. In the steady state, the number of electrons per second flowing through the thick wire must be equal to the number of electrons per second flowing through the thin wire. If the electric field $E_1$ in the thick wire is $1\times 10^{-2}N/C$, what is the electric field $E_2$ in the thinner wire?

Suppose that wire A and wire B are made of different metals and are subjected to the same electric field in two different circuits. Wire B has the 6 times the cross sectional area, 1.3 times as many mobile electrons per cubic centimetre and 4 times the mobility of wire A. In the steady state $\mathbf{2}\times \mathbf{1}{\mathbf{0}}^{\mathbf{18}}$ electrons enters wire A every second. How many electrons enter wire B every second?

Inside a chemical battery it is not actually individual electrons that are transported from the + end to the – end. At the + end of the battery an “acceptor” molecule picks up an electron entering the battery, and at the – end a different “donor” molecule gives up an electron, which leaves the battery. Ions rather than electrons move between the two ends to support the charge inside the battery.

When the supplies of acceptor and donor molecules are used up in a chemical battery, the battery is dead because it can no longer accept or electron. The electron current in electron per second times the number of seconds of battery life, is equal to the number of donor molecules in the battery.

A flashlight battery contains approximately half a mole of donor molecules. The electron current through a thick filament bulb powered by two flashlight batteries in series is about 0.3 A. About how many hours will the batteries keep this bulb lit?

The emf of a particular flashlight battery is 1.7 V. If the battery is 4.5 cm long and radius of cylindrical battery is 1 cm, estimate roughly the amount of charge on the positive end plate of the battery.

A Nichrome wire 30 cm long and 0.25 mm in diameter is connected to a 1.5 V flashlight battery. What is the electric field inside the wire? Why you don’t have to know how the wire is bent? How would your answer change if the wire diameter change were 0.35 mm? (Not that the electric field in the wire is quiet small compared to the electric field near a charged tape.)