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Chapter 18: Q2Q (page 755)

Describe the following attributes of a metal wire in steady

state vs. equilibrium:

Metal Wire

Steady-state

Equilibrium

Location of excess charge

Motion of mobile electrons

inside the metal wire

Short Answer

Expert verified

Metal Wire

Steady-state

Equilibrium

Location of excess charge

No excess charge

If present, on the surface

Motion of mobile electrons

In motion

Stationary

inside the metal wire

Non-zero

Zero

Step by step solution

01

Given data

A metal wire in steady state and in equilibrium.

02

Concept of steady state and equilibrium

A conductor with a continuous and steady flow of charges is said to be in a steady state.

A conductor where the charges are stationary and situated at the surface is said to be in equilibrium.

03

Determination of the difference between steady state and equilibrium in a metal wire

A metal wire in equilibrium can have excess charges only at the surface. There are no charges inside the wire. A metal wire in steady state doesn't have any excess charge. It is electrically neutral.

The electric field inside a metal wire in equilibrium is zero but the electric field inside a metal wire in steady state is never zero.

Thus the table can be filled as follows:

Metal Wire

Steady-state

Equilibrium

Location of excess charge

No excess charge

If present, on the surface

Motion of mobile electrons

In motion

Stationary

inside the metal wire

Non-zero

Zero

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Most popular questions from this chapter

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 \({\bf{2 \times 1}}{{\bf{0}}^{{\bf{18}}}}\) electrons enters wire A every second. How many electrons enter wire B every second?

In the circuit shown figure 18.108, two thick copper wires connect a 1.5 V battery to a Nichrome wire. Each thick connecting wire is 17 cm long and has a radius of 9 mm. Copper has 8.4脳1028mobile electrons per cubic meter and electron mobility. The Nichrome wire is 8 cm long and has a radius of 3 mm. Nichrome has 9脳1028mobile electrons per cubic meter and electron mobility of 7脳10-5(ms)(Vm).

(a) What is the magnitude of the electric field in the thick copper wire?

(b) What is the magnitude of the electric field in the thin Nichrome wire?

In the circuit shown in Figure 18.87, bulbs 1 and 2 are identical in mechanical construction (the filaments have the same length and the same cross-sectional area), but the filaments are made of different metals. The electron mobility in the metal used in bulb 2 is three times as large as the electron mobility in the metal used in bulb 1, but both metals have the same number of mobile electrons per cubic meter. The two bulbs are connected in series to two batteries with thick copper wires (like your connecting wires).

(a)In bulb 1, the electron current is i1and the electric field is E1. In terms of these quantities, determine the corresponding quantities i2and E2for bulb 2, and explain your reasoning.

(b)When bulb 2 is replaced by a wire, the electron current through bulb 1 is i0and the electric field in bulb 1 is E0. How big is i1 in terms of i0? Explain your answer, including explicit mention of any approximations you must make. Do not use ohms or series-resistance equations in your explanation, unless you can show in detail how these concepts follow from the microscopic analysis introduced in this chapter.

(c)Explain why the electric field inside the thick copper wires is very small. Also explain why this very small electric field is the same in all of the copper wires, if they all have the same cross-sectional area.

(d)Figure 18.88 is a graph of the magnitude of the electric field at each location around the circuit when bulb 2 is replaced by a wire. Copy this graph and add to it, on the same scale, a graph of the magnitude of the electric field at each location around the circuit when both bulbs are in the circuit. The very small field in the copper wires has been shown much larger than it really is in order to give you room to show how that small field differs in the two circuits.

The circuit shown in Figure 18.107 consists of a single battery, whose emf is 1.8V, and three wires made of the same material but having different cross-sectional areas. Each thick wire has a cross-sectional area 1.4脳10-6m2and is 25cmlong. The thin wire has a cross-sectional area 5.9脳10-6m2and is 6.1cmlong. In this metal, the electron mobility is 5脳10-4(ms)(Vm), and there are 4脳1028mobile electrons/m3.

(a) Which of the following statements about the circuit in the steady state are true? (1) At location B, the electric field points toward the top of the page. (2) The magnitude of the electric field at locations F and C is the same. (3) The magnitude of the electric field at locations D and F is the same. (4) The electron current at location D is the same as the electron current at location F . (b) Write a correct energy conservation (loop) equation for this circuit, following a path that starts at the negative end of the battery and goes counterclockwise. (c) Write this circuit's correct charge conservation (node) equation. (d) Use the appropriate equation(s), plus the equation relating electron current to electric field, to solve for the magnitudes EDand EF of the electric field at locations D and F . (e) Use the appropriate equation(s) to calculate the electron current at location D in the steady state.

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.
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