Ch 27: Current and Resistance

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 27: Current and Resistance

Problem 8a

Chapter 27, Problem 8a

The mean time between collisions for electrons in a gold wire is 25 fs, where 1 fs = 1 femtosecond = 10⁻¹⁵ s. What is the electron drift speed in a 35 mV/m electric field?

Verified step by step guidance

Understand the problem: The drift speed of electrons in a conductor is related to the electric field, the mean time between collisions (relaxation time), and the properties of the electron. The formula to use is:

v

_d=eEτ/m_e, where

v

_d is the drift speed,

e

is the charge of an electron,

E

is the electric field,

τ

is the mean time between collisions, and

m

_e is the mass of an electron.

Identify the given values: The electric field

E

is 35 mV/m =

35 × 10

^-3 V/m, the mean time between collisions

τ

is 25 fs =

25 × 10

^-15 s, the charge of an electron

e

1.6 × 10

^-19 C, and the mass of an electron

m

_e is

9.11 × 10

^-31 kg.

Substitute the known values into the formula:

v

_d=(1.6×10-19)(35×10-3)(25×10-15)/(9.11×10-31).

Simplify the numerator: Multiply the values for

e

E

, and

τ

to calculate the numerator of the formula.

Divide the result of the numerator by the mass of the electron

m

_e to find the drift speed

v

_d. Ensure the units are consistent throughout the calculation to obtain the final drift speed in meters per second (m/s).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Drift Speed

Drift speed refers to the average velocity that charged particles, such as electrons, attain due to an electric field. It is a crucial concept in understanding how electric current flows through conductors. The drift speed can be calculated using the formula v_d = I/(nqA), where I is the current, n is the charge carrier density, q is the charge of the electron, and A is the cross-sectional area of the conductor.

Mean Time Between Collisions

The mean time between collisions is the average time interval that an electron travels before colliding with an atom in a conductor. This concept is significant in determining the mobility of electrons and affects their drift speed. A shorter mean time indicates more frequent collisions, which can slow down the drift speed of electrons in a material.

Electric Field

An electric field is a region around a charged particle where other charged particles experience a force. It is quantified in volts per meter (V/m) and influences the motion of charged particles within it. In this context, the electric field of 35 mV/m provides the driving force that causes electrons to drift, contributing to the overall current in the wire.

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Intro to Electric Fields

Related Practice

Textbook Question

The electron drift speed is 2.0 X 10⁻⁴ m/s in a metal with a mean time between collisions of 5.0 x 10⁻¹⁴. What is the electric field strength?

Textbook Question

The electron drift speed in a 1.0-mm-diameter gold wire is 5.0 x 10⁻⁵ m/s. How long does it take 1 mole of electrons to flow through a cross section of the wire?

Textbook Question

The current in a 2.0 mm x 2.0 mm square aluminum wire is 2.5 A. What are (a) the current density and (b) the electron drift speed?

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Textbook Question

The mean time between collisions for electrons in a gold wire is 25 fs, where 1 fs = 1 femtosecond = 10⁻¹⁵ s. How many times does the electron collide with an ion while moving this distance?

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Textbook Question

A superconducting magnet carries a 100 A current through a 0.50-mm-diameter superconducting wire that is wound into a coil. How much charge flows through the wire in 15 minutes?

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Textbook Question

1.0 x 10²⁰ electrons flow through a cross section of a 2.0-mm-diameter iron wire in 5.0 s. What is the electron drift speed?

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