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?

Verified step by step guidance

Determine the formula for drift speed. The drift speed \( v_d \) is given by \( v_d = \frac{I}{n \cdot A \cdot e} \), where \( I \) is the current, \( n \) is the number density of electrons, \( A \) is the cross-sectional area of the wire, and \( e \) is the charge of an electron.

Calculate the current \( I \). The current is the rate of charge flow, \( I = \frac{Q}{t} \), where \( Q \) is the total charge and \( t \) is the time. Use \( Q = N \cdot e \), where \( N \) is the number of electrons and \( e = 1.6 \times 10^{-19} \; \text{C} \).

Find the cross-sectional area \( A \) of the wire. The wire is circular, so \( A = \pi r^2 \), where \( r \) is the radius of the wire. Convert the diameter of the wire (2.0 mm) to meters and divide by 2 to find the radius.

Determine the number density of electrons \( n \). For iron, the number density of conduction electrons is approximately \( 8.5 \times 10^{28} \; \text{electrons/m}^3 \).

Substitute all known values into the drift speed formula \( v_d = \frac{I}{n \cdot A \cdot e} \) to calculate the drift speed. Ensure all units are consistent (e.g., meters, seconds, coulombs).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

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. In a conductor, this speed is typically very small, as it represents the net movement of electrons in the direction of the electric field, despite their random thermal motion. 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 an electron, and A is the cross-sectional area.

Current

Electric current is the flow of electric charge, measured in amperes (A). It represents the rate at which charge flows through a conductor. In this context, current can be calculated using the formula I = Q/t, where Q is the total charge that passes through a cross-section of the wire in time t. Understanding current is essential for determining the drift speed of electrons in the wire.

Cross-Sectional Area

The cross-sectional area of a wire is the area of its circular end face, which affects how much current can flow through it. It is calculated using the formula A = π(d/2)², where d is the diameter of the wire. A larger cross-sectional area allows more electrons to flow simultaneously, influencing both the current and the drift speed of the electrons within the wire.

Recommended video:

Guided course

08:10

Calculating the Vector (Cross) Product Using Components

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 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?

views

Textbook Question

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?

views