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Chapter 24: Problem 2

A constant electric field generally produces a constant drift velocity. How is this consistent with Newton's assertion that force results in acceleration, not velocity?

Short Answer

Expert verified
Contrary to what it might seem, Newton's law and the concept of drift velocity are not contradictory. In the presence of a constant electric field, charged particles do indeed accelerate initially (due to the force exerted by the field) consistent with Newton's law. However, they also experience a counteracting force due to collisions with other particles. This balances out the applied force, resulting in a constant average velocity - the drift velocity. Thus, while the force by itself would cause acceleration, other factors result in a steady, constant drift velocity.

Step by step solution

01

Understand the concept of an electric field

An electric field is defined as a region around a charged particle wherein any other charged particle experiences an electric force. The strength of this field is directly proportional to the charge of the source and inversely proportional to the square of the distance from the source.
02

Understand the concept of drift velocity

In the context of an electric field, drift velocity refers to the average velocity attained by charged particles, such as electrons, due to an electric field. It depends on the electric field strength and the properties of the medium through which the particles move. Equal force balances the force exerted by the electric field, causing the charged particles to move with a constant average velocity. This is the drift velocity.
03

Understand Newton's law

Newton's second law states that the force on an object is equal to its mass times its acceleration (F=ma). In other words, a force applied to an object will cause it to accelerate, not to move at a constant velocity.
04

Link the concepts

Though it might seem contradictory at first, these concepts are compatible. In an electric field, charged particles do accelerate initially due to the force of the field (as per Newton's law). However, they also experience a counteracting force due to collisions with other particles (like atoms). The net result of these forces is a constant average velocity - the drift velocity. Thus, while force induces an acceleration, other forces come into play which balance this out, resulting in a constant velocity.

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Most popular questions from this chapter

A copper wire joins an aluminum wire whose diameter is twice that of the copper. The same current flows in both wires. The density of conduction electrons in copper is \(1.1 \times 10^{29} \mathrm{m}^{-3}\); in aluminum it's \(2.1 \times 10^{29} \mathrm{m}^{-3} .\) Compare (a) the drift speeds and (b) the current densities in each.

The National Electrical Code specifies a maximum current of \(10 \mathrm{A}\) in 16 -gauge \((1.29-\mathrm{mm} \text { -diameter })\) copper wire. What's the corresponding current density?

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