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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
This does not contradict Newton's assertion that force results in acceleration because there are other forces involved. The charge initially does accelerate under the influence of the electric field. However, it also encounters a drag force from the medium, which grows with velocity until it equals the electric force. At this point, the net force on the charge is zero, meaning it doesn't accelerate any further and moves with a constant drift velocity.

Step by step solution

01

Identify the Laws at Play

To answer this question, one needs to understand two concepts: the principle of an electric field producing a constant drift velocity and Newton's second law of motion. Newton's second law states that force results in acceleration, not constant velocity. However, in electric fields, we generally observe that a constant field (a consistent force) produces a constant drift velocity, which seems contradictory to Newton's law.
02

Distinguish Different Forces

We need to take into account that the charged particle experiences another force in addition to the electric force - namely, the frictional force or 'drag' due to the medium (the conducting material). This resisting force increases with the velocity of the charge until it equals the electric force, at which point the net force on the charge becomes zero.
03

Apply Principles of Equilibrium

Once the net force is zero, the charge does not accelerate any further according to Newton's First Law of Motion (an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force). This equilibrium point defines the constant drift velocity, and from then, the charge moves with this constant velocity, not accelerating, hence not contradicting Newton's laws.

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