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Chapter 26: Problem 1

A charged particle moves through a region containing only a magnetic field. Under what condition will it experience no force?

Short Answer

Expert verified
A charged particle moving through a magnetic field will experience no force under the following conditions: if it is neutral (q=0), if it is at rest (v=0), or if it moves parallel or antiparallel to the magnetic field (i.e., the angle between v and B is either 0 or 180 degrees).

Step by step solution

01

Identify Relevant Principle

Make use of the Lorentz force law, which states that the force experienced by a charged particle moving in a magnetic field is given by, \( F = q(v 脳 B) \), where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the magnetic field.
02

Set Force to Zero

Set the force 'F' resulting from the equation to zero. So, we have \( 0 = q(v 脳 B) \). This sets up the condition where no force is experienced by the charged particle.
03

Determine the Condition

The right-hand side of the equation is zero when either 'q' is zero, 'v' is zero, or the angle between 'v' and 'B' is zero or 180 degrees (which makes the cross-product zero). So, there are three conditions: 1. The particle is neutral (q=0), 2. The particle is at rest (v=0), 3. The particle moves parallel or antiparallel to the magnetic field (angle between v and B is 0 or 180 degrees).

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