(a) Is it possible for the magnetic force on a charge moving...

Name: Problem 2, Chapter 11: University Physics
Uploaded: 2020-07-03T22:19:38-08:00
Duration: 2 min 7 s
Channel: Joseph Petrullo
Description: (a) Is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) Is it possible for the electric force on a charge moving in an electric field to be zero? (c) Is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?

(a) Is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) Is it possible for the electric force on a charge moving in an electric field to be zero? (c) Is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?

Key Concepts

Lorentz Force

The Lorentz force is the fundamental force experienced by a charged particle moving in electric and magnetic fields, expressed as F = q(E + v × B). It combines the effects of the electric force, which acts in the direction of the electric field, and the magnetic force, which is perpendicular both to the velocity of the particle and the magnetic field.

Magnetic Force Conditions

The magnetic force, given by q(v × B), becomes zero when the velocity vector is parallel or antiparallel to the magnetic field, since the sine of the angle between them is zero, or when the particle is at rest. This condition implies that despite the presence of a magnetic field and a moving particle, the configuration of motion relative to the field can nullify the magnetic force.

Electric Force Characteristics

The electric force acting on a charged particle is given by F = qE. Unlike the magnetic force, it is not dependent on the particle's velocity but solely on the magnitude and direction of the electric field and the charge. Therefore, in a nonzero electric field acting on a nonzero charge, the electric force is inherently nonzero unless the charge is zero.

Combined Field Cancellation

When a charged particle moves through both electric and magnetic fields, the net force is the sum of the electric and magnetic contributions, F = qE + q(v × B). It is possible for these forces to cancel each other out if the electric field is precisely adjusted to counterbalance the magnetic force. This principle is applied in devices like velocity selectors, where the cancellation condition allows particles with specific velocities to pass through undeflected.

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