The electric field is defined to be in the direction of the...

Name: Problem 4, Chapter 18: Essential College Physics
Uploaded: 2021-05-30T13:24:58-08:00
Duration: 1 min 31 s
Channel: Ajay Singhal
Description: The electric field is defined to be in the direction of the electric force on a positively charged particle. Why isn't the magnetic field defined to be in the direction of the magnetic force on a positively charged particle?

The electric field is defined to be in the direction of the electric force on a positively charged particle. Why isn't the magnetic field defined to be in the direction of the magnetic force on a positively charged particle?

Key Concepts

Test Charge Convention

In the context of electric fields, the convention uses a positive test charge to define the field direction, because its response to the field is unambiguous when at rest. This approach cannot be similarly applied to magnetic fields since a test charge must have a velocity for the magnetic force to act, meaning that the observed force also depends on the chosen velocity, thereby preventing a unique definition of the magnetic field based on force direction.

Electric Field

The electric field is conceptualized as the force per unit positive charge experienced by a stationary test charge. This provides a clear, unambiguous direction and magnitude for the electric field, independent of any additional variables such as velocity, making it a straightforward field to define and measure.

Magnetic Field

The magnetic field, unlike the electric field, exerts a force on moving charges that is determined by the cross product of the charge's velocity and the magnetic field (v × B). Because the force depends on both the direction and magnitude of the velocity as well as that of the magnetic field, it does not provide a unique or direct definition of the field's direction solely based on the force experienced.

Lorentz Force

The combined force experienced by a charged particle moving in electric and magnetic fields is given by the Lorentz force equation (F = q(E + v × B)). This equation highlights that while the electric component of the force can be directly associated with the direction of the electric field, the magnetic component is inherently velocity dependent, complicating any attempt to define the magnetic field by the force alone.

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