Magnetic Force

Authored by TheAstroChemist (This page was claimed first by TheAstroChemist - check the page history)

The Main Idea

We know so far that an electric field will act on a charged particle in a specific manner. In effect, a charged particle in the vicinity of any electric field will undergo a force based upon the magnitude and sign of the charged particle. This electric field is generated regardless of whether the charge is stationary or moving.

In the case of a moving charged particle, it is also known to generate a magnetic field. Whenever any charge maintains some velocity, it will necessarily produce a magnetic field. This applies whether you're dealing with a single point charge or a charge distribution such as a uniformly charged rod or disk.

Now, you might reasonably guess that because an electric field brings about a force on a charged particle, then so too a magnetic field should bring about a force on a particle. However, in order for a magnetic field to implement this force, the particle of interest must be moving. These two forces (electric and magnetic) can be combined to be known as the Lorentz Force, but that will be covered in further detail later. For now, we shall only focus on the specifics of the magnetic force and ignore the effects of an electric field on our system of interest.

A Mathematical Model

Suppose we have a moving particle. It has a charge given by q. It has a velocity given by [math]\displaystyle{ {\vec{v}} }[/math]. It is also in the presence of a magnetic field given by [math]\displaystyle{ {\vec{B}} }[/math]. The force that this particle will experience is given by the following:

[math]\displaystyle{ {\vec{F} = q\vec{v}\times\vec{B}} }[/math]

Therefore, for a particle at rest ([math]\displaystyle{ {\vec{v} = \vec{0}} }[/math]), the particle will experience a force given by [math]\displaystyle{ {\vec{F} = \vec{0}} }[/math].

The units? Force is in Newtons (N), magnetic field is in Tesla (T), and velocity is in meters per second (m/s).

A Computational Model

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