Magnetic Field

This page discusses the general properties of magnetic fields

Electric Field

Magnetic Field is a field created by a moving electric charge. It is measured in units of Teslas (T) and has a direction, making it a vector quantity. The magnetic field created by a moving charge exists at all points in space and exerts a force on other charged objects. The field can be drawn as an arrow with tail at the observation location pointing in the direction of the field. The magnetic field obeys superposition, so the net magnetic field at a point in space can be determined by summing all the individual fields present at that location.

Dependence on frame of reference

Because the magnetic field relies on the velocity of a particle, it can vary with frame of reference. That is to say, one observer could observe a magnetic field while another does not observe a field due to the relative velocity of the particle. Consider a moving proton, a moving compass, and a stationary compass. The proton and moving compass are moving with identical velocity, so to the compass, the proton appears to be stationary ([math]\displaystyle{ \vec{v} = 0 }[/math]), so the observed magnetic field is is also 0. The stationary compass, however, observes a certain velocity so a magnetic field is observed.

Magnetic field due to a single charged particle

The magnetic field [math]\displaystyle{ \vec{B} }[/math] created by a single charged particle is given by the equation [math]\displaystyle{ \vec{B} =\frac{\mu_0}{4\pi} \frac{(q\vec{v} \times \hat{r})}{|r^2|} }[/math], where [math]\displaystyle{ \frac{\mu_0}{4\pi} }[/math] is a fundamental constant equal to [math]\displaystyle{ 1 \times 10^-7 T }[/math], q is the charge of the particle, [math]\displaystyle{ \vec{v} }[/math] is the velocity of the particle, and [math]\displaystyle{ \vec{r} }[/math] is the vector that points from source to observation location. You may notice that this equation involves a cross product.