Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.

Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line joining the source to the field point. The magnitude of the magnetic field is proportional to the particle’s speed, and it also depends on the sine of the angle; the velocity vector subtends with the line joining the source and the field point (Equation1).

Considering a unit vector along a distance r to a field point, the equation for the magnetic field at field point P can be expressed as the cross-product of the velocity vector and the unit vector, as shown in Equation 2. 

The constant, µ_o, is the permeability of free space, and its value is 4π x 10⁻⁷ T·m·A⁻¹.

The unit of the magnetic field is the Tesla, named after Nikola Tesla, and is expressed as “T”.