Magnetic Field due to Moving Charges

The presence of a charge produces an electric field. If the charge moves, it also creates a magnetic field.

If the positive charge moves with a constant velocity, the electric field and the magnetic field at any point are directly proportional to the charge magnitude and inversely proportional to the square of the distance between the source and the field point.

However, unlike the electric field, the direction of the magnetic field is perpendicular to the plane containing the unit vector along the line joining the point P, and the charge velocity.

For the moving charge, the magnetic field at point P is also proportional to the cross product of its velocity and the unit vector.

Adding the proportionality constant as the permeability of free space, the final expression for the magnetic field is obtained.

The expression states that the field is maximum in the plane perpendicular to the charge velocity.

Conventionally, if the thumb gives the velocity direction, then the curled fingers show the magnetic field direction. For a negative charge, the field direction reverses.