29.1:
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.
29.1:
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, µo, 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”.
Suggested Reading
- Young, H.D and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. Pp. 923–925.