Field Due to Moving Charge Particles
Electric and magnetic fields are generated by a moving charge according to Maxwell's equations. The electric field (E) due to a moving charge can be described by Coulomb's law, which states that the electric force (F) between two point charges is proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them:
where k is the Coulomb constant. The electric field due to a single moving charge can be found by considering the force that it would exert on a test charge (q0) placed at a given location:
The magnetic field (B) due to a moving charge is given by the Biot-Savart law, which states that the magnetic field (dB) at a point due to a small element of current (dl) is proportional to the cross product of the current element and the displacement (r) from the element to the point:
where μ0 is the vacuum permeability. The magnetic field due to a moving charge can be found by integrating the contribution from each element of the current along the trajectory of the charge.
In the case of a uniformly moving point charge, the electric and magnetic fields are perpendicular to each other and to the direction of motion of the charge. These fields change in time and space as the charge moves, leading to the emission of electromagnetic waves, such as light or radio waves.