Electric Current

1. Electric Current Electric current is a flow of electric charge or the rate of flow of electric charge. This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both. In a real wire, the current is defined as the charge per unit time passing through a cross section of the wire: If the current in a wire is due to charges q moving with a mean velocity v, and the number of charges per unit volume is n, then

2. volume current density Local conservation of charge continuity equation (local conservation of charge)

3. Magnetostatics Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field B is defined in terms of force on moving charge in the Lorentz force law: In the presence of both electric and magnetic fields, the force acting on charge Q is: Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole. The SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law F = qvB to be composed of (Newton x second)/(Coulomb x meter). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss). The direction of the Lorentz force is given by the right hand rule:

4. We see from the Lorentz equation that the force exerted by the magnetic field on a particle is always normal to its velocity. Therefore, the magnetic field cannot increase the energy of the particle, and so energy is conserved during movement in a purely magnetic, time-independent field. Magnetic forces do not work Force on a current-carrying wire

5. Example: Helical or circular motion of charge in uniform magnetic field If cyclotron formula