Lorentz Forces

Lorentz Forces ... Lorentz Force and the Railgun In 1878 Lorentz, formulated his theory ...
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In 1878 Lorentz, formulated his theory of electromagnetism, which became the theoretical basis for railguns. This most famous formulation, known as the Lorentz Force Law, predicts the force resulting from an interaction between a current source (i-), a uniform magnetic field (B), and a moving (v) charge (q). The equation

expresses this mathematically. Note that the force is the result of the cross product of the moving charge and the magnetic field. This means that the direction of the force is perpendicular to that of both the moving charge and the magnetic field, it is upon this that the railgun's operation hinges.

In its simplest form, a rail gun (Fig.1) consists of two parallel rails joined together by a movable armature. This armature acts as a conductor between the two rails, completing the electrical circuit. When current flows in the circuit, a circular spiral magnetic field is created around each of the parallel rails.
Notice that at the center of aperture of the two rails, the magnetic field lines are vertically up or down. This creates the uniform magnetic field (B) of the Lorentz equation. In addition, as the current flows through the armature it causes the armature to act akin to a moving charge, with. Consequently, an adapted version of the Lorentz equation for railguns is given as follows with dw being the aperture between the rails.

Another equivalent expression that is commonly used is:

where L1 is the inductance per unit length of the railgun. Both equations show that the force produced is proportional to the square of the current (remembering that the current also generates the magnetic field intensity (B)). Therefore, the majority of developmental efforts, including those in the present, have concentrated increasing the current. However, the number of problems that arise also seems to be proportional to the current. These problems pose an effective limit on the amount of current until they can be solved, after which more current can be used until another problem arises. The task of solving these problems has been the occupation of railgun scientists in the past centuries.