How to determine Lorentz force

How to determine Lorentz force

Action of magnetic field on the conductor with current means that magnetic field influences moving electric charges. Force operating on moving charged particle from magnetic field is called Lorentz force in honor of the Dutch physicist H. Lorentz


1. Force is size vector, means it is possible to define its numerical value (module) and the direction (vector). The module of the Lorentz force (Fl) is equal to the relation of the module of force of F operating on the site of the conductor with current ∆l length to number N of the charged particles ordered moving on this site of the conductor: Fl = F/N (formula 1). Owing to, simple physical transformations, force of F can be presented in the form: F = q*n*v*S*l*B*sina (formula 2) where q is a charge of a moving particle, n is concentration of particles on the site of the conductor, v is the speed of a particle, S is the cross-sectional area of the site of the conductor, l is length of the site of the conductor, B is magnetic induction, sina is a sine of the angle between vectors of speed and induction. And to transform quantity of moving particles to a look: N=n*S*l (formula 3). Substitute formulas 2 and 3 in formula 1, reduce sizes n, S, l, the settlement formula for Lorentz force turns out: Fl = q*v*B*sin a. Means, to the solution of simple tasks on finding of Lorentz force, determine the following physical quantities in a task condition: a charge of a moving particle, its speed, induction of magnetic field in which the particle moves, both a corner between the speed and induction.

2. Before the solution of a task make sure that all sizes are measured in units corresponding each other or an international system. For receiving in the answer of newtons (N - force unit), the charge has to be measured in pendants (K), speed – in meters for a second (m/s), induction – in teslas (T), a sine an alpha – not measured number. Example 1. In magnetic field which induction 49 mtl, moves charged particle 1 nkl, with a speed of 1 m/s. Vectors of speed and magnetic induction of a vzaimoperpendikulyarna. Decision. B = 49 mtl = 0.049 T, q =1 nkl = 10 ^ (-9) C, v = 1 m/s, sin a = 1, Fl =? Fl = q*v*B*sin a = 0.049 T * 10 ^ (-9) C * 1 m/s * 1 =49 * 10 ^ (12).

3. The direction of Lorentz force is defined by the rule of the left hand. For its application present the following interposition of three vectors perpendicular each other. Arrange the left hand so that the vector of magnetic induction entered a palm, four fingers were directed towards the movement positive (against the movement negative) particles, then the thumb unbent by 90 degrees will specify the direction of Lorentz force of cm the drawing). Lorentz force in television tubes of monitors, TVs is used.

Author: «MirrorInfo» Dream Team