§ 7 The motion of charged particles in a magnetic field

 

Lorentz force is always perpendicular to the velocity of motion of a charged particle, so it only changes the direction of the velocity without changing its value. Consequently, the Lorentz force does not do work

 

 because

 

ie static magnetic field does not do work on a moving charged particle in it and the kinetic energy of the particle in a magnetic field does not change.

1. ie static magnetic field does not do work on a moving charged particle in it and the kinetic energy of the particle in a magnetic field does not change.  parallel to the vector , then sinα = 0°, FL = 0, and the particle moves in a rectilinearly inertia evenly.

FL = 0;                  S=vt.

 

2.  If the particle enters the magnetic field and the velocity vector  is perpendicular to the vector , thensinα = 90°, FL = qvB. Because Force Lorenz  perpendicular to the velocity , thenForce Lorenz is the centripetal force, and the motion of the particle will be in a circle, the center of which coincides with one of lines of force vector

mv^2/R=qvB

 

 

 

 

.

  1. A charged particle enters the magnetic field at an arbitrary angle to the field lines vector : . A particle moves along a helix (spiral). In this case, the velocity of the particle can be decomposed into two components  and , and spiraling considered as the sum of two movements: the movement in a circle at a speed of and linear motion along a force line  with speed .

F L   .

Determine the radius and pitch of helix

equation

.

The period of the spiral :

 

Pitch of helix: 

 

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