240 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



Action of the magnetic field on a moving charged particle. 

 Figure 171 represents a charged particle moving upwards through 

 a magnetic field, the lines of force of which are perpendicular to 

 the plane of the figure. The moving particle is equivalent to an 

 electric current, and the side force F is equal to qvh where q 

 is the charge on the particle in abcoulombs, v is its velocity in 

 centimeters per second, and h is the intensity of the magnetic 

 field in gausses. Therefore the acceleration of the particle in the 

 direction of F is qvhjm. The force F is continuously at right 

 angles to v so that the particle describes a circular orbit. But 

 the acceleration of a particle moving in a circular orbit is i^jr, 

 and the relation between the radius of the circle r t the semi- 

 chord D, and the versed sine d is 



D 2 



r= ^d 

 Therefore we have 



qvh 



whence 



m hi? 



-- ( iv) 



q 2dv 



Determination of velocity of particles. Reduced to the simplest 

 terms, the method of determining velocity may be described as 

 follows : An electrical field e in the plane of the paper, Fig. 

 1 70, and a magnetic field h at right angles to the- plane of the 

 paper in Fig. 170 are adjusted so that together they produce no 

 deflection of the particles which are being studied. When this 

 condition is realized, the force qe with which the electrical field 

 acts on the moving particles is equal and opposite to the force 

 qvh with which the magnetic field acts on the moving particles, 

 so that, disregarding sign, we have 



qe = qvh 

 or 



e 



M 



