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8 RA FS OF POSITIVE ELECTRICITY

to consider the theory of the deflection of a moving electrified

by a magnetic field. The force acting on the moving

particle is at right angles to the magnetic force, at right angles

to the direction of motion of the particle and equal to

where H is the magnetic force at the particle, ^ the

velocity of the particle, $ the angle between H and v, and e

the charge on the particle. Since this force is always at right

to the direction of motion of the particle it will not alter

the of the particle but only the direction in which it is

moving. Suppose that the particle is originally projected with

a velocity v parallel to the axis of x, and that it is moving in

a field arranged so as to be very approximately in

the direction of the axis of ^, the direction of the force along

the particle will be parallel to the axis of y and this will be

the direction in which it will be deflected. If y is the deflec-

in this direction at the time /, m the mass of the particle,

H the magnetic force parallel to the axis of Z, and e the

charge carried by the particle, the equation of motion of the

particle is

d²y _w dx
~~d? ⁼ ~dt*

Integrating: this equation we get

fH ""jT ^==r

if the origin of co-ordinates is taken at the point of projection;

for since the particle was projected parallel to the axis of JT,

•j£**o when x^o. Now if the deflection of the particle is small

ft will, neglecting the squares of small quantities, be equal to

^1/9 ' & ^to ^v ~dx' *kk ^assumPtion equation (i) may be

written



	8 RA FS OF POSITIVE ELECTRICITY to consider the theory of the deflection of a moving electrified by a magnetic field. The force acting on the moving particle is at right angles to the magnetic force, at right angles to the direction of motion of the particle and equal to where H is the magnetic force at the particle, ^ the velocity of the particle, $ the angle between H and v, and e the charge on the particle. Since this force is always at right to the direction of motion of the particle it will not alter the of the particle but only the direction in which it is moving. Suppose that the particle is originally projected with a velocity v parallel to the axis of x, and that it is moving in a field arranged so as to be very approximately in the direction of the axis of ^, the direction of the force along the particle will be parallel to the axis of y and this will be the direction in which it will be deflected. If y is the deflec- in this direction at the time /, m the mass of the particle, H the magnetic force parallel to the axis of Z, and e the charge carried by the particle, the equation of motion of the particle is d²y _w dx ~~d? ⁼ ~dt* Integrating: this equation we get fH ""jT ^==r

	if the origin of co-ordinates is taken at the point of projection; for since the particle was projected parallel to the axis of JT, dy •j£o when *x^o.* Now if the deflection of the particle is small dx ft will, neglecting the squares of small quantities, be equal to

	^1/9 ' & ^to ^v ~dx' *kk ^assumPtion equation (i) may be written