Early black-and-white television sets used an electron beam to draw a picture on the screen. the electrons in the beam were accelerated by a voltage of 3.0 kv m kv; the beam was then steered to different points on the screen by coils of wire that produced a magnetic field of up to 0.67t

a

what is the speed of electrons in the beam?

b

what acceleration do they experience due to the magnetic field, assuming that it is perpendicular to their path? what is this acceleration in units of g image for early black-and-white television sets used an electron beam to draw a picture on the screen. the electrons in?

c

if the electrons were to complete a full circular orbit, what would be the radius?

A)

Assuming the electrons start from rest, their final kinetic energy is equal to the electric potential energy lost while moving through the potential difference :

where

is the mass of each electron

v is the final speed of the electrons

is the charge of the electrons

is the potential difference

Solving the equation for v, the speed, we find

B) Centripetal acceleration, , in units of g: 3898 g

When the electrons cross the region of the magnetic field, they experience a magnetic force which is perpendicular to their trajectory: therefore they start moving in a circular motion. The acceleration they experience is not tangential, but centripetal, and it is given by

where v is the speed and r the radius of the trajectory.

We can equate the magnetic force exerted on the electrons to the centripetal force:

and isolate to find the centripetal acceleration:

And since , the acceleration can be rewritten as

c)  

The radius of the circular trajectory can be found by using the formula for the centripetal acceleration:

Solvign for r, we find

+15-35=-20

going in opposite directions