Question

Older televisions display a picture using a device called a cathode ray tube, where electrons are emitted at high speed and collide with a phosphorescent surface, causing light to be emitted. The paths of the electrons are altered by magnetic fields. Consider one such electron that is emitted with an initial velocity of 1.85 107 m/s in the horizontal direction when magnetic forces deflect the electron with a vertically upward acceleration of 5.45 1015 m/s2. The phosphorescent screen is a horizontal distance of 5.6 cm away from the point where the electron is emitted. (a) How much time does the electron take to travel from the emission point to the screen? (b) How far does the electron travel vertically before it hits the screen?

Answer 1

Answer:

a)  t = 3.027 10⁻⁹ s ,  b)   y = 2.25 10⁻² m

Explanation:

We can solve this problem using the kinematic relations

a) as on the x-axis there is no relationship

          vₓ = x / t

          t = x / vₓ

We reduce the magnitudes to the SI system

          x = 5.6 cm (1m / 100 vm) = 0.056 m

we calculate

          t = 0.056 / 1.85 10⁷

          t = 3.027 10⁻⁹ s

b) the time is the same for the two movements, on the y axis

         y = v₀t + ½ a t²

         

as the beam leaves horizontal there is no initial vertical velocity

         y = ½ a t²

         

let's calculate

         y = ½  5.45 10¹⁵ (3.027 10⁻⁹)²

         y = 2.25 10⁻² m