Express final answers in terms of v1, Vb, L, d and any necessary physical consta

Question

Express final answers in terms of v1, Vb, L, d and any necessary physical constants in simplest algebraic form.

A) Find an expression for the magnitude of the acceleration of the electron while its between the plates.  What is the the direction of the acceleration of the electron while it is between the plates?

a=?

direction of a=?

B) What is the electron's horizontal velocity component at the moment that it leaves the region between the plates?

vfx=?

C) What is the electron's vertical velocity component at the moment that it leaves the region between the plates?  Is it towards the top of bottom of the page (i.e.; upwards or downward)?

Vfy=?

direction of Vfy=?

Explanation / Answer

v = velocity of electron = 3.3 x 10^7 m/s

d = distance between capacitor plates = 0.024 m

V = voltage across plates = 156 V

e = charge of electron = -1.602 x 10^-19 C

m = mass of electron = 9.11 x 10^-31kg

A)

The electrostatic force one a charge particle is calculate by:

Force = (Electric Field) x (electron charge)

= E*e

But what is the electric field (E) between the plates? For a parallel plate capacitor it is:

E = V / d

So now the force on the electron is:

F = E*e = (V / d)*e

= (156V / 0.024m) * (-1.602 x 10^-19C)

= 1.04 x 10^-15 Newtons

The electrostatic force on the electron is -1.04 x 10^-15 Newtons.

B)

By Newton's 2nd Law:

Force = mass x acceleration = F = m*a

Solving for acceleration:

a = F / m

= -1.04x10^-15N / 9.11x10^-31kg

= -1.14 x 10^15 m/s^2

The acceleration of the electron is 1.14 x 10^15 m/s^2 DOWN.

The velocity of the electron in the x-direction does not affect the acceleration as there is NO force in the x-direction (i.e. the right/left direction).

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