An electron is accelerated horizontally from rest by a potential difference of 2

Question

An electron is accelerated horizontally from rest by a potential difference of 2200 V . It then passes between two horizontal plates 6.5cm long and 1.3cm apart that have a potential difference of 240 V (refer to (Figure 1)).

Part A

At what angle will the electron be traveling after it passes between the plates?

Express your answer to two significant figures and include the appropriate units.

nothing

An electron is accelerated horizontally from rest by a potential difference of 2200 V . It then passes between two horizontal plates 6.5cm long and 1.3cm apart that have a potential difference of 240 V (refer to (Figure 1)).

An electron is accelerated horizontally from rest by a potential difference of 2200 V . It then passes between two horizontal plates 6.5cm long and 1.3cm apart that have a potential difference of 240 V (refer to (Figure 1)).

Part A

At what angle will the electron be traveling after it passes between the plates?

Express your answer to two significant figures and include the appropriate units.

=

nothing

    

Explanation / Answer

Potential difference between the plates is given as -

V = 240 V for diflection

And potential difference for acceleration is -

V = 2200 V

Now -  

W = eV = 1.6*10^-19*2200 = 3.52 x 10^-16 Joule

We know that -

delta Ke = Kef - Kei = Kef = (1/2)*m*u^2

So -

1/2*m*u^2 = 3.52 x 10^-16 J

=> u^2 = 2 x 3.52 x 10^-16/m
= 7.04 x 10^-16/m
=> u = root(7.04 x 10^-16/(9.11x10^-31))
= root(7.73 x 10^14)
=> u = 2.78 x 10^7 m/s

constant speed through the plates so takes
the plate length 6.5 cm
u = x/t

=> t = x/u = 0.065/ (2.78 x 10^7)

=> t = 2.34 x 10^-9 seconds

So, this is the time it spends in the plates so that will be used to find the deflection

When it passes through the plates..
F = Ee = (V/d)*e = eV/d
d = 1.3 cm = 0.013 m
a = F/m = eV/(m*d)

Vy = at
= eV/(m*d)* (2.34*10^-9)
= (1.6*10^-19*240/(9.11*10^-31*0.013))*(2.34*10^-9)
= 7587 x 10^3 m/s

= 7.59 x 10^6 m/s

Therefore, the angle the electron will travel after it passes between the plates = arc tan(Vy/Vx)

= arc tan(7.59x10^6 /2.78 x 10^7)

= arc tan( 0.273) = 15.3 deg. (Answer).

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