A electron with an initial speed of 500,000 m/s is brought to rest by an electric field. what was the potential difference that stopped electron?
We are given the initial velocity of the electron:
vi =500000 m/s
To answer the given questions, let's look at the relation between speed and required quantities.
a) The potential is given by the following formula:
V= q/U
The speed of the electron at the end is:
v f =0
As the electron has a negative charge and slows down while travelling, we can conclude that its potential is greater at the beginning. Thus, the electron moves towards the region of lower potential.
b) We will get a potential difference from the law of energy conservation:
Ki+Ui= Kf+Uf
m⋅v i2/2 +q⋅Vi= m⋅v f2/2 +q⋅V f
q⋅V i −q⋅Vf=m⋅v 2f − 2m⋅v i2/2
−q⋅(V f −V i )=m⋅v f2/2 +q⋅V f
ΔV=- m⋅v 2f − 2m⋅v i2/2/q -(1)
An electron has the following charge value:
q=e − =−1.602⋅10 −19 C
The speed of the electron at the end is:
v f =0
The mass of the electron is:
m e =9.109⋅10 −31 kg
Equation (1) gives us the potential difference that stopped the electron:
ΔV=− e − 0− 2m e ⋅v i2 = 2⋅(−1.602⋅10 −19 )9.109⋅10 −31 ⋅(500000) 2
ΔV=−0.71 V
To learn more about law of energy:
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