Question

Please see attached for question about an electron accelerating through a uniform electric field.

Answer 1

Basing from the formula E=V/d, where E is the lectric field strength, V the voltage and d the distance between plates.
First, let us work in terms of m/s. For that , you have to convert the 4cm to 0.04m.
You have E and d. Making V, subject of the formula, you get 90000*0.04=3600V.
Voltage is the energy given to each charge or electron and the formula for this is V=W/Q, where W is energy and Q is charge. A charge of an electron is 1.6*10^-19C. Making W subject of the formula, we shall have W= 3600*1.6*10^-19= 5.76*10^-16J.
From this energy, you consider it as iinetic energy, therefore we shift this value to such formula of Ke=mv^2/2, where v is the speed, m is the mass and Ke is kinetic energy. The mass of an electron is 9.11*10^-31kg. Making v subject of the formula you get v=sqrt(ke*2/m) or sqrt[5.76*10^-16*2/(9.11*10^-31)]=3.56*10^7m/s.
Converting this into km/s, you have to divide by 1000, having then 3.56*10^4km/s.

Answer 2

I have to go back a an double check to make sure I understand, but you are both the only answer and the best answer so thanks and here is a medal.

Answer 3

If you work out the final speed of the electron using non relativistic mechanics you get an answer that is a significant fraction of the speed of light.
That made me think that you really need to use the relativistic expression for the electron energy to calculate its velocity.
The correct (relativistic) answer is significantly lower than the non relativistic prediction.