Calculating the electric field in an electron gun

[sylvarant]

Homework Statement

I have given a cathode and a anode being -1000V and 1000V each respectivily
I know the distance between the cathode and anode its 3mm
What I have to do now is calculate the electric field between the cathode and anode and use that to find the acceleration of an electron in that electric field.

Homework Equations

well the acceleration = F/me with F being qe*E
now qe=-1.60e-19;
and me=9.11e-31;

The Attempt at a Solution

All I need now is the E I tried using the following Vanode -Vcathode = Integral(E(r)dr)
but I have no idea how to form this E as I have no given charge :(

 

[Doc Al]

You don't need to know the charge to find the E field. Hint: Assume that the E field is uniform between cathode and anode.

 

[sylvarant]

You don't need to know the charge to find the E field. Hint: Assume that the E field is uniform between cathode and anode.

Well integrating a constant would give a result of the form
E*(0.003)-E*(0) = Vanode-Vcathode
so E then is 2000/0.003 = giving a whopping 6.667e5
and making my electron accelerate at a speed of -1.15e17
Is that even possible ?

 

[Doc Al]

Why not? Electrons are pretty tiny. (That's an acceleration, not a speed.)

 

[sylvarant]

Why not? Electrons are pretty tiny. (That's an acceleration, not a speed.)

You're correct :)

now I have to calculate the speed after those 3mm and the time it takes to do so

for speed I use v = sqrt(v0+2a(0.003)) but as a is negative it results in a complex number so I just calculated it for -a and then reversed the sign at the end.
Is this a correct approach ? the text hints at calculating the time first but you'd need the velocity for that

 

[Doc Al]

for speed I use v = sqrt(v0+2a(0.003)) but as a is negative it results in a complex number so I just calculated it for -a and then reversed the sign at the end.

Whether the acceleration is negative or positive just depends on your sign convention. But the acceleration and the distance will have the same sign, so their product will always be positive. (If the electron accelerates to the right, it also moves to the right.)

Is this a correct approach ? the text hints at calculating the time first but you'd need the velocity for that

It's a fine approach. But you could certainly calculate the time first (using a different kinematic formula) without needing the velocity.

 

[sylvarant]

Ok, thanks

 

[unscientific]

Potential difference = 2000V,


E = V/d = 2000/(3*10^-3) N/C