Electric field needed to accelerate an electron

[rsminsmith]

Homework Statement

The electron gun in a television tube is used to accelerate electrons (mass of 9.10939 X 10 ^ -31, and charge of -1.60218 X 10 ^ -19) from rest to 2 X 10 ^ 7 m/s within a distance of 7.4 cm.
What electric field is required? Answer in units of N/C

Homework Equations

F_e = F_k
F_e = E * Q
F_k = m * a
a = (V ^ 2 * V_0 ^ 2) / 2d

The Attempt at a Solution

I set E * Q = m * a. The only unknown here is the electric field, which is what I'm trying to find, and acceleration. Since we are given a final velocity (2 X 10 ^ 7 m/s), an initial velocity (0 m/s, rest), and a distance (7.4 cm, or .074 m), i plugged in the acceleration equation, so the equation is now E = (m * ((V ^ 2 * V_0 ^ 2) / 2d)) / Q.

Plugging in I find that the acceleration is 2.7027 X 10 ^ 15 m/s^2 (roughly). I multiply that by the mass to get 2.462 X 10^-15 N (roughly), and divide by the electric charge to get -15366.54519 N/C. However, the system is not taking the answer, and I wanted to see if someone could take a look at it to see if I'm doing it right.

 

[ehild]

This equation is wrong. "a = (V ^ 2 * V_0 ^ 2) / 2d" But it should be a typo. Your calculation is correct, but the negative sign is not needed.

ehild