At what distance in a uniform electric field with a strength of 15 kN / C does an electron accelerate

At what distance in a uniform electric field with a strength of 15 kN / C does an electron accelerate from a state of rest to a speed of 1.6 * 10 ^ 7 m / s?

Data: E – field strength (E = 15 kN / Kl = 15 * 10 ^ 3 N / Kl); V is the considered speed of the electron (V = 1.6 * 10 ^ 7 m / s).

Const: me – electron mass (me = 9.11 * 10 ^ -31 kg); qe is the electron charge (qe = -1.6 * 10 ^ -19 C).

1) Field work:

a) A = E * qe * dx, whence we express: dx = A / (E * qe).

b) A = ΔEk = me * V ^ 2/2.

2) Distance: dx = A / (E * qe) = (me * V ^ 2/2) / (E * qe) = me * V ^ 2 / (2 * E * qe) = 9.11 * 10 ^ -31 * (1.6 * 10 ^ 7) ^ 2 / (2 * 15 * 10 ^ 3 * 1.6 * 10 ^ -19) ≈ 0.0486 m = 48.6 mm.

Answer: The electron was accelerated at a distance of 48.6 mm.