# An electron, the initial velocity of which is 1 Mm / s, flew into a uniform electric field with a strength of 100 V / m

**An electron, the initial velocity of which is 1 Mm / s, flew into a uniform electric field with a strength of 100 V / m so that the initial velocity of the electron is opposite to the field strength. Find the electron energy in a time equal to 10 ns.**

m = 9.1 * 10 ^ -31 kg.

q = 1.6 * 10 ^ -19 Cl.

V0 = 1 Mm / s = 10 ^ 6 m / s.

E = 100 V / m.

t = 10 ns = 10 * 10 ^ -9 s.

Ek -?

Since the electron has a negative electric charge and moves in the opposite direction to the direction of the field strength, the electrostatic force F will act on it, which will accelerate it.

We express the acceleration of an electron a by Newton’s 2 law: a = F / m.

F = q * E.

a = q * E / m.

Let us write acceleration a according to its definition: a = (V – V0) / t.

q * E / m = (V – V0) / t.

V – V0 = q * E * t / m.

V = V0 + q * E * t / m.

V = 10 ^ 6 m / s + 1.6 * 10 ^ -19 C * 100 V / m * 10 * 10 ^ -9 s / 9.1 * 10 ^ -31 kg = 1.175 * 10 ^ 6 m / s …

Ek = m * V ^ 2/2.

Ek = 9.1 * 10 ^ -31 kg * (1.175 * 10 ^ 6 m / s) ^ 2/2 = 6.3 * 10 ^ -19 J.

Answer: the electron will have energy Ek = 6.3 * 10 ^ -19 J.