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.