What speed can be imparted to a particle with a mass m = 2 • 10 ^ (- 8) kg and an electric charge

What speed can be imparted to a particle with a mass m = 2 • 10 ^ (- 8) kg and an electric charge q = 2 • 10 ^ (- 12) C, which is at rest, accelerating the potential difference at U = 100 V?

m = 2 * 10 ^ -8 kg.

q = 2 * 10 ^ -12 Cl.

V0 = 0 m / s.

U = 100 V.

V -?

When a charged particle moves, the electric field performs work A, the value of which is expressed by the formula: A = q * U, where q is the magnitude of the particle’s charge, U is the potential difference that the particle has passed.

According to the law of conservation of energy, the work of the electric field A is equal to the change in the kinetic energy of a charged particle ΔEk: A = ΔEk.

The kinetic energy of the body Ek is determined by the formula: Ek = m * V ^ 2/2.

ΔEk = m * V ^ 2/2 – m * V0 ^ 2/2.

Since the initial velocity of the particle is V0 = 0 m / s, the change in kinetic energy will be ΔEk = m * V ^ 2/2.

q * U = m * V ^ 2/2.

V ^ 2 = 2 * q * U / m.

V = √ (2 * q * U / m).

V = √ (2 * 2 * 10 ^ -12 Cl * 100 V / 2 * 10 ^ -8 kg) = 0.15 m / s.

Answer: a charged particle will acquire a velocity of V = 0.15 m / s.