Understanding the Concepts

* Magnetic Force on a Charged Particle: A charged particle moving in a magnetic field experiences a force. The magnitude of this force is given by:

F = qvB sin θ

where:

* F is the magnetic force

* q is the charge of the particle

* v is the velocity of the particle

* B is the magnetic field strength

* θ is the angle between the velocity and the magnetic field

* Alpha Particle: An alpha particle is the nucleus of a helium atom, consisting of two protons and two neutrons. It has a charge of +2e (twice the elementary charge).

Calculations

1. Identify the knowns:

* F = 3.84 x 10^-14 N (magnetic force)

* B = 0.2 Wb/m² (magnetic field strength)

* q = +2e = 2 * 1.602 x 10^-19 C (charge of an alpha particle)

* θ = 90° (velocity is perpendicular to the magnetic field)

2. Use the magnetic force equation:

F = qvB sin θ

Since sin 90° = 1, the equation simplifies to:

F = qvB

3. Solve for the velocity (v):

v = F / (qB)

v = (3.84 x 10^-14 N) / (2 * 1.602 x 10^-19 C * 0.2 Wb/m²)

v ≈ 5.99 x 10^5 m/s

Answer: The speed of the alpha particle is approximately 5.99 x 10^5 m/s.