Real-Life Examples of the Lorentz Force

📚 Quick Study Guide

• ⚡ The Lorentz force describes the force exerted on a charged particle moving in electric and magnetic fields.
• ✏️ The formula for the Lorentz force is: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$, where:
  • $q$ is the charge of the particle,
  • $\vec{E}$ is the electric field,
  • $\vec{v}$ is the velocity of the particle,
  • $\vec{B}$ is the magnetic field.
• 🧭 The direction of the magnetic force component is perpendicular to both the velocity of the charge and the magnetic field (right-hand rule).
• 📺 Applications include mass spectrometers, cyclotrons, and magnetic confinement in fusion reactors.

Practice Quiz

1. A proton is moving with velocity $\vec{v} = (2 \times 10^5 \text{ m/s}) \hat{i}$ in a magnetic field $\vec{B} = (0.5 \text{ T}) \hat{k}$. What is the magnitude of the magnetic force on the proton? (Charge of proton $e = 1.6 \times 10^{-19} \text{ C}$)

   • A) $8.0 \times 10^{-15} \text{ N}$
   • B) $1.6 \times 10^{-14} \text{ N}$
   • C) $3.2 \times 10^{-14} \text{ N}$
   • D) $6.4 \times 10^{-14} \text{ N}$

2. In a mass spectrometer, ions are separated based on their mass-to-charge ratio. What force is primarily responsible for the circular motion of the ions within the magnetic field?

   • A) Electric Force
   • B) Gravitational Force
   • C) Lorentz Force
   • D) Tension Force

3. An electron is moving through a region with both electric and magnetic fields. If the electric force and magnetic force on the electron are in opposite directions, and the net force is zero, what can you say about the magnitudes of the electric and magnetic forces?

   • A) The electric force is greater than the magnetic force.
   • B) The magnetic force is greater than the electric force.
   • C) The electric and magnetic forces are equal in magnitude.
   • D) The net force is always non-zero.

4. Which of the following devices directly applies the principles of the Lorentz force to accelerate charged particles to high speeds?

   • A) A resistor
   • B) A capacitor
   • C) A cyclotron
   • D) A transformer

5. What is the direction of the force on a positive charge moving to the east in a magnetic field that points vertically upwards?

   • A) North
   • B) South
   • C) East
   • D) West

6. In magnetic confinement fusion reactors, the Lorentz force is used to:

   • A) Heat the plasma
   • B) Cool the reactor
   • C) Confine the plasma
   • D) Generate electricity directly

7. A charged particle moves perpendicularly into a uniform magnetic field. What is the shape of its path?

   • A) Straight line
   • B) Parabola
   • C) Circle
   • D) Spiral