Lecture Notes on Proton Motion in a Magnetic Field

Overview

• Proton Velocity: A proton moving with a velocity of (6 \times 10^7) m/s, which is 1/5 the speed of light.
• Magnetic Field Impact: As it crosses a magnetic field, the force on the proton is calculated to be (4.8 \times 10^{-12}) N.
• Direction of Force: Using the right-hand rule, the force is determined to be perpendicular to the velocity and the magnetic field.

Motion in Magnetic Fields

• Initial Deflection: The proton experiences a downward force, causing it to deflect and change the direction of its velocity.
• Constant Magnitude of Force: Despite changes in orientation, the force magnitude remains constant since the velocity remains perpendicular to the magnetic field.
• Circular Motion: The proton moves in a circular path due to this centripetal force. The constant change in orientation leads to a centripetal force.

Calculating the Radius of Circular Motion

• Centripetal Force Formula: Given by mass times velocity squared divided by the radius of the circle.
• Equating Forces: The centripetal force is equal to the magnetic force ((4.8 \times 10^{-12}) N).
• Radius Calculation:
  • Formula: (radius = \frac{mass \times velocity^2}{force})
  • With known values, the radius is calculated to be 1.25 meters for a proton in a 0.5 Tesla magnetic field.

Applications

• Television Technology: Old cathode ray TVs utilize magnetic fields to scan electron beams across the screen.
• Particle Accelerators: Cyclotrons use magnetic fields to circle protons rapidly, facilitating collisions.
  • Particles move in circles due to magnetic fields.
  • Differences in radii due to charge, velocity, and mass variations.

Electron Motion in Magnetic Fields

• Comparison with Protons:
  • Formula for force remains same but uses the charge of an electron.
  • The charge of an electron is negative, resulting in opposite force direction compared to proton.
• Path Differences:
  • Electrons follow a circular path in the opposite direction.
  • Due to smaller mass, electrons have a tighter circular path.
• Radius Relation: The radius is smaller for electrons due to their smaller mass compared to protons.

Conclusion

• Discussion on the impact of magnetic fields on particle motion.
• Further exploration is suggested for better understanding of applications in technology and scientific research.