Resource Lesson
Magnetic Forces on Particles (Part II)
Printer Friendly Version
As initially discussed in the
introductory lesson on magnetism
, moving charges when exposed to magnetic forces are constrained to move in circular paths. The formula that allows you to calculate the radius of these circular paths is:
where F
_{C}
represents the centripetal force which is being supplied by F
_{B}
, the magnetic force. Solving for r yields
Note that the radius is directly proportional to the particle's momentum and inversely proportional to the magnitude of the charge and the strength of the magnetic field. (
Physlet: Charged Particles in a Magnetic Field
)
Right Hand Rule
The
right hand rule, RHR
, for determining the direction of the force experienced by a moving positive charge in a magnetic field is:
thumb
points in the direction of a moving positive charge's velocity,
v
fingers
point in the direction of magnetic field,
B
palm
faces in the direction of the magnetic force,
F
In the following diagram, the use of the RHR can help us distinguish between the tracks for positive charges and the tracks for negative charges.
Reflecting on the
top circle
, if our right thumb (v) points to the left (+x), our fingers (B) into the plane of the page (-z), then our palm (F) would point down (-y). Our palm points to the center of the circle which confirms that the particle is positively charged.
Reflecting on the
bottom circle
, if our right thumb (v) points to the left (+x), our fingers (B) into the plane of the page (-z), then our palm (F) would point down (-y). Our palm NO LONGER points to the center of the circle which confirms that the particle is NOT positively charged. This path must therefore be one of a negatively charged particle. This can be confirmed by using the LHR in which your palm will once again point to the center of the circle.
Natural Radioactivity
Magnetic fields can be used to distinguish emissions from naturally radioactive elements. The three natural modes of radioactive decay are: alpha (α), beta (β), gamma (γ).
Alpha particles are helium nuclei (particles containing two protons and two neutrons) and are positively charged (+2e).
Beta particles are electrons released from the nucleus when neutrons decay according to the reaction n → p
^{+}
+ β
^{-}
+ anti-electron neutrino. These particles have the same charge and mass as "normal" electrons.
Gamma radiation is electromagnetic energy that is released when a nucleus goes through "de-excitation". Gamma radiation has no charge.
Refer to the following information for the next three questions.
Which track represents each type as they pass through a magnetic field?
alpha particles?
beta particles?
gamma particles (or rays)?
Accelerating Potentials
Often charged particles are accelerated across an electric potential before entering a region containing a magnetic field.
In this situation, the electric field has done work on the charged particle to change its kinetic energy. That work can be calculated using the equation W = |q
ε
| = ΔKE. For either an electron or proton, |q| would equal 1
.
6 x 10
^{-19 }
coulombs. The formula is
|q
ε
| = ΔKE = ½mv
_{f}
^{ 2 }
- ½mv
_{o}
^{2}
The final velocity in this equation (just as the particle leaves the electric field between the plates) represents the velocity of the charged particle at the instant it enters the magnetic field.
Velocity Selector
If you want the proton to travel in a straight path through the magnetic field instead of a circular one, a second field must be introduced into the region. That second field would have to exert an equal but opposite force on the proton. The second field would be an electric field that is perpendicular to the existing magnetic field. When these forces are balanced, the charged particle will travel straight through both fields at a constant velocity.
The equation for a velocity selector is
F
_{B}
= F
_{E}
qvB = qE
v = E/B
A velocity selector was originally used to isolate different energy beta particles (β) emitted during neutron decay. Remember that beta rays are actually streams of electrons released from the nucleus.
n → p
^{+}
+ β
^{-}
+ anti-electron neutrino
Initially, scientists thought that linear momentum might not be conserved during beta decay. However, the introduction of the anti-electron neutrino accounted for the missing momentum.
Frederick Reines
just recently was awarded the Nobel Prize for his discovery of the neutrino. Today velocity selectors allow scientists to select beta rays with specific velocities to use in their experiments.
Related Documents
Lab:
Labs -
A Physical Pendulum, The Parallel Axis Theorem and A Bit of Calculus
Labs -
Calculation of "g" Using Two Types of Pendulums
Labs -
Conical Pendulums
Labs -
Conical Pendulums
Labs -
Conservation of Energy and Vertical Circles
Labs -
Forces Between Ceramic Magnets
Labs -
Introductory Simple Pendulums
Labs -
Kepler's 1st and 2nd Laws
Labs -
Loop-the-Loop
Labs -
Magnetic Field in a Solenoid
Labs -
Mass of an Electron
Labs -
Moment of Inertia of a Bicycle Wheel
Labs -
Oscillating Springs
Labs -
Roller Coaster, Projectile Motion, and Energy
Labs -
Sand Springs
Labs -
Simple Pendulums: Class Data
Labs -
Simple Pendulums: LabPro Data
Labs -
Telegraph Project
Labs -
Video LAB: A Gravitron
Labs -
Video LAB: Circular Motion
Labs -
Video LAB: Looping Rollercoaster
Labs -
Water Springs
Resource Lesson:
RL -
A Comparison of RC and RL Circuits
RL -
A Derivation of the Formulas for Centripetal Acceleration
RL -
A Guide to Biot-Savart Law
RL -
Ampere's Law
RL -
Centripetal Acceleration and Angular Motion
RL -
Conservation of Energy and Springs
RL -
Derivation of Bohr's Model for the Hydrogen Spectrum
RL -
Derivation: Period of a Simple Pendulum
RL -
Eddy Currents plus a Lab Simulation
RL -
Electricity and Magnetism Background
RL -
Energy Conservation in Simple Pendulums
RL -
Famous Experiments: Cathode Rays
RL -
Gravitational Energy Wells
RL -
Introduction to Magnetism
RL -
Kepler's Laws
RL -
LC Circuit
RL -
Magnetic Field Along the Axis of a Current Loop
RL -
Magnetism: Current-Carrying Wires
RL -
Maxwell's Equations
RL -
Meters: Current-Carrying Coils
RL -
Period of a Pendulum
RL -
Rotational Kinematics
RL -
SHM Equations
RL -
Simple Harmonic Motion
RL -
Springs and Blocks
RL -
Symmetries in Physics
RL -
Tension Cases: Four Special Situations
RL -
The Law of Universal Gravitation
RL -
Thin Rods: Moment of Inertia
RL -
Torque on a Current-Carrying Loop
RL -
Uniform Circular Motion: Centripetal Forces
RL -
Universal Gravitation and Satellites
RL -
Vertical Circles and Non-Uniform Circular Motion
Review:
REV -
Review: Circular Motion and Universal Gravitation
Worksheet:
APP -
Big Al
APP -
Maggie
APP -
Ring Around the Collar
APP -
The Satellite
APP -
The Spring Phling
APP -
The Tree House
APP -
Timex
CP -
Centripetal Acceleration
CP -
Centripetal Force
CP -
Magnetism
CP -
Satellites: Circular and Elliptical
NT -
Bar Magnets
NT -
Circular Orbits
NT -
Magnetic Forces
NT -
Meters and Motors
NT -
Pendulum
NT -
Rotating Disk
NT -
Spiral Tube
WS -
Basic Practice with Springs
WS -
Inertial Mass Lab Review Questions
WS -
Introduction to Springs
WS -
Kepler's Laws: Worksheet #1
WS -
Kepler's Laws: Worksheet #2
WS -
Magnetic Forces on Current-Carrying Wires
WS -
Magnetic Forces on Moving Charges
WS -
More Practice with SHM Equations
WS -
Pendulum Lab Review
WS -
Pendulum Lab Review
WS -
Practice with Ampere's Law
WS -
Practice: SHM Equations
WS -
Practice: Uniform Circular Motion
WS -
Practice: Vertical Circular Motion
WS -
SHM Properties
WS -
Static Springs: The Basics
WS -
Universal Gravitation and Satellites
WS -
Vertical Circular Motion #1
TB -
36A: Magnets, Magnetic Fields, Particles
TB -
36B: Current Carrying Wires
TB -
Centripetal Acceleration
TB -
Centripetal Force
TB -
Exercises on Current Carrying Wires
PhysicsLAB
Copyright © 1997-2017
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton