PhysicsLAB Resource Lesson
Magnetic Forces on Particles (Part II)

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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 FC represents the centripetal force which is being supplied by FB, 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 = |qε| = ΔKE. For either an electron or proton, |q| would equal 1.6 x 10-19 coulombs. The formula  is
|qε| = ΔKE = ½mvf 2 - ½mvo2
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
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.

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