"The great tragedy of Science - the slaying of a beautiful hypothesis by an ugly fact"
T. H. Huxley

• An electric charge +q, moving with velocity v, in a magnetic field B, feels a force whose magnitude is given by
  
  
  
  where theta is the angle between the velocity and the magnetic field. This expression is the magnetic equivalent of  F_E = q E.
  
  
  
  
  
• The direction of the force is perpendicular to both the magnetic field (B) and the velocity (v).  The sense is determined by another "right hand rule", indicated below
  
  
  

   The direction given by this right hand rule applies for a positive charge.  If the charge is negative the direction of the force is opposite to that obtained above.
  
  
• Some special cases


• When v = 0 there is no magnetic force.  Stationary charges do not feel magnetism.


• When  v and B are parallel (or opposite) then sin (theta)  = 0 and once again there is no magnetic force.  Charged particle moving along magnetic field lines do not feel a magnetic force.


• For a given q, v and B the magnetic force is a maximum when v and B are at right angles.




• The magnetic force does no work on a charged particle.  Therefore a magnetic field cannot be used to increase the energy of a charged particle.  If v and B are perpendicular the particle will move in a circular path.  (If v also has a component along the direction of B the path will be a helix).  This property is employed in the use of magnets to constrain charged particle in accelerator and fusion applications.


• Electric and Magnetic forces.
  With the velocity (v) and the electric (E) and magnetic (B) fields at right angles, the electric and magnetic forces can be adjusted to produce a net zero force.
  qE = qvB
  v = E/B
  Particles with this velocity are undeflected.  This is the basis for the mass spectrometer.

   Supplementary Problems 

One day our professor was discussing a particularly complicated physics concept. A pre-med student rudely interrupted to ask, "Why do we have to learn this pointless information."
"To save lives." the professor responded quickly and continued the lecture.
A few minutes later, the same student spoke up again. "So how does physics save lives?" he persisted. "It keeps the ignoramuses like you out of medical school," replied the professor.

 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu