Watch This
Complete the Force on a Charge tutorial to explore the nature of the magnetic force acting on a charged particle travelling through a magnetic field.

 
Self-Check

Answer the following self-check (SC) questions then click the "Check your work" bar to assess your responses.

  

SC 6.  

Calculate the magnitude and direction of the acceleration of a proton (1.67x10-27kg) that is travelling east at a speed of 9.00 ×104 m/s through a magnetic field of 3.00 × 10-1  T that is directed south.  Refer to "Practice Problem" 2 on page 600 of the textbook for a hint.

 

Questions SC 7, SC 8, and SC 9 relate to another experiment about cleaning flue gases from a power plant. A particle present in the flue gas, with a charge of -3.2 × 10 -17 C, enters a region with a magnetic field strength of 2.5 × 10-2 T. The magnitude of the particle's velocity was 12.0 m/s. The following diagram illustrates the details. Use this information to answer SC 7 to SC 9.

 

 

SC 7.  

Determine the direction of the magnetic force acting on the particle once it enters the magnetic field.

 

SC 8.

In addition to the magnetic force, the force of gravity also acts on the particle.  Under the right conditions, the effect of the magnetic force could be balanced by the force of gravity, allowing the particle to pass through the magnetic field undeflected.  Draw a free-body diagram to illustrate the forces that would act on the particle in this case.

 

SC 9.

Determine the necessary mass of the flue gas particle for it to pass through the magnetic field undeflected.  Remember to use the GRASP method for solving problems.

 

   Self-Check Answer

Contact your teacher if your answers vary significantly from the answers provided here.

 

SC 6.

 

Required

The acceleration of the proton.

 

Analysis and Solution

Find the force acting on the proton.


F m  =  qvB
F m  = (1.60 × 10 -19  C)(9.00 × 10 4  m/s)(3.00 × 10 -1  T)
F m  = 4.32 × 10 -15  N [downwards]

 

Find the acceleration of the proton.

 

 

Paraphrase

The acceleration of the proton is 2.59 × 10 12  m/s 2  [downwards, into the page]

 

SC 7.

 

SC 8.

 

SC 9.

 

Given

 

Required

the mass of the flue gas particle,  m

 

Analysis and Solution

The gravitational force acting on the flue gas particle has a magnitude of   and is directed downward. The magnetic force acting on the glue gas particle has a magnitude of   and is directed upward.

 

 

Since the forces balance,  . Therefore,

 

 

Paraphrase

The mass of the flue gas particle is 9.8 × 10 -19  kg.

 

In 1897 Sir Joseph John Thomson (1856-1940) conducted an original study of cathode rays that resulted in the discovery of the electron.  He was awarded the Nobel Prize in 1906 "in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases."

 


 

The following quote is taken from his Nobel Lecture on Physics on December 11, 1906:



In this lecture I wish to give an account of some investigations which have led to the conclusion that the carriers of negative electricity are bodies, which I have called corpuscles, having a mass very much smaller than that of the atom of any known element, and are of the same character from whatever source the negative electricity may be derived. 

The first place in which corpuscles were detected was a highly exhausted tube through which an electric discharge was passing .

Nobel Lectures: Physics, 1901...1921 (Amsterdam: Elsevier, 1967)


In his lecture Thomson continued to describe a series of experiments he had conducted on cathode rays.  In one experiment he subjected the cathode ray to an external magnetic field to verify that the cathode ray consisted of nothing other than a stream of negative charges.  Then he verified this in a second experiment where he successfully observed the cathode ray being deflected by an electric field-in a direction consistent with a negative charge.  This had not been observed previously, and Thomson correctly assumed that this was due to leftover gases that could not be evacuated from the cathode ray tube due to imperfections in the equipment.  Thomson's equipment was able to achieve a greater vacuum than previous attempts.

 

In the third experiment Thomson measured the charge-to-mass ratio of the electron (which he described as a corpuscle).