In 1897 J. J. Thomson attempted to measure both the mass and charge of the negative particles making up the cathode ray.  He was unable to measure either the charge or mass by itself, but he was able to measure them both as a ratio.  In other words, he designed an experiment to determine the amount of charge per unit of mass for the particles in the cathode ray.  The design of his experiment was based on electric and magnetic forces that act on charged particles.  Recall the equations and hand rules that describe these forces.

An electrical force can deflect the charged particles in the cathode ray.


The direction of the force depends on the type of charge and the direction of the electric field. For example,

 

 

A magnetic force can deflect charged particles in a cathode ray.

 

 

The direction of the force is determined using hand rules. For example,

 

 

 

Recall:   In the open palm left-hand rule for negative charges, the thumb goes in the direction of movement ( ), the fingertips go in the direction of the magnetic field (out of the page in this case), and the palm points in the direction of the force on the charge.


Equation 1

Using only these two forces, Thomson designed an experiment that consisted of two basic investigations.  First, he used his apparatus to determine the speed of a cathode ray particle in the tube; then, knowing the speed, he used the apparatus to determine the charge-to-mass ratio of the particle.

 

Determining the Speed of a Cathode Ray Particle

A magnetic field or an electric field acting alone will deflect a charged particle that is traveling perpendicularly to it.  Thomson used this knowledge to determine the speed of a traveling particle using both a magnetic and electric field simultaneously.  He set up his apparatus in such a way that the electric force was oriented opposite to the magnetic force.  This way, if the magnetic force were equal in magnitude to the electric force, the particle would travel straight through the apparatus.  When the particle travels straight through, Equation 1 (above) can be used to calculate its speed.

 

 Self-Check

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

SC 1. A beam of electrons is fired to the right into a set of perpendicular electric and magnetic fields. The electric field is oriented downward and the magnetic field is into the page.

  1. Explain the direction of the electric force acting on the electrons.
  2. Explain the direction of the magnetic force acting on the electrons.
  3. If the electrons travel undeflected, draw a free-body diagram of the electrons.

SC 2. A particle travels undeflected (straight) through a Thomson apparatus that has a magnetic field of 2.0 T and an electric field of -100 V/m oriented perpendicularly to one another.  Use Equation 1 to determine how fast it is traveling.  Show your work and use the Charge-Mass simulation to verify your understanding. You should observe that the particle travels undeflected through the apparatus if your velocity calculation is correct.  


Self-Check

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

SC 1.

  1. The direction of the electric field is the direction in which a positive particle is pushed; therefore, in a downward field, the negatively charged electron will be influenced by an electric force in the opposite direction, upward.

  2. Using the left hand rule for negatively charged particles in magnetic fields, the current is traveling to the right (thumb), the magnetic field is into the page (fingers) and the force on the particle is downward (palm faces down).

  3. Since the electrons are undeflected, the forces-electrical force upward and magnetic force downward-are the same magnitude. The force of gravity is insignificant on such a small particle compared to the other forces, so it is ignored.


SC 2.

Given

Required


the velocity of the undeflected particle

Analysis and Solution

Paraphrase

The velocity of the particle is 50 m/s.