Schuster's experiment

SCHUSTER'S EXPERIMENT

By researching the behavior of the cathode rays when in the magnetic field and assuming their consistence as some positive charged particles, Schuster discovered that some information can be achieved about the equivalents describing that particles. The path they make in the perpendicular, with the respect to their movement, magnetic field is a part of circumference of circle. So the field influences the cathode rays with the centripetal force. Assuming that every particle of the rays has mass m and charge q, and the magnetic field intensity (in which the particles move along the circle with the radius R) is equal B, of two shown below formulas for force:

(1)

(of the magnetic part of Lorentz force)

(2)

(z of the second Newton's law)

we get:

(3)

and of that:

(4)

Schuster didn't know the value of the q, m. and v quantities. Assuming that q/m. was constant he noticed that the curving of the rays trajectory depends only on the voltage applied to the tube and on the value of the intensity B.
In 1890 he evaluated the higher and the lower value of the q/m. He assumed that the kinetic energy of the particles of the cathode rays is equal:

(5)

Whereas the energy can not exceed the value of the V*q, where V is the potential of the cathode. So there is:

(6)

Hence the maximal value of the q/m. is equal:

(7)

But from the other hand calculating v from the formula (4) and placing it into the formula (6) we get:

(8)

    All the quantities of the right side of the equation were known for Schuster. After placing the values in the formula he achieved the maximal value of q/m equal 10¹⁰ coulombs per kilogram.
    In order to calculate the minimal value of q/m Schuster placed the approximate value of the velocity of the air particle (in the room temperature) to the formula (4). After placing the numerical values in the formula he achieved the minimal value of q/m. equal 5*10⁶ coulombs per kilogram.
    And so the ratio q/m. for the particle of the cathode rays is equal no less than 5*10⁶ and no more than 10¹⁰ coulombs per kilogram. He noticed that it was the same with the q/m. ratio of the ion of the atom of hydrogen.