# Problem: In the late 19th century, great interest was directed toward the study of electrical discharges in gases and the nature of so-called cathode rays. One remarkable series of experiments with cathode rays, conducted by J. J. Thomson around 1897, led to the discovery of the electron.With the idea that cathode rays were charged particles, Thomson used a cathode-ray tube to measure the ratio of charge to mass, q/m, of these particles, repeating the measurements with different cathode materials and different residual gases in the tube.What is the distance Δy between the two points that you observe? Assume that the plates have length d, and use e and m for the charge and the mass of the electrons, respectively.Express your answer in terms of e, m, d, v0, L, and E0.

###### FREE Expert Solution

Electric force:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{q}}{\mathbf{·}}{\mathbf{E}}}$

Newton's second law:

$\overline{){\mathbf{\Sigma }}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

Uniform accelerated motion (UAM) equations:

Distance:

$\overline{){\mathbf{d}}{\mathbf{=}}{\mathbf{v}}{\mathbf{·}}{\mathbf{t}}}$

Assume the x-axis points horizontally while the y-axis points vertically.

The horizontal velocity is v0 is directed along the x-axis. The length of the plates is also along the x-axis. The time, t0, taken to cover the region with electric field due to the plates is:

t = d/v = d/v0

Charge, q, of the electron = e

We'll solve for acceleration using electric force and Newton's second law expressions.

may = eE

90% (42 ratings) ###### Problem Details

In the late 19th century, great interest was directed toward the study of electrical discharges in gases and the nature of so-called cathode rays. One remarkable series of experiments with cathode rays, conducted by J. J. Thomson around 1897, led to the discovery of the electron.

With the idea that cathode rays were charged particles, Thomson used a cathode-ray tube to measure the ratio of charge to mass, q/m, of these particles, repeating the measurements with different cathode materials and different residual gases in the tube.

What is the distance Δy between the two points that you observe? Assume that the plates have length d, and use e and m for the charge and the mass of the electrons, respectively.

Express your answer in terms of e, m, d, v0, L, and E0.