# 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.Now imagine that you place your entire apparatus inside a region of magnetic field of magnitude B0. The magnetic field is perpendicular to E0 and directed straight into the plane of the figure. You adjust the value of B0 so that no deflection is observed on the screen.What is the speed v0 of the electrons in this case?Express your answer in terms of E0 and B0.

###### FREE Expert Solution

Electric force:

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

Magnetic force:

$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{q}}{\mathbf{v}}{\mathbf{B}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta }}}$

Charge, q, of an electron = e

The velocity and the magnetic field are perpendicular to each other:

82% (38 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.

Now imagine that you place your entire apparatus inside a region of magnetic field of magnitude B0. The magnetic field is perpendicular to E0 and directed straight into the plane of the figure. You adjust the value of B0 so that no deflection is observed on the screen.

What is the speed v0 of the electrons in this case?