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Force on ions subjected to electric and magnetic fields

A uniform electric field of 1.6 x 10^3 V/m and a uniform magnetic field of 3.34 x 10^-3 Wb/m^2 are parallel to each other and are acting along the Z-direction. A beam of Hydrogen ions of energy 150 eV is released in the X direction. A photographic plate is placed normal to the motion of the ions at a distance of 0.5m from the origin.
(1) How long after leaving the gun, will the ions hit the plate?
(2) Calculate the displacement of the ions in the Y and Z directions.

Solution Preview

Please see the file.

Mass of hydrogen ion MH = 1.67 x 10 -27 kg
Energy of the ion KE = ½ mv2 = 150 eV
150 x 1.6 x 10 -19 Joule

Therefore v = {2KE/MH} 1/2 = {2 x 150 x 1.6 x 10 -19 /1.67 x 10 -27} ½
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Solution Summary

Explanations with the underlying physics.

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