# Deflection tube

The deflection tube may be used to measure the specific charge (e/m) of the electron. This is a most useful quantity - the ratio of the charge to mass of the electron. For the electron the value of the specific charge is 1.76 x 1011 C kg-1

## The Deflection tube

This tube uses crossed electric and magnetic fields and is very similar to that used by Thomson in 1897. The electrons are accelerated through a potential V by the electron gun and are then acted on by an electric and magnetic field placed at right angles.

This means that the electric and magnetic forces oppose each other. If the current in the coils and the voltage across the plate are adjusted so that the electric force (Ee) and the magnetic force (Bev) are equal then:

Bev = eE

The kinetic energy of the electrons is :
½ mv2 = eV

And so combining these two equations gives:

Deflection tube
Specific charge :   e/m = V/[2B2d2)

since E =V/d, where d is the separation of the deflecting plates.

You can see that if the value of e/m is known and e has been found using Millikan's method it is possible to calculate the mass of the electron (m).

m = e/1.76x1011 = 1.6x10- 19/1.76x1011 = 9x10-31 kg

The study of charged particle paths is of considerable importance in nuclear physics in the analysis of cloud chamber and bubble chamber photographs.

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