Question 4: How e/m ratio for electron is determined using magnetic field?

The principle of the circular trajectory of the charged particle in a magnetic field is also used to determine the e/m (charge to mass) ratio for the electron.

Charge on an electron is e and the force experienced by an electron shot perpendicularly in a magnetic field is

This force is equal to the centripetal force that keeps the charge in the circular path. Therefore,

So if the values of the velocity of electron, its radius of the path and magnetic field are known, e/m can be calculated.

In actual experiments, we shot the electron into a magnetic field of known value. In order to find the radius of the circular path, the path of the electron is made visible by filling a glass tube with a gas like Hydrogen at low pressure. The tube is then placed in the known uniform magnetic field and electrons are shot into the tube. The electrons on their circular path collide with the atoms of the gas and emit light thereby making their path visible. The diameter (and hence the radius r) of this circle can be found from the apparatus.

In order to find velocity v, if V is the fall in potential difference before entering the electric field, then the KE gain is eV. Therefore, K E = Ve

Substituting this value for v and the calculated length of the radius in equation (1),

Squaring both sides

e/m is common on both sides. Therefore, cancelling the common e/m,

Through experiments, the accurate value of e/m for an electron is 1.7588×1011Ckg-1.