Answer to Question #157131 in Electric Circuits for Carty

Question

Briefly describe and experiment to determine the specific charge (e/m) of an electron using the combination of electric and magnetic fields.

Answer 1

Answer

The ratio of charge to mass is known as the specific charge.

Thomsons experiment

The apparatus consists of a cathode C and anode A which are enclosed in an evacuated discharge tube. When a high potential difference is applied between cathode and anode, a narrow beam of cathode rays emerges from a small hole in the anode and passes between two parallel plates P₁ and P₂. A uniform electric field is applied to the plane of paper with the help of horizontal plates   and the electrons will deflect upwards in the plane of the paper. On the other hand, a uniform magnetic field is also applied in this region perpendicular to the plane of the paper and inward direction. The magnetic field will deflect the electrons downwards in the plane of the paper.

Equation for specific charge can be obtain as

Centripetal force will be provided by the force on electron on in magnetic field

$Bev=\frac{mv^2}{r}\\$

$\colorbox{aqua}{$\frac{e}{m}=\frac{B}{rv}$}$