Answer to Question #162446 in Atomic and Nuclear Physics for Ali

Question

Explain What formula you have used to determine the charge to mass ratio of the electron and what is

the origin of it?

Answer 1

Suppose the electron moves in electric $\mathbf{E}$ and magnetic $\mathbf{B}$ fields. The charge to mass ratio of the electron can be found from two formulas: second Newton's law:

$$\mathbf{F} = m\mathbf{a}$$

and Lorentz force law:

$$\mathbf{F} = e(\mathbf{E} + \mathbf{v}\times \mathbf{B})$$

where $\mathbf{v}$ is the velocity of electron. Since forces are equal, obtain:

$$\left( \dfrac{e}{m} \right)(\mathbf{E} + \mathbf{v}\times \mathbf{B}) = \mathbf{a}$$

This is the most general expression to determine the charge to mass ratio of the electron.