Question

An electron is moving with a speed $\mathit{v}$ in the plane of the page (Figure 20.81), and there is a uniform magnetic field $\mathit{B}$into the page throughout this region; the magnetic field is produced by some large coils that are not shown. Draw the trajectory of the electron, and explain qualitatively.

Short answer

The trajectory of the electron is as follows:

Step-by-step solution

Given data

Speed of the electron is$v$ .

Magnetic field in the region is$B$ .

Magnetic force

Magnetic force on a moving charge is the product of the magnitude of the charge and the cross product of the velocity vector and the magnetic field.

Determination of the trajectory of the electron

The cross product of the velocity and the magnetic field will be on the plane of the paper perpendicular to the velocity. As the particle turns due to this force, the direction of force turns too. The particle thus follows a circular path on the plane. Since the charge of the electron is negative, the circle will be clockwise. The trajectory will be as follows: