Trajectory of Electron in Magnetic Field

Use the equation $F=qvB\sin \theta$ to find the magnitude of the force on the proton. The angle between the magnetic field vectors and the velocity vector of the proton is $\mathrm{90°}\text{.}$ The direction of the force may be found by using the right-hand rule.

The charge of the proton is $q=1.60\times {10}^{\mathrm{-19}}\text{C}$ . Entering this value and the given velocity and magnetic field strength into the equation $F=qvB\sin \theta$ gives

To find the direction of the force, first join the velocity vector end to end with the magnetic field vector, as shown in Figure 20.21. Now place your right hand so that your fingers point in the direction of the velocity and curl them upward toward the magnetic field vector. The force is in the direction in which your thumb points. In this case, the force is downward in the plane of the paper in the $\widehat{z}$ -direction, as shown in Figure 20.21.

Figure 20.21 The velocity vector and a magnetic field vector from Figure 20.20 are placed end to end. A right hand is shown with the fingers curling up from the velocity vector toward the magnetic field vector. The thumb points in the direction of the resulting force, which is the $\widehat{z}$ -direction in this case.

Thus, combining the magnitude and the direction, we find that the force on the proton is $\left(9.6\times {10}^{\mathrm{-13}}\text{N}\right)\widehat{z}\text{.}$