Question

Find the magnetic force FB acting on a moving charged particle by evaluating the cross product q (V×B) in unit-vector notation and magnitude- angle notation.

Answer 1

Unit-vector notation:

$$\vec{F}=q(\vec v\times \vec B).$$

To write the force in unit-vector notation, we need to know the mutual location of velocity and magnetic field vectors. For instance, if B is directed along k, v is directed along j, the force will be directed along i.

This may look like

$$\vec F=(3\textbf i+0.3\textbf j-16\textbf k)\text{ N}.$$

Magnitude-angle notation: again, we need to know the exact position or arrangement of the velocity and field. This may look like

$$\vec F=|F|\angle\theta\text{ N}.$$