Right-hand rule

Problem

Explain the right-hand rule for $\vec F = q\vec v\times\vec B$ on a positive charge, and how it changes for a negative one. Give an example with $\vec v$ horizontal pointing right and $\vec B$ coming out of the page.

Solution

For the cross product $\vec F = q\,\vec v\times\vec B$ the right-hand rule is used: point the index finger along $\vec v$, the middle finger along $\vec B$, and the thumb indicates the direction of $\vec F$. This holds for a POSITIVE charge.

For a NEGATIVE charge the factor $q < 0$ reverses the result: the force has the same magnitude and line of action, but OPPOSITE direction.

Example: $\vec v$ pointing right and $\vec B$ coming out of the page. Applying the rule, the thumb points UPWARDS. So for $+q$ the force points upwards, while for $-q$ it points downwards. $\ev{+q:\ \vec F \text{ upwards};\quad -q:\ \vec F \text{ downwards}}$

Links

Topics: Magnetismo Concepts: Forza di Lorentz Skills: Regola della mano destra