Worked exercise — charge in an outward field

Problem

A positive charge moves to the right with velocity $\vec{v}$ in a region where the magnetic field points out of the page. In which direction does the Lorentz force point?

Solution

Apply the right-hand rule to $\vec{F} = q\,\vec{v}\times\vec{B}$. Index finger to the right (direction of $\vec{v}$), middle finger out of the page (direction of $\vec{B}$): the thumb points upward.

Since the charge is positive, the force has the same direction as the cross product:

$\ev{\vec{F} \text{ directed upward}}$

If the charge were negative, $\vec{F}$ would point downward. The magnitude, with $\vec{v}\perp\vec{B}$, is $|F| = qvB$.

Collegamenti

Argomenti: Magnetismo Concetti: Forza di Lorentz Competenze: Regola della mano destra