Motion of Charged Particles in Magnetic Fields
Observe how charged particles move in a uniform magnetic field. Adjust the particle's properties and the field to see circular and helical paths!
Lorentz Force ($ \vec{F} = q(\vec{v} \times \vec{B}) $)
A charged particle ($q$) moving with velocity ($\vec{v}$) in a magnetic field ($\vec{B}$) experiences a force perpendicular to both $\vec{v}$ and $\vec{B}$. This force is responsible for the particle's curved trajectory.
Circular & Helical Motion
- If velocity ($\vec{v}$) is perpendicular to magnetic field ($\vec{B}$), the force provides centripetal acceleration, resulting in circular motion.
- If $\vec{v}$ has a component parallel to $\vec{B}$, that component is unaffected, leading to helical motion (a spiral along the field lines).
- The radius of the circular path is $ R = \frac{mv}{|q|B} $.