Charged Particle in Magnetic Field

Charged Particle in Magnetic Field Simulation

Simulation Controls

Particle Charge:

Positive (+q) Negative (-q)

Charge Magnitude (q):

Particle Mass (m):

Initial Velocity (v):

Magnetic Field Strength (B):

Magnetic Field Direction:

Into Screen (X) Out of Screen (•)

Number of Particles:

Calculated Values

Theoretical Radius (r): – (units)

Force Magnitude (|F|): – (units)

Time Step (Δt): – s

Simulation Area

Explanation

This simulation demonstrates the path of charged particles when they enter a region with a magnetic field perpendicular to their initial velocity. The force on the particle is given by the Lorentz force, $\vec{F} = q(\vec{v} \times \vec{B})$.

When $\vec{v}$ is perpendicular to $\vec{B}$, the force magnitude is $|F| = |q|vB$. This force is always perpendicular to the velocity vector, causing the particle to move in a circular path. The direction of the circular path depends on the sign of the charge and the direction of the magnetic field (Right-Hand Rule for positive charges, Left-Hand Rule for negative charges).

The radius of this circular path is called the cyclotron radius and is determined by the particle’s momentum ($mv$) and the magnetic force strength ($|q|B$):

$$ r = \frac{mv}{|q|B} $$

Use the controls on the left to change the particle properties and magnetic field parameters. Observe how the radius of curvature changes according to the formula. Higher momentum ($mv$) leads to a larger radius, while a stronger magnetic field ($B$) or charge ($|q|$) leads to a smaller radius.

Magnetic Field Visualization:

Dots (•) represent the magnetic field pointing out of the screen.
Crosses (X) represent the magnetic field pointing into the screen.

The particles enter the magnetic field region from the left.