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Projection of a point charge into a magnetic field with velocity perpendicular to the magnetic field
 
Motion of Charge in Magnetic Field

Motion of a Point Charge in Magnetic Field

Basic Equations:

Lorentz Force Law:

\[\vec F_B=q.\vec v.\vec B\]

Where:
F: Magnetic force (Newton)
q: Charge value (Coulomb)
v: Velocity (m/s)
B: Magnetic field strength (Tesla)

Circular Path Radius:

\[r =\frac{ mv}{qB}\]

Where:
r: Radius of rotation (meter)
m: Particle mass (kg)

Angular Velocity:

\[ω =\frac { qB}{m}\]

ω: Angular velocity (radian/second)

Explanation:

  • When a charge is projected with velocity perpendicular to the magnetic field, the Lorentz force acts perpendicular to both directions
  • This force causes centripetal acceleration leading to uniform circular motion
  • The path radius is directly proportional to the particle's mass and velocity, and inversely proportional to the field strength and charge value
  • The angular velocity does not depend on the particle's initial velocity

 
When a charged particle is projected into a region of uniform magnetic field perpendicular to the field, the particle experiences a constant force equal to \[\vec F=q.\vec v.\vec B\] This force is always perpendicular to the velocity and field and has a constant magnitude, causing the particle to follow a circular path. The direction can be determined using the right-hand rule. In this simulation of a charged particle launched in a magnetic field, you can explore the relationships between mass, charge, velocity, magnetic field strength, and the resulting radius of the particle's path within the field. Use the sliders to adjust the particle's mass, charge, initial velocity, and magnetic field intensity.
Charged Particle in Magnetic Field Experiment

Charged Particle in Magnetic Field Experiment

Results:

Experiment Explanation:

When a charged particle moves in a magnetic field, it experiences the Lorentz magnetic force calculated by:

F = q × v × B × sin(θ)

Where:

  • F: Magnetic force (Newton)
  • q: Particle charge (Coulomb)
  • v: Particle velocity (m/s)
  • B: Magnetic field strength (Tesla)
  • θ: Angle between motion direction and magnetic field direction

If the motion is perpendicular to the field (θ = 90°), the particle moves in a circular path with radius:

r = (m × v) / (|q| × B)

Where m is the particle mass.


Source: https://ophysics.com/index.html
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