The path of a particle in a uniform magnetic field can be determined by applying the Lorentz force equation. This equation states that the force experienced by a charged particle moving in a magnetic field is given by the equation F = qvBsinθ, where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.

Explanation:
When a charged particle enters a uniform magnetic field, it experiences a force perpendicular to its velocity. This force causes the particle to move in a curved path. The path of the particle can be determined by analyzing the direction and magnitude of the force acting on it.

Force acting on the particle:
The force acting on the particle is given by the equation F = qvBsinθ. The magnitude of the force is directly proportional to the charge of the particle, the magnitude of its velocity, the strength of the magnetic field, and the sine of the angle between the velocity vector and the magnetic field vector. The direction of the force is perpendicular to both the velocity vector and the magnetic field vector, following the right-hand rule.

Movement of the particle:
Since the force acting on the particle is always perpendicular to its velocity, it causes the particle to move in a curved path. The direction of this curved path can be determined by the right-hand rule. If the velocity vector, magnetic field vector, and force vector are represented by the thumb, index finger, and middle finger of the right hand respectively, the curved path of the particle will be in the direction indicated by the palm of the hand.

Path of the particle:
The dark line in the figure represents the path of the particle inside the magnetic field. Since the particle experiences a force perpendicular to its velocity, it moves in a circular path. The radius of this circular path can be determined by analyzing the magnitude of the force and the mass of the particle. The speed of the particle remains constant throughout its motion inside the magnetic field.

Conclusion:
In conclusion, when a charged particle enters a uniform magnetic field, it experiences a force perpendicular to its velocity. This force causes the particle to move in a curved path. The path of the particle is determined by the magnitude and direction of the force acting on it.