Motion of a Charged Particle in a Magnetic Field?

📌 CONCEPT: The motion of a charged particle in a magnetic field is determined by the force acting on the particle due to the magnetic field, which is perpendicular to the particle's velocity and the magnetic field direction.

📐 RULE / FORMULA: The force on a charged particle due to a magnetic field is given by F = qvBsinθ, where q is the charge, v is the velocity, B is the magnetic field strength, and θ is the angle between the velocity and the magnetic field direction.

💡 WORKED EXAMPLE: A charged particle with mass 9 × 10^-31 kg and charge 1.6 × 10^-19 C is moving at a speed of 5 × 10^6 m/s perpendicular to a magnetic field of strength 0.5 T. If the magnetic field is doubled to 1 T, the force on the particle will increase by a factor of 2, causing the particle's trajectory to change. Since the force is proportional to the magnetic field strength, doubling the field will double the force, resulting in a new trajectory.

⚠️ COMMON MISTAKE: Students often forget to consider the angle between the velocity and the magnetic field direction, which affects the force on the particle. They should always check if the velocity and magnetic field are perpendicular to correctly apply the formula F = qvBsinθ.