Introduction: Why Do Charged Particles Curve?
Imagine firing a charged particle into a magnetic field and watching it trace a perfect circle instead of travelling in a straight line. This behaviour is not an accident , it is a direct consequence of how magnetic forces work on moving charges, and it underpins some of the most important technologies in modern physics, from particle accelerators to medical imaging devices.
In this subtopic, we explore:
- The magnetic force on a moving charge and how its direction is determined
- Why magnetic fields cause circular motion (and not acceleration)
- How crossed electric and magnetic fields can act as a velocity selector
- The force experienced by a current-carrying conductor in a magnetic field
This subtopic connects directly to your understanding of circular motion (Topic B) and electric fields (D.2). Keep those ideas fresh , you will need them here.
The Magnetic Force on a Moving Charge
Magnetic Force: The force experienced by a charged particle moving through a magnetic field. Its magnitude is given by , where is the angle between the velocity vector and the magnetic field direction.
When a charge moves with velocity through a magnetic field of strength , the magnetic force acting on it is:
Where:
- = magnetic force (N)
- = charge of the particle (C)
- = speed of the particle (m s⁻¹)
- = magnetic field strength (T)
- = angle between the velocity and the magnetic field
Two special cases:
- If (velocity perpendicular to field): , maximum force
- If or (velocity parallel to field): , no force
Right-Hand Rule: Point your fingers in the direction of , curl them toward , and your thumb points in the direction of the force on a positive charge. For a negative charge, reverse the direction of the thumb.
The magnetic force is always perpendicular to the velocity of the particle. This means it can never do work on the particle and can never change its speed , only its direction of motion.
