Motion of Charged Particle in Uniform Field

A moving charged particle or a current carrying conductor placed in a magnetic field experiences Lorentz force. The work done by a force on a body depends on its component in the direction of motion of the body. When the force on a charged particle in a magnetic field is perpendicular to its direction of motion, no work is said to be done.

Hence the particle keeps the same speed and kinetic energy which it had while moving in the field, even though it is deflected. On the other hand, the speed and energy of a charged particle in an electrical field is always affected due to the force by the field on the particle. A charged particle moving perpendicular to a magnetic field follows a circular path because it experience a force at right angles to the direction of motion at every position.

To know the radius R of the circular path of the charged particle, the magnetic force provides the particle with the centripetal force that keeps it moving in a circle.

qvB = mv²/R

R = mv/qB

The radius of the path traced by a charged particle in a uniform magnetic field is directly proportional to its momentum (mv) and inversely proportional to its charge and the magnetic field. It means that greater the momentum, larger the circle, and stronger the field, the smaller the circle.

The time period of rotation of the particle in a circular path is given by

T = 2πR/v = 2πm/Bq

The time period is independent of velocity of the particle and radius of the orbit. It means that once the particle is in the magnetic field, it would go round and round in a circle of the same radius. If m, B, q, remain constant, the time period does not change even if v and R are changed.