Q: A charged species traveling at a constant velocity ( v ) through a magnetic field ( B ) will experience a force if the direction of motion is at a 900 angle with the B-field. How can trigonometry be used to quantify this phenomena?
A: The magnetic force ( Fm ) on the charged species is generically quantified with the following equation:
Fm = qvB
The magnitude of charge ( q ), velocity, and magnetic field are all directly proportional to the magnitude of the force experienced by the traveling particle. Notice, however, that the equation, in its current form, mistakenly implies that the charge can enter the B-field from any direction. Fortunately, trigonometry is used to give clarity to the equation. The sin θ function has the following useful characteristic:
sin 900 = 1
sin 00 = 0
The value of sin θ and other trigonometric functions varies from 0, 1, and -1 relative to the value of θ. The sin θ function, however, has a maximum value ( 1 ) when 900 is the input value. Thus, the magnetic force equation is expressed accordingly:
Fm = qvBsin θ
Regardless of how great a charge is, how fast it moves, or how great the magnitude of a magnetic field happens to be, these factors will be of no consequence unless the charged particle moves through the field at a 900 angle.
RENAISSANCE PHYSICS 