Chapter 11 - Magnetic Forces and Fields

Chapter 11.1 - Magnetism and Its Historical Discoveries

If a particle is moving in a direction perpendicular to a magnetic field, then the particle will take on a circular orbit.

The centripetal force experienced by the particle, due to the magnetic field:

$$ F_B = q v B = \frac{m v^2}{r} $$

The radius of orbit that the particle will circle around:

$$ r = \frac{m v}{q B} $$

The period of motion for the particle in orbit:

$$ T = \frac{2 \pi r}{v} = \frac{2 \pi}{v} \frac{m v}{q B} = \frac{2 \pi m}{q B} $$

The maximum speed of a particle in a cyclotron:

$$ v_{max} = \frac{q B R}{m} $$

The kinetic energy of a particle in a cyclotron:

$$ KE = \frac{1}{2} m v^2 = \frac{q^2 B^2 R^2}{2m} $$

The angular speed $\omega$ of a particle in orbit:

$$ \omega = \frac{v}{r} = \frac{q B}{m} $$

The perpendicular component of helical motion, which causes the particle to orbit in a circular path:

$$ v_{perp} = v \ sin(\theta) $$

The parallel component of helical motion, which causes the particle to travel forward:

$$ v_{parallel} = v \ cos(\theta) $$

The pitch $p$ of the helix, the distance between adjacent turns

$$ p =v_{parallel} * T $$