Mechanics of Magnetic Interactions Review

Magnetic Force

The force exerted on a charged particle moving through a magnetic field.

Lorentz Force Law

Describes the magnetic force on a charged particle as $ ext{F}_B = q( ext{v} \times ext{B})$.

Coulombs (C)

The unit of electric charge.

Tesla (T)

The unit of magnetic field strength.

$ heta$ (theta)

The angle between the velocity vector $ ext{v}$ and magnetic field vector $ ext{B}$.

Perpendicularity of Magnetic Force

The magnetic force is always perpendicular to both the velocity vector and magnetic field vector.

Zero Force Conditions

No magnetic force is exerted if the particle is stationary or moving parallel to the magnetic field.

Work Done by Magnetic Force

The work done by a magnetic field on a charged particle is always zero.

Right-Hand Rule (RHR)

A method to determine the direction of the force on a positive charge in a magnetic field.

Current (I)

The flow of electric charge, measured in Amperes (A).

Differential length vector ($d ext{l}$)

A small component of length pointing in the direction of current flow in a wire.

Uniform Circular Motion

Motion of a charged particle moving perpendicular to a magnetic field, resulting in circular paths.

Cyclotron Radius ($r$)

The radius of the circular path of a charged particle in a magnetic field, given by $r = \frac{mv}{qB}$.

Period ($T$)

The time taken for one complete cycle of motion; independent of velocity in a magnetic field.

Helical Motion

Path of a charged particle entering a magnetic field at an angle, resulting in a spiral trajectory.

Velocity Selector

A device that filters particles by speed using crossed electric and magnetic fields.

Mass Spectrometer

An instrument that separates particles based on their charge-to-mass ratio.

Electric Force ($F_E$)

The force exerted by an electric field on a charged particle, given by $F_E = qE$.

Magnetic Force ($F_B$)

The force exerted by a magnetic field on a moving charge, given by $F_B = qvB$.

Centripetal Force

The force required to keep an object moving in a circular path, provided by the magnetic force in this case.

Work-Energy Principle

In a magnetic field, the magnetic force does no work on particles; hence it cannot change their speed.

Angular Position of Charged Particle

The angular position in a magnetic field can change but the speed remains constant due to zero work done.

Motion Analysis of Charged Particles

The study of charged particles' trajectories in magnetic fields leading to uniform motion analysis.

Magnetic Field Strength

Strength of the magnetic field affecting the force on charged particles, measured in Tesla.

Order of Cross Product

The importance of order in calculating cross products; $ ext{v} \times ext{B} \neq \text{B} \times ext{v}$.

Charge-to-Mass Ratio ($q/m$)

A key variable in mass spectrometry that allows for identification of particles based on their curvature.

Units of Magnetic Field

Magnetic fields are often expressed in Tesla (T) or Gauss (G), with the conversion $1 ext{ T} = 10,000 ext{ G}$.