Graviational, Electric & Magnetic Fields

Gravitational and Electric Fields Compared

Type of Field	Gravitational	Electric
Force between	Objects with mass	Objects with charge
Constant of Proportionality	$G$ is a physical constant	$k = \frac{1}{4 π ε_{0}} \approx 9 \times 10^{9}$ Note: $ε_{0}$ is a physical constant
Field Strength in a Radial Field	$g = \frac{G m}{r^{2}}$ $[g] = N {kg}^{-1} = m s^{-2}$ $g$ is a vector and is the graviational field strength.	$E = \frac{k Q}{r^{2}}$ $[E] = N C^{-1} = V m^{-1}$ $E$ is a vector and is the electric field strength.
Definition of Field Strength	Force per unit mass $g = \frac{F}{m}$ $m$ is a test small test mass.	Force per unit charge $E = \frac{F}{Q}$ $Q$ is a test small test charge.
Force in a Radial Field	$F = \frac{G m_{1} m_{2}}{r^{2}}$ Always attractive This is a vector	$F = \frac{k Q_{1} Q_{2}}{r^{2}}$ Can be attractive or repulsive This is a vector
Potential in a Radial Field	$V = - \frac{G m}{r}$ $[V] = J {kg}^{-1}$ Always less than zero. This is a Scalar	$V = \frac{k Q}{r}$ $[V] = J C^{-1}$ Sign depends on charges This is a Scalar
Definition of Potential	Work done in bringing a unit mass from infinity to the point in the field.	Work done in bringing a unit positive charge from infinity to the point in the field.
Potential for a Uniform Field	$g = \frac{Δ V}{Δ r}$	$E = \frac{Δ V}{Δ r}$
Potential Energy	$E_{p} = V m$	$W = V Q$

Linear Accelerator
(LINAC)

Prerequiste Materials:

Electric Fields
(Care of revisionworld.com)

Alternating Currents
(Care of www.savemyexams.com)

Describing a LINAC

A linear particle accelerator (often shortened to linac) is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear beamline. The principles for such machines were proposed by Gustav Ising in 1924, while the first machine that worked was constructed by Rolf WiderÃ¸e in 1928 at the RWTH Aachen University.

Linacs have many applications:: they generate X-rays and high energy electrons for medicinal purposes in radiation therapy;; serve as particle injectors for higher-energy accelerators;; and are used directly to achieve the highest kinetic energy for light particles (electrons and positrons) for particle physics.

The design of a linac depends on the type of particle that is being accelerated: electrons, protons or ions. Linacs range in size from a few tens of centimetres in cathode ray tubes (which is a type of linac) to the 3.2 km long linac at the SLAC National Accelerator Laboratory in Menlo Park, California.

(Above scrapped from en.wikipedia.org/wiki/Linear_particle_accelerator)

Animation showing how a linear accelerator works.

Velocity Selector

Prerequisite Materials:

Definition of the force in an electric field, $F = q E$

Magnetic Field Strength, $F = q v B$

Velocity Selector (or Wien Filter)

Derivation of the Velocity Selector Equation

The forces on the charged particle passing through the velocity selector due to the electric, $E$ , and magnetic field, $B$ , are opposite directions. For a particle of the selected velocity these forces are also equal in magnitude.