# Electricity and Magnetism

Term | Units | Overview |
---|---|---|

Force (F) | Force from a charge: F = E q Two charges q_{1} and q_{2} exert a force on each other: F_{12} = k q_{1} q_{2} / r_{12}^{2} | |

Electric Field (E) | Volts / meter | E vector = E Electric field from a charge: E = F / q Electric field of a point charge: E = k q / r^{2}
(where r is distance from charge) |

Peak Electric Field (E_{0}) |
Volts / meter | E_{0} = B_{0} c = µ_{0} ε_{0} ω c |

Magnetic Field (B) | Tesla | B vector = B_{0} ( x , t ) zˆ → B is z direction → B_{0} sin (k x - ω t ) z
B = B_{0} cos ( k x - ω t )
B = µ_{0} ε_{0} ω cos ( k x - ω t ) |

Peak Magnetic Field (B_{0}) |
Tesla (T) | B_{0} = c / E_{0}
B_{0} = µ_{0} ε_{0} ω |

Charge (q or Q) | Coulumbs (C) | |

Electric Potential (V) | Potential energy per charge. Electric potential by some source point charge: V = k q / r Electric potential between two point charges: V = k q_{1} / r_{1} + k q_{2} / r_{2} | |

Light Speed (c) | 3 × 10^{8} m / s |
c = E c = v = ƒ λ c^{2} = 1 / ( µ_{0} ε_{0} ) |

Energy Density (u) | J m^{-3} |
u _{B} = ½ B^{2} / µ_{0} |

Poynting Vector (S) | J m^{-2} s^{-1} |
Rate at which wave carries energy across unit area per unit time.
Average S = ½ ε_{0} c E_{0}^{2} = ½ E_{0} B_{0} / µ_{0}
= E_{rms} B_{rms} / µ_{0} = E_{rms}^{2} / ( µ_{0} c ) = B_{rms} c / µ_{0} |

Radiation Pressure (P) | Pressure equals the average Poynting vector times α and divided by c. It is independent of area. P = α S / c α is thecoefficient of reflection and refers to a materials ability to absorb or reflect. 1 (fully absorbing) < α < 2 (fully reflecting). A common material in homework problems is a metal plate, which is assumed to fully reflect and thus have α = 2. | |

Power | Power = Intensity × Area | |

Power Received | Consider a spherical lightbulb with power output ℘; what is the power received by another sphere with radius R at distance D from the lightbulb? (A common homework problem involves the sun and a planet.) The power received is I _{received} = ( ℘ R^{2} ) / ( 4 D^{2} ) | |

Intensity | Consider a spherical light bulb with power output ℘. Its intensity is its power output ℘ divided by its surface area (4πr |

## Constants

Term | Description |
---|---|

Energy Constant = k | 8.99 x 10^{9} N m^{2} C^{-2} |

Permittivity Constant ε_{0} |
8.8542 x 10^{-12} C^{2} N m^{-2} |

Magnetic Constant = µ_{0} |
4 π × 10^{−7} V s / ( A m ) |

## Directions for Electrogmagnetic Waves

k is parallel to v, the propagation direction

k is perpendicular to E and to B

E is perpendicular to B

Form the letter L with your right hand. Stick your middle finger at yourself. Your index finger (pointing up) is E. Your thumb (pointing right) is k. Your middle finger (pointing at you) is B.

## Doppler Effect for Electromagnetic Waves

ƒ = ƒ_{0} [ ( c - v ) / ( c + v ) ]^{½}

ƒ_{0} is the emitted frequency; ƒ is the shifted frequency