physics / fields2.mdon commit planner (a589bb9)
   1# Fields
   2
   3Non-contact forces:
   4- strong nuclear force
   5- weak nuclear force
   6- electromagnetic force
   7- - electric fields (dipoles & monopoles)
   8- - magnetic fields (dipoles only)
   9- gravitational force (monopoles only)
  10
  11Gravitational & -ve electric monopoles - field lines radiate towards central object
  12Magnetic & electric dipoles - field lines go from + to -, or N to S
  13
  14---
  15
  16## Gravity
  17
  18### Newton's law of universal gravitation
  19
  20$$F_g=G{{m_1m_2}\over r^2}$$
  21
  22where
  23$F_g$ is the gravitational force between $m_1$ and $m_2$
  24$G$ is the gravitational constant, $6.67 \times 10^{-11} \operatorname{N m^2kg^{-2}}$
  25$r$ is the distance between centre of $m_1$ and $m_2$
  26
  27
  28- inverse square law
  29- acceleration can be calculated from $F_g$, since $F=ma$
  30- all objects with mass attract each other with $F_g$
  31- $F_g$ acts equally on $m_1$ and $m_2$
  32- acceleration of an object close to earth's surface can be approximated by ignoring its mass ($m_2 \approx 0$)
  33- apparent weight may be different to gravitational (normal) weight
  34
  35### Gravitational fields
  36
  37$$g={F_g \over m}=G{M \over r^2}$$
  38
  39where
  40$g$ is the gravitational field strength
  41$F_g$ is the force due to gravity ($=G{{m_1m_2}\over r^2}$)
  42$m$ is the mass of object in the field
  43$M$ is the mass of the central body
  44
  45- arrows towards centre of object
  46- closer arrows mean larger force
  47- parallel field lines - uniform field strength (vector)
  48
  49Characteristics of gravitational fields:
  50- monopoles
  51- attractive force
  52- extends to infinite distance, but diminishes with inverse square law
  53- charge produced by gravity = $GM$
  54
  55### Work in a gravitational field
  56
  57Gravitational potential energy: $E_g = mg \Delta h$
  58Work: $W = \Delta E_g = Fx$
  59
  60Area under force-distance graph = $\Delta E_g$
  61Area under field-distance graph = $\Delta E_g / \operatorname{kg}$
  62
  63### Satellites
  64
  65## Magnetic fields
  66
  67### Characteristics
  68- field lines always go from N -> S
  69- dot means out of page, cross means into page
  70- ${E_1 \over E_2}={r_1 \over r_2}^2$
  71- flux: change in magnetic field
  72
  73
  74## Electric fields
  75
  76### Characterisics
  77
  78- surrounds +ve and -ve charges
  79- exerts force on other changes in its field
  80- monopoles and dipoles
  81- attractive/repulsive forces
  82- can be constrained to a fixed distance (conductors / insulators)
  83- current flows from +ve to -ve
  84
  85### Field lines
  86- +ve to -ve
  87- start and end $\perp$ to surface
  88- field lines never cross
  89- point charges - radiate from centre
  90
  91### Forces
  92
  93$$F=qE$$
  94
  95where
  96$F$ is the force on charged particle
  97$q$ is the charge of object experiencing force (Coulombs)
  98$E$ is the strength of the electric field (Newtons / Coloumb or Volts / metre)
  99
 100### Work in electric fields
 101
 102$$W=qV$$
 103
 104where
 105$W$ is the work done on +ve point charge or in field
 106$q$ is the charge of point charge being acted on
 107$V$ is the potential (voltage) between points
 108
 109### Coulomb's law
 110
 111
 112$$F=k{{q_1q_2}\over r^2}$$
 113
 114where
 115$k$ is Coulomb's constant $9.0 \times 10^9 \operatorname{N m^2 C^{-2}}$
 116$q_1$ and $q_2$ are the charges on the interacting points
 117
 118
 119### Electric field at distance from a charge
 120
 121$$E=k{Q \over r^2}$$
 122
 123### Lenz's law
 124- Right hand grip rule (relationship between directions of $I, F$)
 125- Eddy currents counter movement within a field
 126- Represented by -ve sign in Faraday's law
 127
 128### Solenoids
 129- Coil around core (like a transformer but field is transferred to kinetic energy)
 130
 131### Magnetic force on charged particles
 132
 133$$F=qvB$$
 134
 135where
 136$v$ is the component of velocity which is $\perp$ to magnetic field
 137
 138### Right hand slap rule
 139
 140
 141**Field, current and force are all 90 degree to each other**
 142<pre>
 143force
 144|      /    field
 145|   /
 146|/  90 de=
 147 \
 148   \   +ve charge
 149</pre>
 150
 151Force is given by $F=nBIl$
 152
 153
 154### Faraday's law of induction
 155
 156$$\epsilon = -N{{\Delta \Phi_B}\over{\Delta t}}$$
 157
 158where
 159$\epsilon$ is induced EMF (voltage)
 160$N$ is the number of turns in the primary coil
 161$\Phi_B$ is the magnetic flux (Wb or V / s)
 162$\Delta t$ is the change in time for one cycle (can be derived from period or frequency)
 163
 164### Flux through coils
 165$$\Phi_B = B_{\perp}A$$
 166
 167where
 168$B_\perp$ is the field strength (Tesla)
 169$A$ is the area of the field perpendicular to field lines
 170
 171if $B {\not \perp} A, \Phi_B \rightarrow 0$
 172if $B \parallel A, \Phi_B = 0$
 173
 174- flux-time graphs ($t$ on $x$-axis): $\operatorname{gradient} \times n = \operatorname{emf}$
 175
 176
 177**EMF is proportionate to change in flux**
 178
 179**Induced EMF opposes (counters) change in flux**
 180
 181### Transformer equation
 182
 183$${V_p \over V_s}={N_p \over N_s}$$
 184$${I_p \over I_s}={N_s \over N_p}$$
 185
 186- core strengthens and "focuses" ac flux $\Phi$ through secondary coil
 187
 188
 189### Root mean square
 190
 191$$V_{\operatorname{rms}} = {V_{\operatorname{p\rightarrow p}} \over \sqrt{2}}$$
 192
 193## Power transmission
 194- 240 V / 50 Hz in Australia
 195- higher voltages have lower $V_{\operatorname{loss}}$
 196- ac is used because its voltage is easily changed with xfmrs
 197
 198### Safety
 199- $\ge 30 \operatorname{mA}$ through heart is dangerous
 200
 201### Transmission $P_{\operatorname{loss}}$
 202
 203$$P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R}$$
 204
 205where
 206$R$ is the total resistance (derived from resistance per distance)
 207
 208To reduce power loss, use lower resistance (thicker) wires or increase voltage / reduce current with transformers
 209
 210
 211
 212### Motors
 213
 214#### DC
 215
 216- current-carrying wire experiences magnetic force $F$ equal to $nBIl$
 217- torque: $\tau = r_{\perp} F$
 218- split ring and brushes