From: Andrew Lorimer Date: Mon, 18 Jun 2018 06:53:56 +0000 (+1000) Subject: add to fields notes X-Git-Tag: yr11~96 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/d8241c18decdbed0d5a818db8e5d7398f4ae463d add to fields notes --- diff --git a/physics/fields2.md b/physics/fields2.md index c4ec99a..4b5439a 100644 --- a/physics/fields2.md +++ b/physics/fields2.md @@ -3,8 +3,10 @@ Non-contact forces: - strong nuclear force - weak nuclear force -- electromagnetic force (dipoles) -- gravitational force (monopoles) +- electromagnetic force +- - electric fields (dipoles & monopoles) +- - magnetic fields (dipoles only) +- gravitational force (monopoles only) --- @@ -45,6 +47,7 @@ Characteristics of gravitational fields: - monopoles - attractive force - extends to infinite distance, but diminishes with inverse square law +- charge produced by gravity = $GM$ ### Work in a gravitational field @@ -56,9 +59,17 @@ Area under field-distance graph = $\Delta E_g / \operatorname{kg}$ ### Satellites -## Electromagnetism +## Magnetic fields -### Electric fields +### Characteristics +- field lines always go from N -> S +- dot means out of page, cross means into page +- ${E_1 \over E_2}={r_1 \over r_2}^2$ + + +## Electric fields + +### Characterisics - surrounds +ve and -ve charges - exerts force on other changes in its field @@ -67,13 +78,13 @@ Area under field-distance graph = $\Delta E_g / \operatorname{kg}$ - can be constrained to a fixed distance (conductors / insulators) - current flows from +ve to -ve -#### Field lines +### Field lines - +ve to -ve - start and end $\perp$ to surface - field lines never cross - point charges - radiate from centre -#### Forces +### Forces $$F=qE$$ @@ -82,7 +93,7 @@ $F$ is the force on charged particle $q$ is the charge of object experiencing force (Coulombs) $E$ is the strength of the electric field (Newtons / Coloumb or Volts / metre) -#### Work in electric fields +### Work in electric fields $$W=qV$$ @@ -91,7 +102,7 @@ $W$ is the work done on +ve point charge or in field $q$ is the charge of point charge being acted on $V$ is the potential (voltage) between points -#### Coulomb's law +### Coulomb's law $$F=k{{q_1q_2}\over r^2}$$ @@ -101,26 +112,25 @@ $k$ is Coulomb's constant $9.0 \times 10^9 \operatorname{N m^2 C^{-2}}$ $q_1$ and $q_2$ are the charges on the interacting points -#### Electric field at distance from a charge +### Electric field at distance from a charge $$E=k{Q \over r^2}$$ -### Electromagnetism - -#### Lenz's law +### Lenz's law - Right hand grip rule (relationship between directions of $I, F$) +- Eddy currents counter movement within a field -#### Solenoids +### Solenoids - Coil around core (like a transformer but field is transferred to kinetic energy) -#### Magnetic force on charged particles +### Magnetic force on charged particles $$F=qvB$$ where $v$ is the component of velocity which is $\perp$ to magnetic field -#### Right hand slap rule +### Right hand slap rule **Field, current and force are all 90 degree to each other** @@ -135,6 +145,65 @@ force Force is given by $F=nBIl$ + +### Faraday's law of induction + +$$\epsilon = -N{{\Delta \Phi_B}\over{\Delta t}}$$ + +where +$\epsilon$ is induced EMF (voltage) +$N$ is the number of turns in the primary coil +$\Phi_B$ is the magnetic flux (Wb or V / s) +$\Delta t$ is the change in time for one cycle (can be derived from period or frequency) + +### Flux through coils +$$\Phi_B = B_{\perp}A$$ + +where +$B_\perp$ is the field strength (Tesla) +$A$ is the area of the field perpendicular to field lines + +if $B {\not \perp} A, \Phi_B \rightarrow 0$ +if $B \parallel A, \Phi_B = 0$ + +- flux-time graphs ($t$ on $x$-axis): $\operatorname{gradient} \times n = \operatorname{emf}$ + + +**EMF is proportionate to change in flux** + +**Induced EMF opposes (counters) change in flux** + +### Transformer equation + +$${V_p \over V_s}={N_p \over N_s}$$ +$${I_p \over I_s}={N_s \over N_p}$$ + +- core strengthens and "focuses" ac flux $\Phi$ through secondary coil + + +### Root mean square + +$$V_{\operatorname{rms}} = {V_{\operatorname{p\rightarrow p}} \over \sqrt{2}}$$ + +## Power transmission +- 240 V / 50 Hz in Australia +- higher voltages have lower $V_{\operatorname{loss}}$ +- ac is used because its voltage is easily changed with xfmrs + +### Safety +- $\ge 30 \operatorname{mA}$ through heart is dangerous + +### Transmission $P_{\operatorname{loss}}$ + +$$P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R}$$ + +where +$R$ is the total resistance (derived from resistance per distance) + +To reduce power loss, use lower resistance (thicker) wires or increase voltage / reduce current with transformers + + + ### Motors #### DC