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zLSfag^S7ep=R;xDp)_Ep2a!K*C^NI7b@k(+6DF6QwzzsGgo10w$^S0i^;orY=4e35` zy*+lJBJP%Yx-Azc%nxRh=dCQ2)WN>9CZ1C%W{*tXTBbbZHp?_2{c8#R<1?q(5{Blo z=s#$^Xk^diVC`tA79g+?Co=WjU?;hU~Yh8Cz_0`%_q-uHE`R~+fz1s;3 z^x4}p!n8>*M}KG|Do&Pa(@klrF+n%Ilx0LP)HrwzNDHUmy{{p*svEcv! diff --git a/physics/final.tex b/physics/final.tex index 1db6640..9a64a9d 100644 --- a/physics/final.tex +++ b/physics/final.tex @@ -190,9 +190,11 @@ % ----------------------- \subsection*{Energy and work} + Total energy = mass energy + $E_{\text{rest}} = mc^2, \quad E_K = (\gamma-1)mc^2$ - $E_{\text{total}} = E_K + E_{\text{rest}} = \gamma mc^2$ + $E_{\text{total}} = \gamma E_{\text{rest}} = E_K + E_{\text{rest}} = \gamma mc^2$ $W = \Delta E = \Delta mc^2=(\gamma-1)m_{\text{rest}} c^2$ @@ -249,18 +251,18 @@ \[v=\sqrt{GM \over r} = \sqrt{gr} = {{2 \pi r} \over T}\] - \[T={\sqrt{4 \pi^2 r^3 \over {GM}}}\tag{period}\] + \[T={\sqrt{4 \pi^2 r^3 \over {GM}}}=2 \pi \sqrt{r_{\text{alt}} \over g_{\text{alt}}}\tag{period}\] \[r = \sqrt[3]{{GMT^2}\over{4\pi^2}}\tag{radius}\] % ----------------------- \subsection*{Magnetic fields} - \begin{itemize} - \item field strength $B$ measured in tesla - \item magnetic flux $\Phi$ measured in weber - \item charge $q$ measured in coulombs - \item emf $\mathcal{E}$ measured in volts - \end{itemize} + % \begin{itemize} + % \item field strength $B$ measured in tesla + % \item magnetic flux $\Phi$ measured in weber + % \item charge $q$ measured in coulombs + % \item emf $\mathcal{E}$ measured in volts + % \end{itemize} % \[{E_1 \over E_2}={r_1 \over r_2}^2\] @@ -290,6 +292,8 @@ \textbf{Right hand grip:} thumb points to $I$ (single wire) or N (solenoid / coil) + \textbf{Magnet through ring:} consider $g$ + \includegraphics[height=2cm]{graphics/slap-2.jpeg} \includegraphics[height=3cm]{graphics/grip.png} @@ -303,6 +307,8 @@ \textbf{Xfmr} core strengthens \& focuses $\Phi$ + \columnbreak + % ----------------------- \subsection*{Particle acceleration} @@ -311,6 +317,7 @@ e- accelerated with $x$ V is given $x$ eV \[W={1\over2}mv^2=qV \tag{field or points}\] + \[V_{\text{point}} = (V_1 - V_2) \div 2 \tag{if midpoint} \] \[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\] Circular path: $F\perp B \perp v$ @@ -331,14 +338,13 @@ {\item Series $V$ shared within branch} \end{itemize} - \includegraphics[height=4cm]{graphics/ac-generator.png} - % ----------------------- \subsection*{Motors} % \begin{wrapfigure}{r}{-0.1\textwidth} \includegraphics[height=4cm]{graphics/dc-motor-2.png} - \includegraphics[height=3cm]{graphics/ac-motor.png} \\ + % \includegraphics[height=3cm]{graphics/ac-motor.png} \\ + \includegraphics[height=4cm]{graphics/ac-generator.png} \\ Force on I-carying wire, not Cu \\ $F=0$ for front & back of coil (parallel) \\ @@ -439,7 +445,7 @@ \subsection*{Refraction} \includegraphics[height=3.5cm]{graphics/refraction.png} - When a medium changes character, light is \emph{reflected}, \emph{absorbed}, and \emph{transmitted}. $\lambda$ changes, not $f$. + When a medium changes character, light is \emph{reflected}, \emph{absorbed}, and \emph{transmitted}. $\lambda$ changes, not $f$. $n$ changes slightly with $f$ (dispersion) angle of incidence $\theta_i =$ angle of reflection $\theta_r$ @@ -549,7 +555,7 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & \item $E$ and $f$ of photon: $E_2 - E_1 = hf = {hc \over \lambda}$ \item Ionisation energy - min $E$ required to remove e- \item EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) - \item No. of lines - include all possible states + \item No. of lines - include all possible states. \Delta E \ne |\Delta E| \end{itemize} \subsection*{Uncertainty principle} @@ -562,8 +568,8 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & \subsubsection*{wave model} \begin{itemize} - \item cannot explain photoelectric effect - \item $f$ is irrelevant to photocurrent + % \item cannot explain photoelectric effect + \item any $f$ works, given $t$ \item predicts delay between incidence and ejection \item speed depends on medium \item supported by bright spot in centre @@ -573,9 +579,10 @@ $f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & \subsubsection*{particle model} \begin{itemize} - \item explains photoelectric effect + % \item explains photoelectric effect \item rate of photoelectron release $\propto$ intensity \item no time delay - one photon releases one electron + \item threshold frequency \item double slit: photons interact. interference pattern still appears when a dim light source is used so that only one photon can pass at a time \item light exerts force \item light bent by gravity -- 2.43.2