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feat: complete AP Physics C handbook — all E11-E13 concepts, unit assemblies, and fixes

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Krishna Ayyalasomayajula
2026-04-29 22:13:11 -05:00
parent eb6959b896
commit eba21764a1
3 changed files with 9 additions and 45 deletions
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6
concepts/em/u11/e11-5-kirchhoff.tex
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@@ -138,7 +138,6 @@ Substitute equation (1) into equation (2):
\[
7.0\,I_1 + 3.0\,I_2 = 12.
\]
\label{eq:a}
Substitute equation (1) into equation (3):
\[
@@ -158,9 +157,8 @@ so
\[
I_1 = 2.0 - 3.0\,I_2.
\]
\label{eq:b}
Substitute equation (\ref{eq:b}) into equation (\ref{eq:a}):
Substitute equation (3) into equation (2):
\[
7.0\,(2.0 - 3.0\,I_2) + 3.0\,I_2 = 12,
\]
@@ -177,7 +175,7 @@ Substitute equation (\ref{eq:b}) into equation (\ref{eq:a}):
I_2 = \frac{2.0}{18.0} = \frac{1}{9}\,\mathrm{A}.
\]
From equation (\ref{eq:b}):
From equation (3):
\[
I_1 = 2.0 - 3.0\left(\frac{1}{9}\right) = 2.0 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}\,\mathrm{A}.
\]

5
concepts/em/u12/e12-3-force-on-current.tex
View File

@@ -111,9 +111,10 @@ U = -\mu B\,\cos\phi = -\vec{\mu}\cdot\vec{B}.
\nt{The SI unit of magnetic dipole moment $\vec{\mu}$ is ampere-square meter, $\mathrm{A\cdot m^2}$. This is equivalent to joules per tesla, $\mathrm{J/T}$.}
\ex{Illustrative example}{A coil with $N=50$ turns, each of area $A = 8.0\,\mathrm{cm^2} = 8.0\times 10^{-4}\,\mathrm{m^2}$, carries current $I = 2.0\,\mathrm{A}$ in a field $B = 0.40\,\mathrm{T}$. The maximum torque occurs at $\phi = 90^\circ$:
\ex{Illustrative example}{A coil with $N=50$ turns, each of area $A = 8.0\,\mathrm{cm^2} = 8.0\times 10^{-4}\,\mathrm{m^2}$, carries current $I = 2.0\,\mathrm{A}$ in a field $B = 0.40\,\mathrm{T}$. The maximum torque occurs at $\phi = 90^\circ$:}
\[
\tau_{\text{max}} = N\,I\,A\,B = (50)(2.0\,\mathrm{A})(8.0\times 10^{-4}\,\mathrm{m^2})(0.40\,\mathrm{T}) = 3.2\times 10^{-2}\,\mathrm{N\cdot m}.}
\tau_{\text{max}} = N\,I\,A\,B = (50)(2.0\,\mathrm{A})(8.0\times 10^{-4}\,\mathrm{m^2})(0.40\,\mathrm{T}) = 3.2\times 10^{-2}\,\mathrm{N\cdot m}.
\]
\qs{Worked example}{A rectangular wire loop has width $a=0.10\,\mathrm{m}$ (horizontal side) and height $b=0.050\,\mathrm{m}$ (vertical side). The loop has $N=100$ turns and carries current $I=2.0\,\mathrm{A}$ in the direction shown: clockwise when viewed from the front (from the $+x$-axis toward the $yz$-plane). The loop sits in a uniform magnetic field $\vec{B} = (0.60\,\mathrm{T})\,\hat{\imath}$ pointing to the right. The normal vector $\hat{n}$ points along the $-\hat{k}$ direction (into the page) by the right-hand rule for clockwise current.