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\begin{document}



\section{26}
\label{sec:orgf4c4750}
\subsection{B from x\textsubscript{dist} On axis of a current loop of radius a}
\label{sec:org00b53ee}
\(B = \frac{\mu_0 I a^2}{2(x_{dist}_{}^2 + a^2)^{3/2}}\)


\subsection{B on axis from magnetic dipole}
\label{sec:org6813b5a}
\(B = \frac{\mu_0}{2 \pi} \frac{\mu}{x^3}\)


\subsection{Net Torque on closed loop with area A at orientation \(\theta\)}
\label{sec:org0128423}
\(\tau = I A B \text{sin}(\theta)\)


\subsection{Field outside, inside any current distribution with line symmetry}
\label{sec:orge95f90c}
\(B = \frac{\mu_0 I}{2 \pi r}\)

\(B = \frac{\mu_0 I r_{inside}}{2 \pi R_{outside}^2}\)

\subsection{Sheet with uniform current density J}
\label{sec:orge9e2a8c}
\subsection{Solenoid with turns n per unit length}
\label{sec:org1db4f9c}

\section{27}
\label{sec:org95cec61}
\subsection{Flux through solenoid with n turns per unit length}
\label{sec:orgdb8f31e}
\(\phi_B = BA = \mu_0 n I \pi R^2\)


\subsection{Flux through rectangular loop with \(l\) parallel to wire at distance \(a\)}
\label{sec:org046d4b3}

\(\phi_B = \int B dA = \int_{a}^{a+w} \frac{\mu_0 I}{2 \pi r} l dr = \frac{\mu_0 I l}{2 \pi} \text{ln}(\frac{a+w}{a})\)


\subsection{Induced current through circuit with bars at distance \(l\) and moving bar velocity \(v\)}
\label{sec:org865a9be}
\(I = \frac{Blv} {r}\)

\subsection{Flux through coil with \(N\) turns turning at frequency \(f\) in field \(B\)}
\label{sec:org252abf7}
\(\phi_B = N B \pi r^2 \text{cos}(2 \pi f t)\)

\(E = - \frac{d \phi_B}{dt}\)

\subsection{Inductance of a solenoid}
\label{sec:orgf5ed5cf}
\(L = \frac{\phi_B}{I} = \mu_0 n^2 A l\)

\subsection{Electric field of a solenoid of radius \(R\) at loop radius \(r\) with \(B = bt\)}
\label{sec:org5396fcb}
\(E = \frac{R^2 b}{2r}\)
\end{document}