From: W. Trevor King Date: Wed, 25 Jul 2012 12:42:42 +0000 (-0400) Subject: Fix subscripting (E{600} -> E_{600}) in Serway and Jewett v8's 24.13. X-Git-Url: http://git.tremily.us/?p=course.git;a=commitdiff_plain;h=538b0f767f91732bb27fc87062421fab119d4127;hp=2987081fa75539cd4a45b632a264d2c320ec0698 Fix subscripting (E{600} -> E_{600}) in Serway and Jewett v8's 24.13. --- diff --git a/latex/problems/Serway_and_Jewett_8/problem24.13.tex b/latex/problems/Serway_and_Jewett_8/problem24.13.tex index 98034e8..6b19c69 100644 --- a/latex/problems/Serway_and_Jewett_8/problem24.13.tex +++ b/latex/problems/Serway_and_Jewett_8/problem24.13.tex @@ -17,14 +17,14 @@ at the end caps. If the area of the end cap is $A$, that flux is where $E_{500}=120\U{N/C}$ and $E_{600}=100\U{N/C}$. From Gauss's law, \begin{align} - \Phi_E &= \frac{q_\text{in}}{\varepsilon_0} = (E_{500}-E{600})A \\ - q_\text{in} &= (E_{500}-E{600})A\varepsilon_0 \;. + \Phi_E &= \frac{q_\text{in}}{\varepsilon_0} = (E_{500}-E_{600})A \\ + q_\text{in} &= (E_{500}-E_{600})A\varepsilon_0 \;. \end{align} This gives an average volume charge density of \begin{equation} \rho \equiv \frac{q_\text{in}}{V} - = \frac{(E_{500}-E{600})A\varepsilon_0}{A(h_{600}-h_{500})} - = \frac{E_{500}-E{600}}{h_{600}-h_{500}}\varepsilon_0 + = \frac{(E_{500}-E_{600})A\varepsilon_0}{A(h_{600}-h_{500})} + = \frac{E_{500}-E_{600}}{h_{600}-h_{500}}\varepsilon_0 = \frac{20\U{N/C}}{100\U{m}}\cdot8.85\E{-12}\U{C$^2$/N$\cdot$m$^2$} = \ans{1.77\E{-12}\U{C/m$^3$}} \;. \end{equation}