From 0938fd91a91e40e3546e366882c01a8968beb066 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Tue, 7 Jul 2009 17:56:33 -0400 Subject: [PATCH] Added recitation week 3 recitation questions --- asymptote/Mechanics.asy | 6 +- .../Young_and_Freedman_12/problem23.21.tex | 45 ++++++++++++++ .../Young_and_Freedman_12/problem23.22.tex | 17 ++++++ .../Young_and_Freedman_12/problem23.25.tex | 15 +++++ .../Young_and_Freedman_12/problem23.27.tex | 16 +++++ .../Young_and_Freedman_12/problem23.58.tex | 16 +++++ .../Young_and_Freedman_12/problem23.60.tex | 42 ++++++++++++++ .../Young_and_Freedman_12/problem23.63.tex | 58 +++++++++++++++++++ 8 files changed, 213 insertions(+), 2 deletions(-) create mode 100644 latex/problems/Young_and_Freedman_12/problem23.21.tex create mode 100644 latex/problems/Young_and_Freedman_12/problem23.22.tex create mode 100644 latex/problems/Young_and_Freedman_12/problem23.25.tex create mode 100644 latex/problems/Young_and_Freedman_12/problem23.27.tex create mode 100644 latex/problems/Young_and_Freedman_12/problem23.58.tex create mode 100644 latex/problems/Young_and_Freedman_12/problem23.60.tex create mode 100644 latex/problems/Young_and_Freedman_12/problem23.63.tex diff --git a/asymptote/Mechanics.asy b/asymptote/Mechanics.asy index 046ac5a..907eac7 100644 --- a/asymptote/Mechanics.asy +++ b/asymptote/Mechanics.asy @@ -118,13 +118,15 @@ Vector Force(pair center=(0,0), real mag=5mm, real dir=0, Label L="") struct Distance { pair pFrom; pair pTo; + real offset; real scale; pen outline; Label L; - void operator init(pair pFrom=(0,0), pair pTo=(5mm,0), real scale=5mm, pen outline=currentpen, Label L="") { + void operator init(pair pFrom=(0,0), pair pTo=(5mm,0), real offset=0, real scale=5mm, pen outline=currentpen, Label L="") { this.pFrom = pFrom; this.pTo = pTo; + this.offset = offset; this.scale = scale; this.outline = outline; this.L = L; @@ -146,7 +148,7 @@ struct Distance { position = pDiff/2 + unit(rotate(90)*pDiff) * pLabelSize.y / 2); //label(pic=picF, L = rotate(degrees(label_rotate)) format("%g", pDiff/scale), position = TODO); - add(pic, picF, pFrom); + add(pic, picF, pFrom+offset*unit(rotate(-90)*pDiff)); } } diff --git a/latex/problems/Young_and_Freedman_12/problem23.21.tex b/latex/problems/Young_and_Freedman_12/problem23.21.tex new file mode 100644 index 0000000..ca5cb0d --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.21.tex @@ -0,0 +1,45 @@ +\begin{problem*}{21} +Two point charges $q_1=+2.40\U{nC}$ and $q_2=-6.50\U{nC}$ are +$0.100\U{m}$ apart. Point $A$ is midway between them; point $B$ is +$0.080\U{m}$ from $q_1$ and $0.060\U{m}$ from $q_2$ (Fig.~23.31). +Take the electric potential to be zero at infinity. Find \Part{a} the +potential at point $A$; \Part{b} the potential at point $B$; \Part{c} +the work done by the electric field on a charge of $2.50\U{nC}$ that +travels from point $B$ to point $A$. +\begin{center} +\begin{asy} +import Mechanics; +import ElectroMag; + +real u = 50cm; +real dOT = 0.1; +real dOB = 0.08; +real dTB = 0.06; + +Charge qO = pCharge((0,0), L="$q_1$"); +Charge qT = nCharge((dOT,0)*u, L="$q_2$"); +pair A = (qO.center+qT.center)/2.0; +// x^2 + y^2 = dOB^2 +// (x-a)^2 + y^2 = dTB^2 where a=qT.center.x +// so +// 2xa - a^2 = dOB^2 - dTB^2 +// x = (dOB^2 - dTB^2 + a^2)/(2a) +// y = (dOB^2-x^2)^0.5 +real Bx = (dOB**2 - dTB**2 + dOT**2)/(2*dOT); +pair B = (Bx,(dOB**2-Bx**2)**0.5)*u; +Distance DOA = Distance(qO.center, A, L=Label("$0.050\U{m}$", align=S)); +Distance DTA = Distance(A, qT.center, L=Label("$0.050\U{m}$", align=S)); +Distance DOB = Distance(qO.center, B, L=Label("$0.080\U{m}$", align=NW)); +Distance DTB = Distance(B, qT.center, L=Label("$0.060\U{m}$", align=NE)); + +DOA.draw(); DTA.draw(); DOB.draw(); DTB.draw(); +dot(A, L="$A$", align=S); +dot(B, L="$B$", align=N); + +qO.draw(); qT.draw(); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Young_and_Freedman_12/problem23.22.tex b/latex/problems/Young_and_Freedman_12/problem23.22.tex new file mode 100644 index 0000000..c9dd3ac --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.22.tex @@ -0,0 +1,17 @@ +\begin{problem*}{22} +Two positive point charges, each of magnitude $q$, are fixed on the +$y$-axis at the points $y=+a$ and $y=-a$. Take the potential to be +zero at an infinite distance from the charges. \Part{a} Show the +positions of the charges in a diagram. \Part{b} What is the potential +$V_0$ at the origin? \Part{c} Show that the potential at any point on +the $x$-axis is +\begin{equation} + V = \frac{1}{4\pi\varepsilon_0}\frac{2q}{\sqrt{a^2+x^2}} +\end{equation} +\Part{d} Graph the potentialon the $x$-axis as a function of $x$ over +the range from $x=-4a$ to $x=4a$. \Part{e} What is the potential when +$x\gg a$? Explain why this result is obtained. +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Young_and_Freedman_12/problem23.25.tex b/latex/problems/Young_and_Freedman_12/problem23.25.tex new file mode 100644 index 0000000..d98b091 --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.25.tex @@ -0,0 +1,15 @@ +\begin{problem*}{25} +A positive charge $q$ is fixed at the point $x=0$, $y=0$, and a +negative charge $-2q$ is fixed at the point $x=a$, $y=0$. \Part{a} +Show the positions of the charges in a diagram. \Part{b} Derive an +expression for the potential $V$ at points on the $x$-axis as a +function of the coordinate $x$. Take $V$ to be zero at an infinite +distance from the charges. \Part{c} At which positions on the +$x$-axis is $V=0$? \Part{d} Graph $V$ at points on the $x$-axis as a +function of $x$ in the range from $x=-2a$ to $x=+2a$. \Part{e} What +does the answer to \Part{b} become when $x\gg a$? Explain why this +result is obtained. +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Young_and_Freedman_12/problem23.27.tex b/latex/problems/Young_and_Freedman_12/problem23.27.tex new file mode 100644 index 0000000..dfa2209 --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.27.tex @@ -0,0 +1,16 @@ +\begin{problem*}{27} +Before the advent of solid-state electronics, vacuum tubes were widely +used in radious and other devices. A simple type of vacuum tube known +as a \emph{diode} consists of essentially two electrodes within a +highly evacuated enclosure. One electrode, the \emph{cathode}, is +maintained at a high temperature and emits electrons from its surface. +A potential difference of a few hundred volts is maintained between +the cathode and the other electrode, known as the \emph{anode}, with +the anode at the higher potential. Suppose that in a particular +vacuum tube the potential of the anode is $295\U{V}$ higher than that +of the cathode. An electron leaves the surface of the cathode with +zero initial speed. Find its speed when it strikes the anode. +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Young_and_Freedman_12/problem23.58.tex b/latex/problems/Young_and_Freedman_12/problem23.58.tex new file mode 100644 index 0000000..0be5b32 --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.58.tex @@ -0,0 +1,16 @@ +\begin{problem*}{58} +\Part{a} Calculate the potential energy of a system of two small +spheres, one carrying a charge of $2.00\U{$\mu$C}$ and the other a +charge of $-3.50\U{$\mu$C}$, with their centers separated by a +distance of $0.250\U{m}$. Assume zero potential energy when the +charges are infinitely separated. \Part{b} Suppose that one of the +spheres is held in place and the other sphere, which has a mass of +$1.50\U{g}$, is shot away from it. What minimum initial speed would +the moving sphere need in order to escape completely from the +attraction of the fixed sphere? (To escape, the moving sphere would +have to reach a velocity of zero when it was infinitely distant from +the fixed sphere.) +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Young_and_Freedman_12/problem23.60.tex b/latex/problems/Young_and_Freedman_12/problem23.60.tex new file mode 100644 index 0000000..c131511 --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.60.tex @@ -0,0 +1,42 @@ +\begin{problem*}{60} +A small sphere with mass $1.50\U{g}$ hangs by a thread between two +parallel vertical plates $5.00\U{cm}$ apart (Fig.~23.36). The plates +are insulateing and have uniform surface charge densitied $+\sigma$ +and $-\sigma$. The charge on the sphere is $q=8.90\E{-6}\U{C}$. What +potential difference between the plates will cause the thread to +assume an angle of $30.0\dg$ with the vertical? +\begin{center} +\begin{asy} +import Mechanics; +import ElectroMag; + +real u = 0.3cm; +real L = 4; +real ds = 5; +real phi = 30; +real dy = 1.8*L*Cos(phi); +int n=3; + +Charge q = pCharge(dir(-90+phi)*L*u, q=1, L="$q$"); +Wire wire = Wire((0,0), q.center); +Angle theta = Angle(q.center, (0,0), (0,-1), L="$\theta$"); +Surface s = Surface((ds/2,0)*u, (-ds/2,0)*u); +Wire right_plate = Wire((ds,0)*u, (ds,-dy)*u, outline=green); +Wire left_plate = Wire((-ds,0)*u, (-ds,-dy)*u, outline=green); +Distance Ds = Distance(left_plate.pTo, right_plate.pTo, + L=Label("$5.00\U{cm}$", align=S)); + +left_plate.draw(); +right_plate.draw(); +s.draw(); +Ds.draw(); +wire.draw(); +draw((0,0)--(0,q.center.y), dashed); +q.draw(); +theta.draw(); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} diff --git a/latex/problems/Young_and_Freedman_12/problem23.63.tex b/latex/problems/Young_and_Freedman_12/problem23.63.tex new file mode 100644 index 0000000..264f5e9 --- /dev/null +++ b/latex/problems/Young_and_Freedman_12/problem23.63.tex @@ -0,0 +1,58 @@ +\begin{problem*}{63} +Cathode-ray tubes (CRTs) are often found in oscilloscopes and computer +monitors. In Fig.~23.38 an electron with an initial speed of +$6.50\E{6}\U{m/s}$ is projected along the axis midway between the +deflection plates of a cathode-ray tube. The uniform electric field +between the plates has a magnitude of $1.10\E{3}\U{V/m}$ and is +upward. \Part{a} What is the force (magnitude and direction) on the +electron when it is between the plates? \Part{b} What is the +acceleration of the electron (magnitude and direction) when acted on +by the force in \Part{a}? \Part{c} How far below the axis has the +electron moved when it reaches the end of the plates? \Part{d} At +what angle with the axis is it moving as it leaves the +plates? \Part{e} How far below the axis will it strike the +fluorescent screen $S$? +\begin{center} +\begin{asy} +import Mechanics; +import ElectroMag; + +real u = 0.5cm; +real L = 6; +real s = 12; +real dy = 2; +int n=3; + +Charge q = nCharge((-1,0)*u, q=1); +Vector v = Velocity(q.center, L="$v$"); +Wire top_plate = Wire((0,0.5*dy)*u, (L,.5*dy)*u); +Wire bottom_plate = Wire((0,-.5*dy)*u, (L,-.5*dy)*u); +Wire screen = Wire((L+s,-.7*dy)*u, (L+s,+.7*dy)*u, L="screen"); + +Vector e; +for (int i=0; i