From: W. Trevor King Date: Thu, 31 May 2012 19:47:54 +0000 (-0400) Subject: Add problems for Serway and Jewett v8's chapter 31. X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=8a8af47f4c40c67f5f910950c54a9ab6f4519da6;p=course.git Add problems for Serway and Jewett v8's chapter 31. --- diff --git a/latex/problems/Serway_and_Jewett_8/problem31.23.tex b/latex/problems/Serway_and_Jewett_8/problem31.23.tex new file mode 100644 index 0000000..b2618d2 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem31.23.tex @@ -0,0 +1,43 @@ +\begin{problem*}{31.23} +Figure~P31.23 shows a top view of a bar that can slide on two +frictionless rails. The resistor is $R=6.00\U{\Ohm}$, and a +$2.50\U{T}$ magnetic field is directed perpendicularly downward, into +the paper. Let $l=1.20\U{m}$. \Part{a} Calculate the applied force +required to move the bar to the right at a constant speed of +$2.00\U{m/s}$. \Part{b} At what rate is energy delivered to the +resistor? +\begin{center} +% +-------+-------- +% Z x x^x | x x Bin +% R Z l | |--> F_app +% Z x xvx | x x x x +% +-------+-------- +\begin{asy} +import Mechanics; +import ElectroMag; +import Circ; + +real u = 1cm; +real w = 1mm; + +MultiTerminal R = resistor(dir=90, "$R$", draw=false); +real rlen = R.terminal[1].y - R.terminal[0].y; +Vector B = BField(phi=-90); +vector_field(R.center + (0.75*u, 0), width=1.5*u, height=rlen, v=B); +R.draw(); +real yt = R.terminal[1].y; +real yb = R.terminal[0].y; +wire((0, yt), (1.5*u, yt)); +wire((0, yb), (1.5*u, yb)); +pair p = (u,(yt+yb)/2); +Vector F = Force(p, Label("$F_\text{app}$", position=EndPoint)); F.draw(); +Block block = Block(p, width=w, height=rlen); block.draw(); +Distance Dl = Distance((u/2, yt), (u/2, yb), Label("$l$", embed=Shift)); +Dl.draw(); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} + diff --git a/latex/problems/Serway_and_Jewett_8/problem31.30.tex b/latex/problems/Serway_and_Jewett_8/problem31.30.tex new file mode 100644 index 0000000..b441fdd --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem31.30.tex @@ -0,0 +1,39 @@ +\begin{problem*}{31.30} +A rectangular coil with resistance $R$ has $N$ turns, each of length +$l$ and width $w$ as shown in Figure~P31.30. The coil moves into a +uniform magnetic fiield $\vect{B}$ with constant velocity $\vect{v}$. +What are the magnitude and direction of the total magnetic force on +the coil \Part{a} as it enters the magnetic field, \Part{b} as it +moves within the field, and \Part{c} as it leaves the field? +\begin{center} +% x x x Bin +% +--+ v x x x x +% w| |-> x x x x +% +--+ x x x x +% l x x x x +\begin{asy} +import Mechanics; +import ElectroMag; + +real w = 5mm; +real l = 6mm; +real u = 1.5cm; + +Vector B = BField(phi=-90); +vector_field((l/2 + 7mm + u/2, 0), width=u, height=u, v=B, outline=dashed); +Vector v = Velocity((l/2, 0), "$\vect{v}$"); v.draw(); +path p = scale(l, w)*shift((-0.5, -0.5))*unitsquare; +draw(p); +draw(shift(1.5pt*dir(-45))*p); +Distance Dl = Distance((-l/2, -w/2), (l/2, -w/2), "$l$", offset=6pt); +Dl.draw(); +Distance Dw = Distance((-l/2, w/2), (-l/2, -w/2), Label("$w$", embed=Shift), + offset=6pt); +Dw.draw(); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} + diff --git a/latex/problems/Serway_and_Jewett_8/problem31.31.tex b/latex/problems/Serway_and_Jewett_8/problem31.31.tex new file mode 100644 index 0000000..5cbcc58 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem31.31.tex @@ -0,0 +1,51 @@ +\begin{problem*}{31.31} +Two parallel rails with negligable resistance are $10.0\U{cm}$ apart +and are connected by a resistor of resistance $R_3=5.00\U{\Ohm}$. The +circuit also contains two metal rods having resistances of +$R_1=10.0\U{\Ohm}$ and $R_2=15.0\U{\Ohm}$ sliding along the rails +(Fig.~P31.31). The rods are pulled away from the resistor at constant +speeds of $v_1=4.00\U{m/s}$ and $v_2=2.00\U{m/s}$, respectively. A +uniform magnetic field of magnitude $B=0.0100\U{T}$ is applied +perpendicular to the plane of the rails. Determine the current in +$R_3$. +\begin{center} +% --+-----+-----+-- +% x | x x Z x x | x +% <-| x x ZR3 x |-> +% v1| x x Z x x |v2 +% --+-----+-----+-- +% R1 R2 +\begin{asy} +import Mechanics; +import ElectroMag; +import Circ; + +real u = 1cm; +real w = 1mm; + +MultiTerminal R3 = resistor(dir=90, "$R_3$", draw=false); +real rlen = R3.terminal[1].y - R3.terminal[0].y; +Vector B = BField(phi=-90); +vector_field(R3.center, width=3*u, height=rlen, v=B); +R3.draw(); +real yt = R3.terminal[1].y; +real yb = R3.terminal[0].y; +wire((-1.5*u, yt), (1.5*u, yt)); +wire((-1.5*u, yb), (1.5*u, yb)); +dot(R3.terminal[0]); +dot(R3.terminal[1]); +pair p1 = (-u,(yt+yb)/2); +Vector v1 = Velocity(p1, dir=180, "$v_1$"); v1.draw(); +Block R1 = Block(p1, width=w, height=rlen); R1.draw(); +label("$R_1$", (p1.x, yb), align=S); +pair p2 = (-p1.x, p1.y); +Vector v1 = Velocity(p2, "$v_2$"); v1.draw(); +Block R2 = Block(p2, width=w, height=rlen); R2.draw(); +label("$R_2$", (p2.x, yb), align=S); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} + diff --git a/latex/problems/Serway_and_Jewett_8/problem31.45.tex b/latex/problems/Serway_and_Jewett_8/problem31.45.tex new file mode 100644 index 0000000..5acdf74 --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem31.45.tex @@ -0,0 +1,59 @@ +\begin{problem*}{31.45} +A circular coil enclosing an area $A=0.0100\U{m$^2$}$ is made of $200$ +turns of copper wire as shown in Figure~P31.45. Initially, a uniform +magnetic field of magnitude $B=1.10\U{T}$ points upward in a direction +perpendicular to the plane of the coil. The direction of the field +then reverses in a time interval $\Delta t$. Determine how much +charge enters one end of the resistor during this time interval if +$R=5.00\U{Ohm}$. +\begin{center} +% B ^ ^ ^ +% | | | (from back of coil) +% +-+-+---+ +% +-+-+ Z R +% +-+-+ Z +% +-+-+---+ +% | | | (from font of coil) +\begin{asy} +import Mechanics; +import ElectroMag; +import Circ; + +real dx = 5mm; +real r = 5mm; +int n = 10; // number of coil loops +real tense = 8; // increasing tension flattens the coil loops + +MultiTerminal R = resistor(dir=90, Label("$R$", align=E)); +real rlen = R.terminal[1].y - R.terminal[0].y; +real xr = R.center.x - dx; +real xl = xr - 2*r; +real dy = rlen / n; +for (int i = 0; i < n; i += 1) { // back sides of coil + pair dout = S; + if (i == n-1) { + dout = E; + } + real y0 = R.terminal[0].y + i * dy; + draw((xl, y0 + dy/2){N}..tension tense ..{dout}(xr, y0 + dy)); +} +Vector B = BField(dir=90); +B.outline += linewidth(0.5mm); +vector_field(((xl+xr)/2, R.center.y+rlen/3), width=2*r, height=2*rlen, v=B); +for (int i = 0; i < n; i += 1) { // front sides of coil + pair din = S; + if (i == 0) { + din = W; + } + real y0 = R.terminal[0].y + i * dy; + draw((xr, y0){din}..tension tense ..{N}(xl, y0 + dy/2)); +} +draw((xr, R.terminal[0].y) -- R.terminal[0]); +draw((xr, R.terminal[1].y) -- R.terminal[1]); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} + diff --git a/latex/problems/Serway_and_Jewett_8/problem31.46.tex b/latex/problems/Serway_and_Jewett_8/problem31.46.tex new file mode 100644 index 0000000..e03c4ab --- /dev/null +++ b/latex/problems/Serway_and_Jewett_8/problem31.46.tex @@ -0,0 +1,28 @@ +\begin{problem*}{31.46} +A circular loop of wire of resistance $R=0.500\U{\Ohm}$ and radius +$r=8.00\U{cm}$ is in a uniform magnetic field directed out of the page +as in Figure~P31.46. If a clockwise current of $I=2.50\U{mA}$ is +induced in the loop, \Part{a} is the magnetic field increasing or +decreasing in time? \Part{b} Find the rate at which the field is +changing in time. +\begin{center} +\begin{asy} +import Mechanics; +import ElectroMag; + +real r = 1cm; +real dr = 6pt; + +Vector B = BField(phi=90); +vector_field(width=2.5*r, height=2.5*r, v=B); +draw(scale(r)*unitcircle); +Distance Dr = Distance((0,0), (r,0), "$r$"); Dr.draw(); +draw(arc((0,0), r+dr, angle1=10, angle2=-10), CurrentPen, ArcArrow); +label("$I$", (r+dr, 0), align=E); +\end{asy} +\end{center} +\end{problem*} + +\begin{solution} +\end{solution} +