Working on PHYS 102 recitation 1 solutions

diff --git a/asymptote/ElectroMag.asy b/asymptote/ElectroMag.asy
index 7db486c512dd7d1f6fa24b8434a7aca534333cf9..4754b15caf9a8bee61ed6cb80d12c30161a760a0 100644 (file)
--- a/asymptote/ElectroMag.asy
+++ b/asymptote/ElectroMag.asy
@@ -3,6 +3,7 @@ import Mechanics;
 
 // ---------------------- Charges -------------------------
 
+// charged particle
 struct Charge {
   pair center;
   real q;
@@ -29,46 +30,49 @@ struct Charge {
   }
 }
 
+// positive charge
 Charge pCharge(pair center=(0,0), real q=1, real radius=2mm, pen outline=currentpen, Label L="")
 {
   Charge c = Charge(center=center, q=q, radius=radius, outline=outline, L=L, fill=red);
   return c;
 }
 
+// negative charge
 Charge nCharge(pair center=(0,0), real q=-1, real radius=2mm, pen outline=currentpen, Label L="")
 {
   Charge c = Charge(center=center, q=q, radius=radius, outline=outline, L=L, fill=blue);
   return c;
 }
 
+// auto-signed charge
+Charge aCharge(pair center=(0,0), real q=1, real radius=2mm, pen outline=currentpen, Label L="")
+{
+  if (q > 0) {
+    Charge c = pCharge(center, q, radius, outline, L);
+  } else {
+    Charge c = nCharge(center, q, radius, outline, L);
+  }
+  return c;
+}
+
 // ---------------------- Vectors -------------------------
 
+// electric field
 Vector EField(pair center=(0,0), real mag=5mm, real dir=0, Label L="")
 {
   Vector v = Vector(center=center, mag=mag, dir=dir, L=L, outline=rgb(1,0.5,0.2)); // orange
   return v;
 }
 
+// magnetic field
 Vector BField(pair center=(0,0), real mag=5mm, real dir=0, Label L="")
 {
   Vector v = Vector(center=center, mag=mag, dir=dir, L=L, outline=rgb(0.1,1,0.2)); // green
   return v;
 }
 
-Vector Velocity(pair center=(0,0), real mag=5mm, real dir=0, Label L="")
-{
-  Vector v = Vector(center=center, mag=mag, dir=dir, L=L, outline=rgb(1,0.1,0.2)); // red
-  return v;
-}
-
 // ---------------------- Forces -------------------------
 
-Vector Force(pair center=(0,0), real mag=5mm, real dir=0, Label L="")
-{
-  Vector v = Vector(center=center, mag=mag, dir=dir, L=L, outline=rgb(0.1,0.2,1)); // blue
-  return v;
-}
-
 // Force of a on b
 Vector CoulombForce(Charge a, Charge b, Label L="", real scale=1mm, real unit=1mm)
 {
@@ -94,80 +98,4 @@ void CoulombForces(Charge c[], real scale=1mm, real unit=1mm)
   }
 }
 
-// ---------------------- Measures -------------------------
-
-// Distance derived from CAD.MeasuredLine
-struct Distance {
-  pair pFrom;
-  pair pTo;
-  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="") {
-    this.pFrom = pFrom;
-    this.pTo = pTo;
-    this.outline = outline;
-    this.L = L;
-  }
-  
-  void draw(picture pic=currentpicture) {
-    picture picF;
-    picture picL;
-    label(picL, L);
-    pair pLabelSize = 1.2 * (max(picL)-min(picL));
-    pair pDiff = pTo - pFrom;
-    path p = (0,0)--pDiff;
-    draw(picF, p, outline, Arrows);
-    label(pic = picF,
-         L = rotate(degrees(pDiff)) * L,
-         position =
-         pDiff/2
-         + unit(rotate(90)*pDiff) * pLabelSize.y / 2);
-    add(pic, picF, pFrom);
-  }
-}
-
-struct Angle {
-  pair B;
-  pair A;
-  pair C;
-  real radius; // radius < 0 for exterior angles.
-  pen outline;
-  Label L;
-
-  void operator init(pair B, pair A, pair C, real radius=5mm, pen outline=currentpen, Label L="") {
-    this.B = B;
-    this.A = A;
-    this.C = C;
-    this.radius = radius;
-    this.outline = outline;
-    this.L = L;
-  }
-  
-  void draw(picture pic=currentpicture) {
-    picture picF;
-    picture picL;
-    label(picL, L);
-    pair pLabelSize = 1.2 * (max(picL)-min(picL));
-    path p = arc(B-A, (0,0), C-A, radius);
-    real t = reltime(p, 0.5);
-    pair P = midpoint(p);
-    pair tang = dir(p, t);
-    
-    draw(picF, p, outline);    
-    label(pic = picF,
-         L = rotate(tang) * L,
-         position =
-         P + unit(P) * pLabelSize.y / 2);
-    add(pic, picF, A);
-  }
-}
-
-// TODO: ihat, ijhat
-
-// ---------------------- Shapes -------------------------
-
-// TODO: ring, plate, block, cylinder, spring, table
-
 

diff --git a/latex/problems/Serway_and_Jewett_4/problem19.07.tex b/latex/problems/Serway_and_Jewett_4/problem19.07.tex
index fdfcf4de213b54aaabfb03645a0957ec822858cc..1e1db2fadb2b03dfdecae9f29bac99b9a0f25fc2 100644 (file)
--- a/latex/problems/Serway_and_Jewett_4/problem19.07.tex
+++ b/latex/problems/Serway_and_Jewett_4/problem19.07.tex
@@ -7,25 +7,33 @@ and the other a charge of $q_2 = -18.0\U{nC}$.
 Find the electric force between the two after they have come to equilibrium.
 \end{problem*} % problem 19.7
 
-\empaddtoprelude{
-  pair A, B;
-  A := origin;
-  B := (3cm, 0);
-}
+%  A := origin;
+%  B := (3cm, 0);
 
 \begin{solution}
 \Part{a}
 \begin{center}
-\begin{empfile}[1a]
-\begin{emp}(0cm, 0cm)
-  label.top("F", draw_force(A, B, -30pt));
-  draw_pcharge(A, 5pt);
-  label.llft(btex $q_1$ etex, A+6pt*dir(-135));
-  draw_ncharge(B, 6pt);
-  label.lrt(btex $q_2$ etex, B+6pt*dir(-45));
-  label.bot("r", draw_length(A, B, 10pt));
-\end{emp}
-\end{empfile}
+\begin{asy}
+import Mechanics;
+import ElectroMag;
+
+real u = 1cm; // Length of 1 m on the page
+real Fscale = .3cm; // Length of 1 N on the page
+qa = 12e-9;
+qb = -18e-9
+
+Charge a = aCharge((0,0)*u, q=qa, L="$q_1$");
+Charge b = aCharge((0,0.03)*u, q=qb, L="$q_2$");
+Distance r = Distance(a.center, b.center, L="$r$");
+Vector Fab = CoulombForce(a, b, scale=Fscale, L="$F$");
+Vector Fba = CoulombForce(b, a, scale=Fscale, L="$F$");
+
+r.draw();
+Fab.draw();
+Fba.draw();
+a.draw();
+b.draw();
+\end{asy}
 \end{center}
 \begin{equation}
  F = k_e \frac{q_1 q_2}{r^2}
@@ -37,17 +45,27 @@ opposites attract.
 
 \Part{b}
 \begin{center}
-\begin{empfile}[1b]
-\begin{emp}(0cm, 0cm)
-  label.top("F", draw_force(A, B, 10pt));
-  draw A--B withcolor (.7,.7,.7) withpen pencircle scaled 1pt;
-  draw_ncharge(A, 3pt);
-  label.llft(btex $Q/2$ etex, A+6pt*dir(-135));
-  draw_ncharge(B, 3pt);
-  label.lrt(btex $Q/2$ etex, B+6pt*dir(-45));
-  label.bot("r", draw_length(A, B, 10pt));
-\end{emp}
-\end{empfile}
+\begin{asy}
+import Mechanics;
+import ElectroMag;
+
+real u = 1cm; // Length of 1 m on the page
+real Fscale = .3cm; // Length of 1 N on the page
+qa = 12e-9;
+qb = -18e-9
+
+Charge a = aCharge((0,0)*u, q=(qa+qb)/2, L="$Q/2$");
+Charge b = aCharge((0,0.03)*u, q=(qa+qb)/2, L="$Q/2$");
+Distance r = Distance(a.center, b.center, L="$r$");
+Vector Fab = CoulombForce(a, b, scale=Fscale, L="$F$");
+Vector Fba = CoulombForce(b, a, scale=Fscale, L="$F$");
+
+r.draw();
+Fab.draw();
+Fba.draw();
+a.draw();
+b.draw();
+\end{asy}
 \end{center}
 The total charge on the both spheres is $Q = q_1 + q_2 = -6.0\U{nC}$.
 The spheres are identical, so at equilibrium, there will be $Q/2 =

diff --git a/latex/problems/Young_and_Freedman_12/problem21.86.tex b/latex/problems/Young_and_Freedman_12/problem21.86.tex
index 8a2cbd0836824e3ddfa7305131416a882f2c95b1..35cbdfc0085d3cbf17e865131a782cb7da2717dc 100644 (file)
--- a/latex/problems/Young_and_Freedman_12/problem21.86.tex
+++ b/latex/problems/Young_and_Freedman_12/problem21.86.tex
@@ -12,4 +12,32 @@ charge must be given to the drop?
 \end{problem*}
 
 \begin{solution}
+\begin{center}
+\begin{asy}
+
+\end{asy}
+\end{center}
+From the forces on the drop in each direction
+\begin{align}
+  F_x &= 0 = m a_x  &
+  F_y &= qE = m a_y \\
+  a_x &= 0  &
+  a_y &= \frac{qE}{m} \;.
+\end{align}
+Now this looks like a projectile motion problem from your
+intro-mechanics class.  No acceleration in the $x$ direction means
+$v_x$ is constant, so the time-of-flight is given by.
+\begin{align}
+  \Delta x &= v_x \Delta t  &
+  \Delta t &= \frac{\Delta x}{v_x} = 1\U{ms} \;.
+\end{align}
+We can plug this time-of-flight into our constant-acceleration
+equation for $y(t)$,
+\begin{align}
+  y(t) &= \frac{a_y}{2}t^2 + v_{y0} t + y_0 \\
+  \Delta y &= \frac{qE}{2m} \Delta t^2 \\
+  q &= \frac{2m \Delta y}{E \Delta t^2}
+    = \frac{2\cdot1.4\E{-11}\U{kg}\cdot3.0\E{-4}\U{m}}{8.0\E{4}\U{N/C}\cdot(1\E{-3}\U{s})^2}
+    = \ans{1.05\E{-13}\U{C}}
+\end{align}
 \end{solution}