\begin{center}
\begin{asy}
import Circ;
-TwoTerminal Bc = source((0,0), DC, 90, "", "$3.0\U{V}$");
+TwoTerminal Bc = source((0,0), ang=90, type=DC, "", "$3.0\U{V}$");
TwoTerminal Rcb = resistor(Bc.beg, ang=-90, "$10\U{\Ohm}$", "");
TwoTerminal Rca = resistor(Bc.end, ang=180, "", "$2\U{\Ohm}$");
pair Jtop = Rca.end, Jbot = (Jtop.x,Rcb.end.y);
\begin{asy}
import Circ;
real u = 0.5cm;
-TwoTerminal B = source((0,0), DC, 90, "$45\U{V}$", "$V$");
+TwoTerminal B = source((0,0), ang=90, type=DC, "$45\U{V}$", "$V$");
pair a = B.end+(0,u);
pair b = B.beg-(0,u);
-TwoTerminal Ra = resistor(a, normal, 0, "$38\U{k\Ohm}$", "$R_1$");
-TwoTerminal Rb = resistor(Ra.end, normal, 0, "$27\U{k\Ohm}$", "$R_2$");
-TwoTerminal I = current((Rb.end.x, (a.y+b.y)/2), -90, "", "$I$");
+TwoTerminal Ra = resistor(a, "$38\U{k\Ohm}$", "$R_1$");
+TwoTerminal Rb = resistor(Ra.end, "$27\U{k\Ohm}$", "$R_2$");
+TwoTerminal I = current((Rb.end.x, (a.y+b.y)/2), ang=-90, "", "$I$");
wire(Rb.end, I.beg, nsq);
wire(I.end, b, udsq);
wire(b, B.beg, nsq);
\begin{asy}
import Circ;
real u = 0.5cm;
-TwoTerminal B = source((0,0), DC, 90, "$45\U{V}$", "$V$");
+TwoTerminal B = source((0,0), ang=90, type=DC, "$45\U{V}$", "$V$");
pair a = B.end+(0,u);
pair b = B.beg-(0,u);
-TwoTerminal Ra = resistor(a, normal, 0, "$38\U{k\Ohm}$", "$R_1$");
-TwoTerminal Ia = current(Ra.end, 0, "", "$I_1$");
-TwoTerminal Rv = resistor(a+(0,4u), normal, 0, "$95\U{k\Ohm}$", "$R_v$");
-TwoTerminal Iv = current(Rv.end, 0, "", "$I_v$");
-TwoTerminal Rb = resistor(Ia.end, normal, 0, "$27\U{k\Ohm}$", "$R_2$");
-TwoTerminal I = current((Rb.end.x, (a.y+b.y)/2), -90, "", "$I_T$");
+TwoTerminal Ra = resistor(a, "$38\U{k\Ohm}$", "$R_1$");
+TwoTerminal Ia = current(Ra.end, "", "$I_1$");
+TwoTerminal Rv = resistor(a+(0,4u), "$95\U{k\Ohm}$", "$R_v$");
+TwoTerminal Iv = current(Rv.end, "", "$I_v$");
+TwoTerminal Rb = resistor(Ia.end, "$27\U{k\Ohm}$", "$R_2$");
+TwoTerminal I = current((Rb.end.x, (a.y+b.y)/2), ang=-90, "", "$I_T$");
wire(Rb.end, I.beg, nsq);
wire(I.end, b, udsq);
wire(b, B.beg, nsq);
pair P = (0,0);
Vector Et = EField(t*P, u*E, 0, L="$E_t$");
-Vector Eb = EField(t*P, u*E, 140, L="$E_b$");
+Vector Eb = EField(t*P, u*E, 140, L=Label("$E_b$", align=LeftSide));
Angle a = Angle(Et.pTip(), Et.center, Eb.pTip(), Et.mag/2, L="$\Delta \phi$");
Et.draw();
Surface surf = Surface(pFrom=(-.7u,-a/2), pTo=(2u,-a/2));
Block b = Block(center=(0,0), width=a);
Spring spring = Spring(pFrom=(b.center+(a/2,0)), pTo=(2u,0));
-Vector Fspring = Force(b.center, mag=2a, dir=0, L="$F_s$");
+Vector Fspring = Force(b.center, mag=2a, dir=0, L=Label("$F_s$", align=N));
Vector Fexternal = Force(b.center, mag=2a, dir=180, L="$F_e$");
Fspring.draw();
pair source = u*dir(theta/2);
pair target = u*dir(-theta/2);
-Angle a = Angle(source, (0,0), (source+target)/2, radius=1cm, L=" $\theta/2$");
-// space before text in the label because inline-asymptote doesn't know
-// how big the label will be when it sets the positions. See
-// http://asymptote.sourceforge.net/doc/LaTeX-usage.html
-// So we add some space by hand.
+Angle a = Angle(source, (0,0), (source+target)/2, L="$\theta/2$");
a.draw();
draw(target--(0,0)--source);
draw((0,0)--((source+target)/2));
pair SpeakerB = (0,2u);
pair Listener = (3u,0);
-// Extra label text for spacing with inline asymptote
-Distance dAB = Distance(SpeakerA, SpeakerB, Label("$L=2\U{m}$", "L=2 m"));
-Distance dAL = Distance(Listener, SpeakerA, Label("$d_a=3\U{m}$", "da=3 m"));
-Distance dBL = Distance(SpeakerB,Listener,
- Label("$\qquad\qquad\qquad\qquad\qquad d_b=\sqrt{L^2+d_a^2}=3.606\U{m}$",
- "$d_b=\sqrt{L^2+d_a^2}=3.606mm$"));
+Distance dAB = Distance(SpeakerA, SpeakerB, L=Label("$L=2\U{m}$", align=W));
+Distance dAL = Distance(SpeakerA, Listener,
+ L=Label("$d_a=3\U{m}$", position=Relative(0.4), align=S));
+Distance dBL = Distance(SpeakerB, Listener,
+ Label("$d_b=\sqrt{L^2+d_a^2}=3.606\U{m}$", align=NE));
dot(SpeakerA);
-label("$S_a$", SpeakerA, W);
+label("$S_a$", SpeakerA, align=SW);
dot(SpeakerB);
-label("$S_b$", SpeakerB, W);
+label("$S_b$", SpeakerB, align=NW);
dot(Listener);
-label("Listener", Listener, E);
+label("Listener", Listener, align=S);
dAB.draw();
dAL.draw();
dBL.draw();
Block vib = Block((-w/2,0), width=w, height=w/3, L="vibrator");
Block obj = Block((L+(1+cos(pi/4))*A, -L/3), width=vib.height, L="$m$");
-Distance dL = Distance((0,vib.height/2), (L,vib.height/2), L=Label("$L$", N));
+Distance dL = Distance((0,vib.height/2), (L,vib.height/2),
+ L=Label("$L$", align=LeftSide));
draw(p, blue);
draw(yscale(-1)*p, blue+dotted);
Charge a = aCharge((0,0)*u, q=qa, L="$q_1$");
Charge b = aCharge((0.03,0)*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="$F$");
-Fab.mag /= 10.0; // Not part of Fscale b/c of rounding
-Fba.mag /= 10.0;
-
+Charge cs[] = {a, b};
+CoulombForces(c=cs, scale=b.center().x, unit=2cm/abs(qa*qb));
r.draw();
-Fab.draw();
-Fba.draw();
a.draw();
b.draw();
\end{asy}
real qa = 12e-9;
real qb = -18e-9;
-Charge a = aCharge((0,0)*u, q=(qa+qb)/2, L="$Q/2$");
-Charge b = aCharge((0.03,0)*u, q=(qa+qb)/2, L="$Q/2$");
+Charge a = aCharge((0,0)*u, q=(qa+qb)/2, L=Label("$Q/2$", align=N));
+Charge b = aCharge((0.03,0)*u, q=(qa+qb)/2, L=Label("$Q/2$", align=S));
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="$F$");
-
+Charge cs[] = {a, b};
+CoulombForces(c=cs, scale=b.center().x, unit=3cm/(qa+qb)^2);
r.draw();
-Fab.draw();
-Fba.draw();
a.draw();
b.draw();
\end{asy}
draw_ijhat();
Charge a = aCharge(q=-2.5, "$q_1$"); a.draw();
Charge b = aCharge(q=6.0, (1u, 0), "$q_2$"); b.draw();
-Distance dab = Distance(a.center(), b.center(), offset=12pt, L="$1\U{m}$");
+Distance dab = Distance(a.center(), b.center(), offset=24pt, L="$1\U{m}$");
dab.draw();
\end{asy}
\end{center}
draw_ijhat();
Charge a = aCharge(q=-2.5, "$q_1$"); a.draw();
Charge b = aCharge(q=6.0, (1u, 0), "$q_2$"); b.draw();
-Distance dab = Distance(a.center(), b.center(), offset=12pt, L="$1\U{m}$");
+Distance dab = Distance(a.center(), b.center(), offset=24pt, L="$1\U{m}$");
dab.draw();
pair c = (-1.82u, 0);
-Distance dac = Distance(c, a.center(), offset=24pt, L="$r_1$"); dac.draw();
-Distance dbc = Distance(c, b.center(), offset=36pt, L="$r_2$"); dbc.draw();
+Distance dac = Distance(c, a.center(), offset=36pt, L="$r_1$"); dac.draw();
+Distance dbc = Distance(c, b.center(), offset=48pt, L="$r_2$"); dbc.draw();
Charge cs[] = {a, b};
CoulombEFields(c, cs, scale=u, unit=u);
dot(c);
pair p = (x*u, -v/w*u);
real r = A*u;
-Vector xaxis = Vector((-1.4r,0), mag=2.8r, dir=0, gray(0.6), "$x$");
+Vector xaxis = Vector((-1.4r,0), mag=2.8r, dir=0, gray(0.6),
+ L=Label("$x$", position=EndPoint, align=RightSide));
xaxis.draw();
-Vector yaxis = Vector((0,1.4r), mag=2.8r, dir=-90, gray(0.6), "$v/\omega$");
+Vector yaxis = Vector((0,1.4r), mag=2.8r, dir=-90, gray(0.6),
+ L=Label("$v/\omega$", position=EndPoint, align=RightSide));
yaxis.draw();
draw(scale(r)*unitcircle);
real a=6.4; // degrees
real force=2u; // magnitude
-Pendulum p = makePendulum(angleDeg=a, length=2u, stringL="$L$");
+Pendulum p = makePendulum(angleDeg=a, length=2u,
+ stringL=Label("$L$", align=E, embed=Shift));
p.mass.lc.radius = 0;
-Vector fg = Force(p.mass.center()/2, dir=-90, mag=force, L="$F_g$");
+Vector fg = Force(p.mass.center()/2, dir=-90, mag=force,
+ L=Label("$F_g$", position=EndPoint, align=W));
Vector fgtan = Force(p.mass.center()/2, dir=a-180, mag=force*sin(a),
- L=Label("$F_{\tan}$"));
-Vector v = Velocity(p.mass.center(), dir=a, mag=0.5u, L="$v$");
+ L=Label("$F_{\tan}$", position=EndPoint, align=W));
+Vector v = Velocity(p.mass.center(), dir=a, mag=0.5u,
+ L=Label("$v$", position=EndPoint, align=S));
fg.draw();
fgtan.draw();
real u = 1cm;
Pendulum p = makePendulum(angleDeg=25, length=2u,
- angleL="$\theta$", stringL="$r$");
+ angleL="$\theta$", stringL=Label("$r$", embed=Shift));
Spring s = Spring(pFrom=p.mass.center(), pTo=p.mass.center()+2u,
- unstretchedLength=2u, L="$k$");
-Vector fs = Force(p.mass.center(), dir=180, mag=5mm, L="$F_s$");
-Vector fg = Force(p.mass.center(), dir=-90, mag=7mm, L="$F_g$");
+ unstretchedLength=2u, L="$k$");
+Vector fs = Force(p.mass.center(), dir=180, mag=5mm,
+ L=Label("$F_s$", position=EndPoint, align=W));
+Vector fg = Force(p.mass.center(), dir=-90, mag=7mm,
+ L=Label("$F_g$", position=EndPoint, align=W));
s.draw();
fs.draw();
real xstart = 8r;
real mag = 16r;
-Vector x = Vector(center=(xstart*u,0), mag=mag*u, dir=180, L="signal");
+Vector x = Vector(center=(xstart*u,0), mag=mag*u, dir=180,
+ L=Label("signal", position=EndPoint, align=N));
path a = scale(r*u)*unitcircle; // antenna
draw(a);
Spring Su = Spring(pFrom=(0,0), pTo=(4u,0), k=500, L=Label("$m$", N));
Spring Sc = Spring(pFrom=(0,-2u), pTo=(3u,-2u), k=500, L=Label("$m'$", N));
Distance d = Distance(pFrom=(4u,-2u), pTo=(3u,-2u), scale=u,
- L=rotate(90)*Label("$1\U{cm}$", S));
+ L=rotate(90)*Label("$1\U{cm}$", align=S));
Su.draw();
Sc.draw();
d.draw();
dot((0,0)); // start
dot(f); // finish
-Vector T1 = Vector((0,0), mag=length(f), dir=degrees(f), "tortoise");
+Vector T1 = Vector((0,0), mag=length(f), dir=degrees(f),
+ L=Label("tortoise"));
T1.draw();
-Vector H1 = Vector((0,0), mag=length(h1), dir=degrees(h1), "hare");
+Vector H1 = Vector((0,0), mag=length(h1), dir=degrees(h1),
+ L=Label("hare", align=S));
H1.draw();
-Vector H2 = Vector(h1, mag=length(h2-h1), dir=degrees(h2-h1), "pause");
+Vector H2 = Vector(h1, mag=length(h2-h1), dir=degrees(h2-h1),
+ L=Label("pause", align=E));
H2.draw();
-Vector H3 = Vector(h2, mag=length(f-h2), dir=degrees(f-h2), "hare");
+Vector H3 = Vector(h2, mag=length(f-h2), dir=degrees(f-h2),
+ L=Label("hare", align=N));
H3.draw();
xaxis("$x$");
pair a = (2u, 6u);
pair b = (3u, -2u);
-Vector A = Vector((0,0), mag=length(a), dir=degrees(a), "$\vect{A}$");
+Vector A = Vector((0,0), mag=length(a), dir=degrees(a),
+ L=Label("$\vect{A}$", align=W));
A.draw();
-Vector B = Vector(a, mag=length(b), dir=degrees(b), "$\vect{B}$");
+Vector B = Vector(a, mag=length(b), dir=degrees(b),
+ L=Label("$\vect{B}$", align=N));
B.draw();
-Vector C = Vector((0,0), mag=length(a+b), dir=degrees(a+b), "$\vect{C}$");
+Vector C = A + B;
+C.label = Label("$\vect{C}$", align=SE);
C.draw();
\end{asy}
\hspace{1cm}
pair a = (2u, 6u);
pair b = (3u, -2u);
-Vector A = Vector((0,0), mag=length(a), dir=degrees(a), "$\vect{A}$");
+Vector A = Vector((0,0), mag=length(a), dir=degrees(a),
+ L=Label("$\vect{A}$", align=E));
A.draw();
-Vector B = Vector(a-b, mag=length(b), dir=degrees(b), "$\vect{B}$");
+Vector B = Vector(a-b, mag=length(b), dir=degrees(b),
+ L=Label("$\vect{B}$", align=N));
B.draw();
-Vector D = Vector((0,0), mag=length(a-b), dir=degrees(a-b), "$\vect{D}$");
+Vector D = A - B;
+D.label = Label("$\vect{D}$", align=W);
D.draw();
\end{asy}
\end{center}
Angle a = Angle((1,0), (0,0), d, red, "$-82.9\dg$");
a.draw();
-Vector vd = Vector((0,0), mag=length(d), dir=degrees(d), "$(1,-8)$");
+Vector vd = Vector((0,0), mag=length(d), dir=degrees(d),
+ L=Label("$(1,-8)$", position=EndPoint, align=W));
vd.draw();
Angle A = Angle((1,0), (0,0), D, blue, "$97.1\dg$");
A.draw();
-Vector vD = Vector((0,0), mag=length(D), dir=degrees(D), "$(-1,8)$");
+Vector vD = Vector((0,0), mag=length(D), dir=degrees(D),
+ L=Label("$(-1,8)$", position=EndPoint, align=W));
vD.draw();
Angle r = Angle(d, (0, 0), D, radius=15mm, green, "$180.0\dg$");
r.draw();
Vector vDrop = Vector((0,0), mag=length(drop), dir=degrees(drop), "drop");
vDrop.draw();
Vector vScramble = Vector(
- drop, mag=length(scramble), dir=degrees(scramble), "scramble");
+ drop, mag=length(scramble), dir=degrees(scramble),
+ L=Label("scramble", align=W));
vScramble.draw();
Vector vPass = Vector(drop+scramble, mag=length(pass), dir=degrees(pass),
"pass");
Angle A3 = Angle((0,-1), (0,0), dir(-90+theta2), "$\theta_2$");
Vector F1 = Force((0,0), mag=T1, dir=180-theta1, "$\vect{F}_1$");
-Vector F2 = Force((0,0), mag=T2, dir=theta2, "$\vect{F}_2$");
+Vector F2 = Force((0,0), mag=T2, dir=theta2,
+ L=Label("$\vect{F}_2$", position=EndPoint, align=N));
Vector F3 = Force((0,0), mag=T3, dir=-90, "$\vect{F}_3$");
a1.draw();
real m2 = 6;
real t = g*m1*m2/(m1+m2)*(1+Sin(theta));
-Vector T = Force((0,0), mag=t, dir=90, "$T$");
+Vector T = Force((0,0), mag=t, dir=90,
+ L=Label("$T$", position=EndPoint, align=E));
T.draw();
-Vector G = Force((0,0), mag=m1*g, dir=-90, "$m_1 g$");
+Vector G = Force((0,0), mag=m1*g, dir=-90,
+ L=Label("$m_1 g$", position=EndPoint, align=E));
G.draw();
dot("$m_1$", (0,0), W);
\end{asy}
real m2 = 6;
real t = g*m1*m2/(m1+m2)*(1+Sin(theta));
-Vector T = Force((0,0), mag=t, dir=180-theta, "$T$");
+Vector T = Force((0,0), mag=t, dir=180-theta,
+ L=Label("$T$", position=EndPoint, align=NE));
T.draw();
-Vector N = Force((0,0), mag=m2*g*Cos(theta), dir=90-theta, "$N$");
+Vector N = Force((0,0), mag=m2*g*Cos(theta), dir=90-theta,
+ L=Label("$N$", position=EndPoint, align=E));
N.draw();
-Vector G = Force((0,0), mag=m2*g, dir=-90, "$m_2 g$");
+Vector G = Force((0,0), mag=m2*g, dir=-90,
+ L=Label("$m_2 g$", position=EndPoint, align=E));
G.draw();
dot("$m_2$", (0,0), SE);
\end{asy}
real mu = 0.1;
real t = f*m1/(m1+m2);
-Vector G = Force((0,0), mag=m1*g*vscale, dir=-90, "$m_1g$");
-Vector N = Force((0,0), mag=m1*g*vscale, dir=90, "$\vect{N}_1$");
-Vector T = Force((0,0), mag=t, dir=0, "$T$");
-Vector F = Force((0,0), mag=mu*m1*g, dir=180, "$\vect{F}_{f1}$");
+Vector G = Force((0,0), mag=m1*g*vscale, dir=-90,
+ L=Label("$m_1g$", position=EndPoint, align=S));
+Vector N = Force((0,0), mag=m1*g*vscale, dir=90,
+ L=Label("$\vect{N}_1$", position=EndPoint, align=NE));
+Vector T = Force((0,0), mag=t, dir=0,
+ L=Label("$T$", position=EndPoint, align=NE));
+Vector F = Force((0,0), mag=mu*m1*g, dir=180,
+ L=Label("$\vect{F}_{f1}$", position=EndPoint, align=W));
G.draw();
N.draw();
real t = f*m1/(m1+m2);
real dy=1mm;
-Vector G = Force((0,0), mag=m2*g*vscale, dir=-90, "$m_2g$");
-Vector N = Force((0,0), mag=m2*g*vscale, dir=90, "$\vect{N}_2$");
-Vector E = Force((0,0), mag=f, dir=0, "$\vect{F}$");
-Vector T = Force((0,dy), mag=t, dir=180, "$T$");
-Vector F = Force((0,-dy), mag=mu*m2*g, dir=180, "$\vect{F}_{f2}$");
+Vector G = Force((0,0), mag=m2*g*vscale, dir=-90,
+ L=Label("$m_2g$", position=EndPoint, align=S));
+Vector N = Force((0,0), mag=m2*g*vscale, dir=90,
+ L=Label("$\vect{N}_2$", position=EndPoint, align=NE));
+Vector E = Force((0,0), mag=f, dir=0,
+ L=Label("$\vect{F}$", position=EndPoint, align=NE));
+Vector T = Force((0,dy), mag=t, dir=180,
+ L=Label("$T$", position=EndPoint, align=NW));
+Vector F = Force((0,-dy), mag=mu*m2*g, dir=180,
+ L=Label("$\vect{F}_{f2}$", position=EndPoint, align=SW));
G.draw();
N.draw();
draw((0,0)--(0, mg));
Angle t = Angle(dir(90), (0,0), dir(90+theta), "$\theta$");
t.draw();
-Vector T = Force((0,0), mag=mg/Cos(theta), dir=(90+theta), "$T$");
+Vector T = Force((0,0), mag=mg/Cos(theta), dir=(90+theta),
+ L=Label("$T$", align=SW));
T.draw();
Vector G = Force((0,0), mag=mg, dir=(-90), "$mg$");
G.draw();
real u = 1cm;
Mass m = Mass((u,0), "$m$");
-Vector F = Force(m.center(), mag=0.7u, dir=180, "$F_f$");
+Vector F = Force(m.center(), mag=0.7u, dir=180, L=Label("$F_f$", align=SW));
draw(scale(u)*unitcircle);
Distance r = Distance((0,0), u*dir(45), "$r$");
real theta = 25;
real mg = 1.3u;
-Vector F = Force((0,0), mag=0.7u, dir=180, "$F_f$");
+Vector F = Force((0,0), mag=0.7u, dir=180,
+ L=Label("$F_f$", position=EndPoint));
F.draw();
-Vector G = Force((0,0), mag=1u, dir=-90, "$mg$");
+Vector G = Force((0,0), mag=1u, dir=-90, L=Label("$mg$", position=EndPoint));
G.draw();
-Vector N = Force((0,0), mag=1u, dir=90, "$N$");
+Vector N = Force((0,0), mag=1u, dir=90, L=Label("$N$", position=EndPoint));
N.draw();
dot((0,0));
real theta = 5;
real E_mag = 0.1cm;
-Vector T = Vector((0,0), mag=E_mag/Sin(theta), dir=90+theta, "$T$");
-Vector G = Vector((0,0), mag=E_mag/Tan(theta), dir=-90, "$mg$");
-Vector E = Vector((0,0), mag=3*E_mag, dir=0, "$F_E$");
+Vector T = Vector((0,0), mag=E_mag/Sin(theta), dir=90+theta,
+ L=Label("$T$", position=EndPoint));
+Vector G = Vector((0,0), mag=E_mag/Tan(theta), dir=-90,
+ L=Label("$mg$", position=EndPoint));
+Vector E = Vector((0,0), mag=3*E_mag, dir=0,
+ L=Label("$F_E$", position=EndPoint, align=E));
T.draw();
G.draw();
Charge q2 = aCharge((d,0), q=1, "$q_2$");
Charge q3 = aCharge((x,0), q=0, "$q_3$");
-Distance dx = Distance((0,0), (x,0), offset=-30pt, "$x$");
-Distance dd = Distance((0,0), (d,0), offset=-12pt, "$d$");
+Distance dx = Distance((0,0), (x,0), offset=30pt, "$x$");
+Distance dd = Distance((0,0), (d,0), offset=12pt, "$d$");
dx.draw();
dd.draw();
Vector f = Force(mag=u, dir=90, Label("$\vect{F}_B$", EndPoint, N));
f.draw();
-Vector v = Velocity(mag=u, phi=90, Label("$\vect{v}$", EndPoint, S));
+Vector v = Velocity(mag=u, phi=90, Label("$\vect{v}$", EndPoint, E));
v.draw();
label("\Part{b}", (0,0), S);
\end{asy}
Vector f = Force(mag=u, dir=180, Label("$\vect{F}_B$", EndPoint, N));
f.draw();
-Vector v = Velocity(mag=u, phi=-90, Label("$\vect{v}$", EndPoint, S));
+Vector v = Velocity(mag=u, phi=-90, Label("$\vect{v}$", EndPoint, E));
v.draw();
label("\Part{c}", (0,0), S);
\end{asy}
}
Charge a = nCharge((-0.5*width-24pt, 0), "$e^-$");
-Vector v = Velocity(a.center(), dir=0, "$\vect{v}$");
+Vector v = Velocity(a.center(), dir=0,
+ L=Label("$\vect{v}$", position=EndPoint, align=RightSide));
v.draw();
a.draw();
draw_ijhat(0.8*low*(-1,-1));
-Vector Ix = Current((-low, 0), (high+low)+12pt, dir=0, "$5.00\U{A}$");
+Vector Ix = Current((-low, 0), (high+low)+12pt, dir=0,
+ L=Label("$5.00\U{A}$", position=EndPoint, align=S));
Ix.draw();
-Vector Iy = Current((0, -low), (high+low), dir=90, "$3.00\U{A}$");
+Vector Iy = Current((0, -low), (high+low), dir=90,
+ L=Label("$3.00\U{A}$", position=EndPoint, align=W));
Iy.draw();
pair P = (0.4d, 0.3d);
real d = 0.5cm;
-Vector Bx = BField(mag=5d, dir=-90, "$\vect{B}_{xP}$");
-Vector By = BField(mag=3d, dir=0, "$\vect{B}_{yP}$");
+Vector Bx = BField(mag=5d, dir=-90,
+ L=Label("$\vect{B}_{xP}$", position=EndPoint));
+Vector By = BField(mag=3d, dir=0,
+ L=Label("$\vect{B}_{yP}$", position=EndPoint));
pair b = Bx.mag*dir(Bx.dir) + By.mag*dir(By.dir);
-Vector B = BField(mag=length(b), dir=degrees(b), "$\vect{B}_P$");
+Vector B = BField(mag=length(b), dir=degrees(b),
+ L=Label("$\vect{B}_P$", position=EndPoint));
Angle t = Angle(dir(0), (0,0), b, "$\theta_P$");
t.draw();
Bx.draw();
between the strings in terms of $E$, $q$, $m$, and $g$. \Part{c} As
the electric field is gradually increased in strength, what does your
result from \Part{b} give for the largest possible angle $\theta$?
-\end{problem*}
-
-\begin{nosolution}
\begin{center}
\begin{asy}
import Mechanics;
Charge a = neutralCharge(dir(-90+phi)*L*u, L="$q_R$");
Charge b = neutralCharge(dir(-90-phi)*L*u, L="$q_L$");
-Wire La = Wire((0,0), a.center(), L=Label("$L$", align=NW, embed=Shift));
-Wire Lb = Wire(b.center(), (0,0), L=Label("$L$", align=NE, embed=Shift));
+Wire La = Wire((0,0), a.center(), L=Label("$L$", align=NE, embed=Shift));
+Wire Lb = Wire((0,0), b.center(), L=Label("$L$", align=NW, embed=Shift));
Angle theta = Angle(a.center(), (0,0), b.center(), L="$\theta$");
Surface s = Surface((a.center().x, 0), (b.center().x, 0));
Vector E = EField(a.center() - (0,dy)*u, mag=(a.center().x - b.center().x),
b.draw();
\end{asy}
\end{center}
-\end{nosolution}
+\end{problem*}
\begin{solution}
\Part{a}
import Mechanics;
import ElectroMag;
-real u = 1cm; // Length of 1 m on the page
-real L = 2; // Length of cable
-real phi = 30; // Half angle between cables
-real dy = .6; // Distance below charges to E field vector
-
-Charge a = nCharge(dir(-90+phi)*L*u, L="$q_{R-}$");
-Charge b = pCharge(dir(-90-phi)*L*u, L="$q_{L+}$");
-Wire La = Wire((0,0), a.center(), L="$L$");
-Wire Lb = Wire(b.center(), (0,0), L="$L$");
-Angle theta = Angle(a.center(), (0,0), b.center(), L="$\theta$");
-Surface s = Surface((a.center().x, 0), (b.center().x, 0));
-Vector E = EField(a.center() - (0,dy)*u, mag=(a.center().x - b.center().x),
- dir=-180, L="$E$");
-
-s.draw();
-La.draw();
-Lb.draw();
-theta.draw();
-E.draw();
-a.draw();
-b.draw();
-\end{asy}
-
-\begin{asy}
-import Mechanics;
-import ElectroMag;
-
real phi = 30; // Half angle between cables
Charge a = nCharge();
-Vector Fq = Force(a.center(), mag=.4cm, dir=-180, L="$F_q$");
-Vector FT = Force(a.center(), mag=1cm, dir=90+phi, L="$F_T$");
-Vector FE = Force(a.center(), mag=Sin(phi)*FT.mag+Fq.mag, dir=0, L="$F_E$");
-Vector Fg = Force(a.center(), mag=Cos(phi)*FT.mag, dir=-90, L="$F_g$");
+Vector Fq = Force(a.center(), mag=.4cm, dir=-180,
+ L=Label("$F_q$", position=EndPoint, align=W));
+Vector FT = Force(a.center(), mag=1cm, dir=90+phi,
+ L=Label("$F_T$", position=EndPoint, align=N));
+Vector FE = Force(a.center(), mag=Sin(phi)*FT.mag+Fq.mag, dir=0,
+ L=Label("$F_E$", position=EndPoint, align=E));
+Vector Fg = Force(a.center(), mag=Cos(phi)*FT.mag, dir=-90,
+ L=Label("$F_g$", position=EndPoint, align=S));
Fq.draw();
FT.draw();
FE.draw();
Fq.dir += 180;
FT.dir -= 2*phi;
FE.dir += 180;
+Fq.label.align = E;
+FE.label.align = W;
Fq.draw();
FT.draw();
FE.draw();
Vector E;
for (int i=0; i<n; i+=1) {
- E = EField((L*(i+.5)/n, -.35*dy)*u, mag=.7*dy*u, dir=90, L="$E$");
+ E = EField((L*(i+.5)/n, -.35*dy)*u, mag=.7*dy*u, dir=90,
+ L=Label("$E$", position=BeginPoint, align=NE));
E.draw();
}
real a = 1;
Charge p = pCharge((0,0), L="$q$");
-Charge n = pCharge((a,0)*u, L="$-2q$");
+Charge n = nCharge((a,0)*u, L=Label("$-2q$", align=N));
draw_ijhat((0,0));
p.draw(); n.draw();
real dBy = supRadius*2/sqrt(3);
int i;
Bs.push(BField(cBar-(0,dBy), phi=-90));
-Bs.push(BField(cBar+(0,dBy), phi=-90, "\vect{B}"));
+Bs.push(BField(cBar+(0,dBy), phi=-90,
+ L=Label("\vect{B}", position=EndPoint, align=N)));
Bs.push(BField(cBar+(-lBar/2,dBy), phi=-90));
Bs.push(BField(cBar+(+lBar/2,dBy), phi=-90));
for (i=0; i<Bs.length; i+=1) {
}
draw(scale(r)*unitcircle, Bs[0].outline+dashed);
-Distance Dwire = Distance((pLL+2*pLR)/3, (pUL+2pUR)/3, "$45.0\U{cm}$");
+Distance Dwire = Distance((pLL+2*pLR)/3, (pUL+2pUR)/3,
+ L=Label("$45.0\U{cm}$", align=LeftSide, embed=Shift));
Dwire.draw();
-Distance DdB = Distance((+r,-r), (-r,-r), offset=-3mm, L="$75.0\U{cm}$");
+Distance DdB = Distance((+r,-r), (-r,-r), offset=-3mm,
+ L=Label("$75.0\U{cm}$", align=LeftSide, embed=Shift));
DdB.draw();
\end{asy}
\end{center}
wbot_seg.draw();
TwoTerminal Ibot = current((0,-Ysep/2), 180, "$24.0\U{A}$");
Distance dSegbot = Distance((-Xsep-Xseg/2,-Ysep/2), (-Xsep+Xseg/2,-Ysep/2),
- offset=2mm, L=Label("$1.50\U{mm}$", S));
+ offset=2mm, L=Label("$1.50\U{mm}$", align=S));
dSegbot.draw();
wtop_seg.draw();
TwoTerminal Itop = current((Ibot.end.x,Ysep/2), "$12.0\U{A}$");
Distance dSegtop = Distance((-Xsep-Xseg/2,Ysep/2), (-Xsep+Xseg/2,Ysep/2),
- offset=-2mm, Label("$1.50\U{mm}$", N));
+ offset=-2mm, Label("$1.50\U{mm}$", align=N));
dSegtop.draw();
\end{asy}
Angle theta2 = Angle((-Xsep,Ysep/2), (0,0), (-Xsep,0), 10mm, "$\theta$");
theta2.draw();
-Vector dL = Vector((-Xsep, Ysep/2), mag=3u, "$\dl$");
+Vector dL = Vector((-Xsep, Ysep/2), mag=3u, L=Label("$\dl$", align=N));
Vector rhat = Vector((-Xsep, Ysep/2), mag=3u, dir=degrees((Xsep,-Ysep/2)),
"$\rhat$");
dL.draw();
real u = 1cm;
Pendulum p = makePendulum(angleDeg=-40, length=2u,
- angleL="$\theta$", stringL="$r$");
+ angleL="$\theta$", stringL=Label("$r$", embed=Shift));
Spring s = Spring(pFrom=p.mass.center(), pTo=(0,p.mass.center().y),
unstretchedLength=abs(p.mass.center().x),
L="$2k$");
Pendulum p = makePendulum(angleDeg=-40, length=2u,
angleL="$\theta$");
-Vector fs = Force(p.mass.center(), dir=180, mag=1u, L="$F_s$");
-Vector fg = Force(p.mass.center(), dir=-90, mag=1u, L="$F_g$");
-Vector dx = Vector(p.mass.center(), dir=-40-180, mag=1.5u, L="$x'$");
-Vector dy = Vector(p.mass.center(), dir=-40-90, mag=1.5u, L="$y'$");
+Vector fs = Force(p.mass.center(), dir=180, mag=1u,
+ L=Label("$F_s$", position=EndPoint, align=W));
+Vector fg = Force(p.mass.center(), dir=-90, mag=1u,
+ L=Label("$F_g$", position=EndPoint, align=S));
+Vector dx = Vector(p.mass.center(), dir=-40-180, mag=1.5u,
+ L=Label("$x'$", position=EndPoint));
+Vector dy = Vector(p.mass.center(), dir=-40-90, mag=1.5u,
+ L=Label("$y'$", position=EndPoint));
Angle xas = Angle(dx.pTip(), p.mass.center(), fs.pTip(), L="$\theta$");
Angle yag = Angle(dy.pTip(), p.mass.center(), fg.pTip(), L="$\theta$");