print "Weekly Practice 12\n"
qelem = 1.6*10^(-19) # C
pi = 4*a(1)
mu0 = 4*pi*10^(-7)
g = 9.81 # m/s^2
scale = 40

print "#1\n"
# magnetic field in this problem is |B| @ theta ccw from +x.
# we find the i and j components. i\times j = k. j\times i = -k.
#params
v1 = 1.25 * 10^6 #i m/s
f1 = 1.64 * 10^(-16) #k N
v2 = 2.49 * 10^6 #j m/s
f2 = -4.04* 10^(-16) #k N

# v1*bj*q = f1
bj = f1/v1/qelem
# v2*bi*q = -f2
bi = -f2/v2/qelem

print "Magnitude (T)\n"
sqrt((bi*10^16)^2 + (bj*10^16)^2)*10^(-16)

print "Angle ccw from +x axis (deg)\n"
a(bj/bi)*180/pi

scale = 40
print "#2\n"
#params
v = 4*10^4 # m/s
b = 5 # mT

m = 1.67*10^(-27) # kg
b = b/1000
a = (b*qelem*v/m)
r = v^2/a
# r = vm/bq
print "Diameter (m)\n"
2*r

print "#3\n"
#params
mf = 27 # mT
v = 5.5 * 10^6 # m/s
thdeg = 30

th = thdeg*pi/180
mf = mf/1000 # T
vx = v*c(th)
melec = 9.1*10^(-31)
r = vx*melec/(mf*qelem)
print "Radius (m)\n"
r
c = 2*pi*r
t = c/vx

print "Pitch (m)\n"
t*v*s(th)

print "#4\n"
#params
l = 52 # mass density - g/m
d = 4 # cm

d = d/100 # m
l = l/1000 # kg/m

w = l*g # N/m
# Up and down cancel out from the two base wires, so we get an mf of
# 2*mu0*I*s(60deg)/(2pi*d) and a force (per meter) of I*mf = w
# i^2 * 2*mu0*s(60*pi/180)/(2*pi*d) = w
i = sqrt(w/(2*mu0*s(60*pi/180)/(2*pi*d)))

print "Current (A)\n"
i

print "#5\n"
#params
s = 5.1 # cm
i = 470 # mA
b = 1.7 # T
thdeg = 30

# We use magnetic moment here

s = s/100 # m
i = i/1000 # A
th = thdeg*pi/180

print "Torque Magnitude (Nm)\n"
s^2*s(th)*b*i

print "#6\n"
#params
k = 12 # N/m - spring constant
d = .7 # cm
b = .5 # T
l = 20 # cm

d = d/100 # m
l = l/100 # m
f = 2*k*d # N (two springs, double the force)
# i*l*b = f
i = f/(l*b)

print "Current (A)\n"
i

print "#7\n"
#params
m = 4 # kg
s = 5.5 # m
i = 25 # A
thdeg = 25

th = thdeg*pi/180

w = m*g
t = w*s/2
a = s^2
# a*i*b = t
b = t/(a*i) # what happened to the angle lmao. this is right (??)

print "Magnetic field (T)\n"
b

print "#8\n"
#params
dv = .02 # V
l = 10 # cm
v = 5 # m/s

l = l/100 # m
ef = dv/l # some stackexchange article said so
# ef = v*b

print "Magnetic field into the page (T)\n"
ef/v

print "#9\n"
#params
b = .45 # T
v = .5 # m/s
ohm = 2 # Ohm
d = 10 # cm

d = d/100 # m
i = v*d*b/ohm # IMPORTANT !!!
p = i^2*ohm
# f*v = p
f = p/v

print "Pushing force (N)\n"
f

print "Power (W)\n"
p

print "Current - induced counterclockwise (A)\n"
i

print "Power dissipated by resistor (W)\n"
p