Physics 1B
Week 10 Questions (p.1)
Fall 1998
1. The figure shows five different loops in a magnetic field. The numbers by the loop indicate the
lengths of the sides. The magnitude and direction of the magnetic fields are also shown. Rank order
the magnetic fluxes through the loops, from the smallest to the largest.
2. A circular loop rotates at constant speed about an axle through the center of the loop. The figure
shows an edge view and defines the angle, which increases from 0o to 360o as the loop rotates. (a)
At what angle or angles is the magnitude of the magnetic flux a maximum? (b) At what angle or
angles is the magnitude of the magnetic flux a minimum? (c) At what angle or angles is the
magnetic flux changing most rapidly?
3. A square wire loop enters a uniform magnetic field with a constant velocity v=1m/s. Each side of
the loop is 1m. The magnetic field is 1 T, and has a width 2m. Calculate the total emf in the loop
as a function of time (t=0 when the right edge of the loop touches the left side of the field).
Suppose the loop has a resistance 1calculate the current in the loop as a function of time.
B
R=1
V
2m
Physics 1B
Week 10 Questions (p.2)
Fall 1998
4. Suppose an apartment complex is supplied single-phase ac from a power plant 5 km away. The
wire that runs from the power plant to the apartment complex and back has a unit resistance of
0.00001/m. Suppose the apartment complex is consuming an electric power of 100,000W (with a
110V voltage), what would be the power wasted by the wire that transports the electricity. (These
numbers are for illustration purpose only. They may not be realistic.)
5. A signal V1=V0cos(100t) with V0=3V is fed to the following circuit. Determine the effective
voltage across the capacitor. What is this effective voltage again if the input signal is changed to
V2=V0cos(200t)? What if both signals are simultaneously fed into the circuit?
200
V in
~
10F
Physics 1B
Week 10 Solutions
Fall 1998
1. The magnetic flux from left to right is 4, 2, 2, 4, 2. The ranking is loop 2, 3 & 5, and then loop 1 &
4.
2. Magnetic flux=Abcos, where A is the area of the loop, and B is the magnitude of the magnetic
field. (a) =0o & 180o. (b) =90o & 270o. (c) The rate of change of the magnetic flux is
proportional to d(ABcos)/ d=ABsin. Therefore the flux changes most rapidly when =90o &
270o.
3. Assume that emf is positive if the current goes counter-clockwise.
emf
1V
t (s)
0
1
2
3
1V
4. The total resistance of the wire is (0.00001/m)(5000m+5000m)=0.1he effective current
through the wire is (100,000W)/(110V)=910A. The power wasted on the wire is then
(910A)2(0.183kW.
5. For signal 1: the capacitive reactance of the capacitor is XC=1/C=1/(100)(10F)=1000The
effective voltage across the capacitor is then (3V)(0.707)(1000)/(1000+200)=1.77V.
For signal 2: the capacitive reactance of the capacitor is XC=1/C=1/(200)(10F)=500The
effective voltage across the capacitor is then (3V)(0.707)(500)/(500+200)=1.52V. When both
signals are input, the effective voltage across the capacitor is 1.77 2  1.52 2  2.3 V .