PHY294 Exam #2
Name:______________________ Student #:_________________
Show work for problems. Include units in answer.
Some physical constants:
e=1.6 X 10-19 C
me = 9.1 X 10-31 kg
mp = 1.67 X 10-27 kg
g = 9.83 N/kg
εo = 8.85 X 10-12 C2/N.m2
1/4πεo = 9 X 109 N.m2/C2
µo=4πX10-7 T.m/A
c=3X108 m/s
1)
A 6.0-µF capacitor is connected in series with a 5.0 MΩ resistor, and this
combination is connected across an ideal 15-V DC battery. What is the current in the
circuit when the capacitor has reached 20% of its maximum charge?
A) 6.5 µA
B) 2.4 µA
C) 1.3 µA
D) 4.7 µA
E) 9.1 µA
I = 0.8* I max = 0.8*
15V
= 2.4µ A
5E6Ω
2)
For the circuit shown in the figure, the current in the 8-Ω resistor is 0.50 A. What
is the current in the 2-Ω resistor?
V across 8Ω resistor is 4 V; current through 16Ω resistor is then 0.25 A; current through
20Ω resistor then is 0.75A; total voltage across top branch then is 19V; current thorugh
2Ω resistor is 19V/2Ω=8.5A
3.)
A long straight conductor has a constant current flowing to the right. A wire
rectangle is situated above the wire, and also has a constant current flowing through it (as
shown in the figure). Which of the following statements is true?
A) The net magnetic force on the wire rectangle is upward, and there is also a net torque
on the it.
B) The net magnetic force on the wire rectangle is zero, and the net torque on it is zero.
C) The net magnetic force on the wire rectangle is downward, and there is also a net
torque on the it.
D) The net magnetic force on the wire rectangle is zero, but there is a net torque on it.
E) The net magnetic force on the wire rectangle is downward, and the net torque on
it is zero.
4)
At what distance from the central axis of a long straight thin wire carrying a
current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the
strength of the Earth's magnetic field of about 5.0 × 10-5 T? Show work.
µo I
2π r
µ I ( 2E07T.m / A) 5A
r= o =
= 0.02m
2π B
5E − 5T
B=
5.)
The three loops of wire shown in the figure are all subject to the same uniform
magnetic field that does not vary with time. Loop 1 oscillates back and forth as the bob
in a pendulum, loop 2 rotates about a vertical axis, and loop 3 oscillates up and down at
the end of a spring. Which loop, or loops, will have an emf induced in them? The loops
never leave the region of constant magnetic field.
A) loop 1 only
B) loop 2 only
C) loop 3 only
D) loops 1 and 2
E) loops 2 and 3
6.)
You are designing a generator to have a maximum emf of 8.0 V. If the generator
coil has 200 turns and a cross-sectional area of 0.030 m2, what should be the frequency
of the generator in a uniform magnetic field of 0.030 T? Show work.
ε = NBAω
ε
8V
ω=
=
= 44.44rad / s
NBA (200)(0.03T )(0.03m 2 )
f = ω / 2π = 7.07hz
7)
The energy per unit volume in an electromagnetic wave is
A) equally divided between the electric and magnetic fields.
B) mostly in the electric field.
C) mostly in the magnetic field.
D) all in the electric field.
E) all in the magnetic field.
8) A planar electromagnetic wave is propagating in the +x direction. At a certain point P
and at a given instant, the electric field of the wave is given by
is the magnetic vector of the wave at the point P at that instant?
A) 0.27 nT
= (0.082 V/m) . What
B) -0.27 nT
C) 0.27 nT
D) 6.8 nT
E) -6.8 nT
9)
An ac source of period T and maximum voltage V is connected to a single
unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = 0
the voltage is zero. At time t = T/4 the current in the unknown element is equal to zero,
and at time t = T/2 the current is I = -Imax, where Imax is the current amplitude. What is
the unknown element?
A) a resistor
B) an inductor
C) a capacitor
D) an inductor or a capacitor
10)
Consider the circuit shown in the figure. The battery has emf ε = 25 volts and
negligible internal resistance. The inductance is L = 0.80 H and the resistances are R1 =
12 Ω and R2 = 9.0 Ω. Initially the switch S is open and no currents flow. Then the switch
is closed.
(a) What is the current in the resistor R1 just after the switch is closed?
(b) After leaving the switch closed for a very long time, it is opened again. Just after it is
opened, what is the current in R1? Show work.
After the switch is closed, all current goes through resistor R1. I=25V/12Ω=2.08A.
After a long time, the current through R2 is 25V/9Ω=2.78A. When switch S is opened, this
current will continue to flow through R2 (and R1).
11.)
What are the strength and direction of the magnetic field at point P due to the
current in the conducting loop? Show work.
If the outer segment were a complete loop, then the magnetic field at point P would be
" 5A %
µI
B = o = 2π E − 7T.m / A $
' = 1.57E − 4T
2r
# .02m) &
out of the plane of the page. The magnetic field from the inner segment (if it were a
complete loop) would be 3.14E-4T going into the plane of the page. The net field would
be 1.57E-4T going into the plane of the page. Since they are half-loops, the fields are
halved, so the net field is 7.85E-5T into the plane of the page.
12.) The value of the line integral of B around the closed path below is 3.77X10-6 Tm.
What is the current I3? Show work.
!∫ B.ds = µ I
∫ B.ds =
I=!
o
3.77E − 6Tm
= 3A
4π E − 07Tm / A
µo
I1 + I 2 + I 3 = 3A
I 3 = 1A