Physics 220 Homework Problems, Spring 2012
1-1. A cat slides down a rubber rod and falls from the rod
into a metal pail A resting on a non-conducting shelf
with two other metal pails, B and C, which are in
contact, but neither is in contact with A. The shelf
breaks when the cat lands in A, transferring charge to
A, and all pails fall separated to the non-conducting
floor. The cat then runs away.
(a) At the end of this process the charge on pail A
1. is positive.
2. is negative.
3. is zero.
(b) At the end of this process the charge on pail B
1. is positive.
2. is negative.
3. is zero.
4. has the same sign as pail A.
5. has the same sign as pail C.
(c) At the end of this process the charge on pail C
1. is positive.
2. is negative.
3. is zero.
4. has the same sign as pail B.
5. both (1) and (4) are correct.
1-2. Consider vectors R = (2.10, y = [01]
, 1.00) and S = (3.30, 4.00, 0.90).
(a) Calculate the magnitude of R. (b) Calculate the z component of unit vector R̂.
(c) Calculate the angle between vectors R and S. (d) Calculate the z component of
R × S. [(a) 3.00, 5.00 (b) 0.200, 0.400 (c) 90.0, 110.0◦ (d) 10.0, 30.0]
1-3. There are identical Q = [02]
µC charges located at three positions: (0, −1, 2),
(1, 2, 0), and (−2, 0, −1). Coordinates are listed in units of meters. (a) What is the
magnitude of the force that a charge of −1.00 µC feels at the origin? (b) What is the
angle between this force and the positive x axis? [(a) 5.00 × 10−3 , 9.00 × 10−3 N
(b) 120.0, 130.0◦ ]
1
1-4. A charged particle with a charge of −7.5 pC is placed at the origin where the electric
field (SI units) is E = (3.75 i − 2.90 j). This force is directed toward which quadrant or
axis of the xy plane?
1.
2.
3.
4.
5.
6.
7.
8.
I
II
III
IV
+x
−x
+y
−y
1-5. The sketch in the square frame represents two negative point
charges and one positive point charge, all of the same magnitude.
The letters “a” and “b” simply designate two positions within the
frame. Note that point “a” is down and to the right from the
positive charge. We label several directions as follows: (1) ↑, (2) %,
(3) →, (4) &, (5) ↓, (6) ., (7) ←, (8) -, (9) magnitude is zero,
(10) none of the above.
A. What is the approximate direction of the electric field at position “a”?
B. What is the approximate direction of the electric field at position “b”?
1-6. In the lab, an object having a net charge of Q = [03]
µC is placed in a
uniform electric field of 500 N/C that is directed vertically. What is the mass of this
object if it “floats” in the field? [0.100, 0.300 g]
2-1. Find the area of region bound by the curve y = b − x2 and the x axis, where
b = [01]
. [1.00, 7.00]
2-2. A long chain lying along the x axis has linear charge density λ = λa sin2 (x) + λb cos2 (x),
where λa = [02]
C/m and λb = [03]
C/m. What is the average
R
1 T
charge density of the chain? Hint: λ̄ = T 0 λ(t). [0.50, 1.50 C/m]
2-3. Consider a paraboloid “drinking cup”, as shown. The height of
the cup is L, and the radius of the cup at the top is a. What is
an appropriate differential volume for determining the total
volume of the cup? The radius r of the cup varies with the
height z according to (r/a)2 = z/L.
1. πa2 dz
2. 21 πLa dr
3. πa2 z dz/L
4. 12 πa2 dL
5. πa2 r dz/L
2
2-4. Consider a cone of height L and base radius a. What is an
appropriate differential area for determining the total outer
surface area?
√
1. 2πa a2 + L2 z dz/L2
2. 2πaz dz/L
3. 2πa dz/L
2
2
4. πa
√ dz/L
5. π a2 + L2 dz
3-1. Two charged particles with charges of ±q = [01]
pC are separated by a
distance of a = 0.820 nm. (a) What is the dipole moment of this charge pair? (b) Using
the dipole approximation (d a), what is magnitude of the electric field at a position
along the dipole axis which is a distance of d = 0.915 cm away from the charge pair?
[(a) 5.00 × 10−19 , 8.00 × 10−19 C·m (b) 0.0100, 0.0200 N/C]
3-2. A uniformly charged ring of radius 11.6 cm has a total charge of Q = [02]
pC.
What is the magnitude of the electric field on the axis of the ring at a distance of 4.81 cm
from the center of the ring? [1.00, 1.60 N/C]
3-3. A charged hemispherical bowl with radius 13.7 cm and charge
density σ = [03]
nC/m2 sits on the xy plane as
shown. Determine the magnitude of (a) the x component,
(b) the y component, and (c) the z component of the vector
electric field at the origin. Hint: Try using spherical coordinates.
[(a) 0, 200 N/C (b) 0, 200 N/C (c) 0, 200 N/C]
4-1. Complete this problem on a separate sheet of paper and submit it with your CID#
prominently displayed.
(a) Two conducting spheres of the same radius r, carrying equal but opposite charges,
are separated by a center-to-center distance of 4r. Sketch the pattern of electric field
lines in a plane that includes the centers of the two spheres.
(b) A negatively charged rod of finite length has a uniform charge per unit length.
Sketch the pattern of electric field lines in a plane that includes the rod.
3
4-2. Consider the pattern of electric field lines in the figure.
(a) By counting field lines, rank the left-hand (L) and
right-hand (R) charges in order of decreasing magnitude.
1. L > R
2. R > L
3. L = R
(b) Rank the points in the figure according to decreasing
electric field magnitude.
1. A = B > C
2. C > A = B
3. A > C = B
4. C > B > A
5. A > B > C
(c) The direction of the electric field at point C is
1. up
2. down
3. left
4. right
5. no direction because magnitude is zero
4-3. An electron is projected from the ground at an angle of 30◦ above the horizontal at a
m/s in a region where an upward electric field has a uniform
speed of v = [01]
magnitude of 400 N/C. Neglecting the effects of gravity, find (a) the time it takes the
electron to return to the ground, (b) the maximum height it reaches along its trajectory,
and (c) its horizontal distance between the launching and landing points.
[(a) 0.100, 0.150 µs (b) 5.0, 15.0 cm (c) 60, 110 cm]
5-1. A uniform electric field E = Ex i + Ey j where Ex = [01]
N/C and
N/C, intersects a surface with area of 2.70 m2 . What is the
Ey = [02]
magnitude of the flux through this area if the surface lies (a) in the yz plane? (b) in the
xz plane? (c) in the xy plane? [(a) 0.00, 9.50 N·m2 /C (b) 0.00, 9.50 N·m2 /C
(c) 0.00, 9.50 N·m2 /C]
5-2. Four closed surfaces, S1 through S4 , are drawn together with three
charges, −2Q, +Q, and −Q. Rank the four surfaces according to the
amount (not magnitude, consider the sign) of electric flux exiting
each one. In answering this problem we are asking about NET flux.
[Exiting flux (field lines going out) is canceled by field lines coming
in.] That is, summing the net charge enclosed is important.
1.
2.
3.
4.
5.
S4
S3
S4
S3
S2
> S2
> S1
= S2
> S1
= S3
> S1
> S2
> S1
> S2
> S1
> S3
> S4
> S3
= S4
= S4
4
5-3. A [03]
nC point charge is located on the z axis a
distance 0.800 m above the circular end cap of the
paraboloidal cup shown in the figure. If L = 2.00 m and
a = 0.510 m, calculate the magnitude of the total electric flux
due to the point charge (a) through the circular end cap and
(b) through the paraboloidal surface. [(a) 20.0, 40.0 N·m2 /C
(b) 20.0, 40.0 N·m2 /C]
5-4. A point charge of q = [04]
pC is placed at the center of
a regular triangular pyramid with an edge dimension of a = 1 cm.
Determine the total electric flux exiting the pyramid.
[0.500, 0.900 N·m2 /C]
6-1. The charge per unit length on a long, straight filament is λ = [01]
µC/m.
(a) Determine the electric field at a distance of 2.50 cm from the filament. Here, define +
to mean outward and − to mean inward. (b) Repeat for a distance of 25.0 cm from the
filament. [(a) 400, 600 kN/C (b) 40.0, 60.0 kN/C]
6-2. A square plate of copper with 52.6-cm sides has no net charge and is placed in a uniform
E = [02]
kN/C electric field directed perpendicular to the plate. (a) Find the
magnitude of the charge density on each face of the plate. (b) Find the magnitude of the
total charge on each face of the plate. [(a) 10.0, 40.0 nC/m2 (b) 4.00, 9.90 nC]
6-3. A thick conducting shell contains a second conducting shell
as well as three conducting balls with charges of −3 nC, +2
nC, and q = [03]
nC, as shown. The conducting
shells have zero net charge. The outer shell has outer radius
5.50 m. (a) Determine the magnitude of the electric field at
point A. (b) Determine the total charge on the inner surface
of the thick shell. (c) Determine the magnitude and
direction of the electric field just outside its outer surface.
Here, + means outward and − means inward.
[(a) 0.00, 3.00 N/C (b) 3.0, 8.0 nC (c) −2.50, 2.50 N/C]
7-1. An electron is placed half way between two parallel plates (A and B). Plate A is held at
0 V and plate B is held at 100 V. The electron will:
1.
2.
3.
4.
5.
6.
Hit
Hit
Hit
Hit
Hit
Hit
plate
plate
plate
plate
plate
plate
A with 0 J of energy.
B with 0 J of energy.
A with 8 × 10−18 J of energy.
B with 8 × 10−18 J of energy.
A with 1.6 × 10−17 J of energy.
B with 1.6 × 10−17 J of energy.
5
7-2. An electron is released from rest in a uniform electric field of magnitude
V/m. (a) Through what potential difference will it have passed after
E = [01]
moving 1.24 cm? (b) How fast will the electron be moving after having traveled that
1.24 cm? [(a) 40.0, 90.0 V (b) 4.00 × 106 , 6.00 × 106 m/s]
7-3. A charge of +q is at the origin and a charge of [02]
q is at x = 2.000 m. (a) For
what finite positive values of x is the electric potential zero? (b) If q = 1.50 nC, what is
the magnitude of the electric field at this point? [(a) 0.300, 0.700 m (b) 40, 120 N/C]
8-1. Calculate the electric potential at a point x = 0.489 m
along the axis of the annulus as shown. The annulus
has a uniform charge density of σ = 1.35 µC/m2 , an
outer radius of b = 1.13 m and an inner radius of
m. [20.0, 60.0 kV]
a = [01]
8-2. Another application of Gauss’s law to charged conductors.
In the figure, each of the dots represent a point charge of
q1 = [02]
µC. The three conducting shells are
represented by circles and carry a net charge of −1.00 µC,
−2.00 µC, and −3.00 µC on the small, medium, and large
shells, respectively. Find the charge on the outer surface
of the largest shell. [0.0, 20.0 µC]
8-3. A set of equipotential lines are shown in the
figure. Their potential values are shown. A
number of locations are labeled with dots. We
also label several directions as follows: (1) ↑,
(2) %, (3) →, (4) &, (5) ↓, (6) ., (7) ←,
(8) -.
(a) Which point has the highest electric field?
(b) What direction is that highest electric field
pointing?
(c) Which point has the lowest electric field?
(d) What direction is that lowest electric field
pointing?
9-1. A uniformly-charged rod of length L = 2.00 m and charge density λ = 2.65 × 10−9 C/m
lies along the x axis with its left end at the origin. Calculate the electric potential at the
point located a distance d = [01]
m beyond the end of the rod along the −x
axis. [10.0, 50.0 V]
6
9-2. A uniformly charged insulating rod of length 60.0 cm is bent into the shape of a
pC. Find the electric
semicircle. If the rod has a total charge of Q = [02]
potential at the center of the semicircle. [−2.50, 2.50 V]
9-3. A hollow spherical metallic shell of radius of R = 25 cm holds a net surface charge of
Q = [03]
pC. (a) Calculate the electric potential at a distance of 2R from the
center of the sphere. (b) Calculate the electric potential at the surface of the sphere.
(c) Calculate the electric potential at the center of the sphere. [(a) −1.00, 1.00 V
(b) −1.00, 1.00 V (c) −1.00, 1.00 V]
10-1. An air filled capacitor consists of two parallel plates each with an area of 7.60 cm2 ,
mm. If a 20-V potential difference is applied
separated by a distance of [01]
to these plates, calculate (a) the electric field between the plates, (b) the capacitance,
(c) the charge on each plate, and (d) the surface charge density. [(a) 9.0, 12.0 kV/m
(b) 3.00, 4.00 pF (c) 60.0, 80.0 pC (d) 8.00 × 10−8 , 9.90 × 10−8 C/m2 ]
10-2. An air filled spherical capacitor is constructed with inner and outer shell radii of 7.0 cm
and [02]
cm, respectively. (a) Calculate the capacitance of the device.
(b) What potential difference between the spheres results in a charge of 4.00 µC on the
capacitor? [(a) 10.0, 30.0 pF (b) 100, 400 kV]
10-3. In the following capacitance network,
C1 = [03]
µF, C2 = 10.0 µF,
and C3 = 15.0 µF. (a) What is the
equivalent capacitance between points a
and b? (b) If a potential difference of
15 V is applied between points a and b,
what charge is stored on C3 ?
[(a) 9.0, 12.0 µF (b) 100, 120 µC]
10-4. You have a capacitor connected across a battery. If you wish to increase the total charge
drawn from this battery, which of the following options will work? Choose all of the
correct answers.
1.
2.
3.
4.
Add
Add
Add
Add
a
a
a
a
larger capacitor in series with the first.
smaller capacitor in series with the first.
larger capacitor in parallel with the first.
smaller capacitor in parallel with the first.
µF are connected in parallel and
11-1. Two capacitors C1 = 25.0 µF and C2 = [01]
charged with a 100 V power supply. (a) Calculate the total energy stored in the two
capacitors. (b) If the same two capacitors were connected in series, what potential
difference would be required to store [02]
mJ of energy? [(a) 0.150, 0.250 J
(b) 50, 150 V]
7
11-2. A parallel plate air gap capacitor is connected across a 12.0 V potential. At this point it
µC of charge. It is then disconnected from the source while still
stores [03]
charged. (a) What is the capacitance of the capacitor? (b) A piece of Teflon is inserted
between the plates. What is the new capacitance? (c) What is the voltage on the
capacitor? (d) What is the charge on the capacitor? [(a) 2.00, 6.00 µF (b) 5.0, 15.0 µF
(c) 5.0, 30.0 V (d) 20.0, 70.0 µC]
nC charges. It is
11-3. A small rigid object carries positive and negative [04]
oriented so that the positive charge is at the point (−1.20 mm, 1.10 mm) and the
negative charge is at the point (1.40 mm, −1.30 mm). The object is placed in an electric
field E = (7800 ı̂ − 4900 ̂) N/C. (a) What is the magnitude of the electric dipole moment
of the object? (b) What is the magnitude of the torque acting on the object? (c) What is
the potential energy of the object in this orientation? (d) If the orientation of the object
can change, what is the difference between its maximum and its minimum potential
energies? [(a) 1.00 × 10−11 , 3.00 × 10−11 C·m (b) 2.00 × 10−8 , 5.00 × 10−8 N·m
(c) 1.00 × 10−7 , 3.00 × 10−7 J (d) 2.00 × 10−7 , 5.00 × 10−7 J]
11-4. You have a square parallel plate capacitor (edge length a and separation d). It however
does not fit in the assigned volume of space. You plan to make a second configuration of
equal capacitance. Which of the following options would work?
1.
2.
3.
4.
5.
half the edge length, and half the separation.
half the edge length, half the separation, and add a dielectric of constant 2.
half the edge length, and add a dielectric with κ = 2.5.
one fourth the edge length and four times the separation.
one fourth the edge length, twice the separation, and add a dielectric with κ = 8.0.
12-1. A uniform metallic rod, with a cross-sectional area of 1.83 cm2 and a length of 7.08 m,
contains 6.24 × 1028 conduction electrons per cubic meter of material, which have a mean
collision time of [01]
femtoseconds. (a) Determine the resistivity of the rod.
When the rod experiences a potential difference of 2.52 mV from end to end, determine
(b) the drift velocity of the electrons and (c) the current density in the rod.
[(a) 1.50 × 10−8 , 3.00 × 10−8 Ω·m (b) 1.00 × 10−6 , 2.00 × 10−6 m/s
(c) 10000, 20000 ± 100 A/m2 ]
12-2. Suppose that the current through a conductor decreases exponentially with time
according to the expression I(t) = I0 e−t/τ , where I0 is the initial current equal to
1.321 mA and τ is a constant equal to [02]
s. Consider a piece of the
conductor. (a) How much charge passes through this piece between t = 0 and t = τ ?
(b) How much charge passes through this piece between t = 0 and t = 4τ ? (c) How much
charge passes through this piece between t = 0 and t = ∞? [(a) 1.00, 4.00 mC
(b) 1.00, 4.00 mC (c) 1.00, 4.00 mC]
12-3. A resistor is constructed of a carbon rod that has a uniform cross sectional area of 5.00
mm2 . When a potential difference of 15.0 V is applied across the ends of the rod, there is
a current of [03]
mA in the rod. What is (a) the resistance of the rod and
(b) the rod’s length? [(a) 2.00 × 103 , 6.00 × 103 Ω (b) 400, 800 m]
8
13-1. When the voltage across a certain conducting filament is doubled, the current flowing
through it is observed to increase by a factor greater than two. What type of material
could the conductor be made of? Hint: Consider the effects of heating.
1.
2.
3.
4.
copper
quartz
lead
silicon
13-2. The resistance of a platinum wire is to be calibrated for low-temperature measurements.
Ω at 20◦ C is immersed in liquid
A platinum wire with a resistance of [01]
nitrogen at 77 K (−196◦ C). If the temperature response of the platinum wire is linear,
what is the expected resistance of the platinum wire in the liquid nitrogen?
(αplatinum = 3.92 × 10−3 /◦ C) [0.100, 0.400 Ω]
13-3. A toaster is rated at [02]
W when connected to a 120-V source. (a) What
current does the toaster carry? (b) What is its resistance? [(a) 4.00, 7.00 A
(b) 10.0, 30.0 Ω]
13-4. An electric car is designed to run off a 12.0-V battery with a total energy storage of
[03]
J. (a) If the electric motor draws 8.00 kW, what is the current delivered
to the motor? (b) If the electric motor draws 8.00 kW as the car moves at a steady speed
of 20.0 m/s, how far will the car travel before it is “out of juice”? [(a) 500, 900 A
(b) 30.0, 60.0 km]
14-1. A battery has an emf of 15.00 V. The terminal voltage of the battery is [01]
V
when it is delivering 20.00 W of power to an external load resistor R. (a) What is the
value of R? (b) What is the internal resistance of the battery? [(a) 6.00, 9.00 Ω
(b) 1.00, 3.00 Ω]
14-2. Consider the circuit shown. R1 = 5.0 Ω,
Ω, and
R2 = 10.0 Ω, R3 = [02]
E = 25.0 V. (a) What is the current in R3 ?
(b) What is Vb − Va ? [(a) 0.100, 0.300 A
(b) 5.00, 6.00 V]
14-3. You have a resistor connected across a battery. If you wish to increase the current drawn
from the battery, which of the following options will work? Choose all of the correct
answers.
1.
2.
3.
4.
Add
Add
Add
Add
a
a
a
a
larger resistor in series with the first.
smaller resistor in series with the first.
larger resistor in parallel with the first.
smaller resistor in parallel with the first.
9
14-4. A resistor is constructed by shaping a material of resistivity ρ into a hollow cylinder of
length L and with inner and outer radii ra and rb , respectively. The resistivity
cm. (a) The
ρ = 3.52 × 105 Ω·m, L is 4.00 cm, ra = 0.50 cm and rb = [03]
application of a potential difference between the ends of the cylinder produces a current
parallel to the axis. What is the resistance in this configuration? (b) If the potential
difference is now applied between the inner and outer surfaces, what is the resistance?
[(a) 10.0, 50.0 MΩ (b) 1.00, 2.00 MΩ]
15-1. The current in a circuit is tripled by connecting a [01]
-Ω resistor in parallel
with the resistance of the circuit. What is the resistance of the circuit in the absence of
the additional resistor? [400, 900 Ω]
Ω,
15-2. In the following circuit, R1 = 5.00 Ω, R2 = [02]
R3 = 25.00 Ω, E1 = 25.00 V, E2 = 15.00 V, and E3 = 5.00 V.
(a) What is I1 ? (b) What is I2 ? (c) What is I3 ? (d) What is the
potential difference across R3 ? [(a) 0.70, 1.10 A
(b) −0.10, −0.50 A (c) −0.50, −0.70 A (d) 14.0, 17.0 V]
15-3. From the diagram, which of the following are true?
1.
2.
3.
4.
5.
6.
7.
I1 + I2 + I3 = 0
I1 + I2 = I3
I2 + I3 = I1
I1 R + E + I2 R = 0
I1 R − I3 R = 0
−I2 R + E − I3 R = 0
I1 R + I3 R = 0
16-1. The circuit shown has been connected for a
long time. R1 = 1.00 Ω,
R2 = [01]
Ω, R3 = 4.00 Ω,
R4 = 2.00 Ω, E = 20.0 V, and C = 1.00 µF.
(a) What is the voltage across the
capacitor? (b) If the battery is
disconnected, how long does it take the
capacitor to discharge to one-tenth its initial
voltage? [(a) 5.0, 14.0 V
(b) 4.00 × 10−6 , 9.90 × 10−6 s]
10
16-2. A [02]
-ft extension cord has two 18-Gauge copper wires, each with a diameter
of 1.024 mm. What is the I 2 R loss in this cord when it carries a current of (a) 1.00 A?
(b) 10.0 A? Note: Because current flows up one wire and down the other, the length of
the current path is twice that of the wire. [(a) 0.050, 0.200 W (b) 5.0, 20.0 W]
16-3. Consider the circuit in the figure.
(a) If at some instant the capacitor in this circuit has no charge,
what is the current in the resistors?
1.
2.
3.
4.
0
E/2R
E/R
2E/R
(b) If at some instant the capacitor in this circuit has charge Q = CE, what is the
current in the resistors?
1.
2.
3.
4.
0
E/2R
E/R
2E/R
(c) If at some instant the capacitor in this circuit has charge Q = 2CE, what is the
current in the resistors?
1.
2.
3.
4.
0
E/2R
E/R
2E/R
17-1. The magnetic field of the earth can be reasonably approximated by assuming the
existence of a point dipole at the center of the earth with a dipole moment of
m = 8.00 × 1022 A·m2 . Using the equation for the magnetic field of a point dipole,
B = (µ0 /4π)[3(m · r̂)r̂ − m]/r3 , determine the magnitude and direction of the magnetic
field on the surface of the earth at (a) the equator and (b) the geographic north pole. For
the direction, use + to indicate geographic north and − to indicate geographic south.
Don’t worry about the geomagnetic angle of declination – assume that it is zero. Use
6.37 × 106 m as the radius of the earth. [(a) −70.0, 70.0 µT (b) −70.0, 70.0 µT]
17-2. Consider an electron moving near the earth’s equator. It experiences a Lorentz force due
to the earth’s magnetic field. Possible directions for this force include (1) vertically
upward away from the center of the earth, (2) vertically downward towards the center of
the earth, (3) east, (4) west, (5) north, (6) south, and (7) zero force. What will be the
direction of the force if the electron is moving
(a) vertically upward?
(b) east?
(c) north?
11
17-3. An electron is projected at a speed of 3.70 × 106 m/s in the i + j + k direction into a
T.
uniform magnetic field B = 6.43 i + By j − 8.29 k (Tesla), where By = [01]
Calculate (a) the x component, (b) the y component, and (c) the z component of the
resulting vector magnetic force on the electron. [(a) 3.00, 4.00 pN (b) −4.00, −6.00 pN
(c) 1.00, 2.00 pN]
18-1. A thin, horizontal copper rod is 1.29 m long and has a mass of 52.6 g. What is the
minimum current in the rod that can cause it to float in a horizontal magnetic field of
[01]
T? [0.100, 0.500 A]
18-2. Assume that in Atlanta, Georgia, the Earth’s magnetic field points northward and
downward at 60◦ below the horizontal, with a field strength of 52.0 µT. A tube in a neon
sign carries a current of 35.0 mA between two diagonally-opposite corners of a shop
window, which lies in a north-south vertical plane. The current enters the tube at the
bottom south corner and exits at the opposite corner which is [02]
m farther
north and 0.85 m higher up. Between these two points, the tube spells out the word
DONUTS. Determine (a) the x component, (b) the y component, and (c) the
z component of the total vector magnetic force on the neon tube. Define coordinate axes
so that the x axis points east, the y axis points north, and the z axis points up.
[(a) −4.00, 4.00 µN (b) −4.00, 4.00 µN (c) −4.00, 4.00 µN]
18-3. A rectangular loop consisting of N = 100 closely
wrapped turns of wire has dimensions a = 0.400 m
and b = 0.300 m and is oriented in a vertical plane so
as to make an angle of 30◦ with the x axis, as shown.
The loop carries a current I = 1.20 A and
experiences a uniform B = [03]
T
magnetic field directed along the +x axis.
(a) Calculate the magnitude of the magnetic moment
of the current-carrying loop. (b) Calculate the
magnitude of the magnetic torque experienced by the
loop. (c) Calculate the magnetic potential energy of
the loop in the field. [(a) 10.0, 20.0 A·m2
(b) 1.00, 4.00 J (c) −1.00, −4.00 J]
19-1. A cosmic-ray proton traveling at [01]
c is heading directly toward the center of
the Earth in the plane of Earth’s equator. Assuming that the Earth’s magnetic field has
a uniform magnitude of B = 50.0 µT in the equitorial plane, determine the radius of
motion of the cosmic-ray proton. Neglect relativistic effects if you know about them.
[4.00, 6.00 km]
19-2. At the equator, assume that the earth’s magnetic field is directed northward with a
magnitude of 50 µT and that there is an electric field of 100 N/C directed radially
inward. The Earth’s radius is roughly 6.37 × 106 m. A hypothetical charged particle is
orbiting the earth in the equatorial plane and near the earth’s surface at
[02]
m/s in an easterly direction under these conditions. What is this
hypothetical particle’s charge to mass ratio (watch the sign)? [−20.0, −40.0 kC/kg]
12
19-3. A long metallic conductor oriented along the z axis has an
oblong cross section in the xy plane as shown and carries current
in the −z direction (a right-handed coordinate system directs −z
into the page). There is a uniform external magnetic field
present with field lines lying parallel to the xy plane. We label
several directions as follows: (1) ↑, (2) %, (3) →, (4) &, (5) ↓,
(6) ., (7) ←, (8) -, (9) magnitude is zero, (10) none of the
above. What is the direction of the external magnetic field if the
most negative potential occurs at point A?
20-1. A loop of wire of length L = 10.8 cm is stretched into the shape of a square and carries a
current of I = [01]
A. Determine the magnitude of the magnetic field at the
center of the loop due to the current-carrying wire. [10.0, 20.0 µT]
20-2. A conductor consisting of a circular loop of
radius R = [02]
m and two straight,
long sections, carries a current of I = 7.00 A. In
the figure, the loop is viewed from the +z
direction. Determine the z component of the
resulting magnetic field at the center of the loop.
[−1.00, −3.00 µT]
20-3. Two long parallel wires, each having mass density
λ = [03]
g/m, are supported in the
horizontal plane by strings 6.00 cm long, as shown.
When both wires carry the same current I in opposite
directions, the wires repel each other so that the angle
θ between the supporting strings is 16.0◦ . Determine
the magnitude of the current. [10.0, 30.0 A]
21-1. Two square current-carrying loops and two closed integration paths, one dashed and one
solid, are arranged as shown. If the positive current direction
H is chosen to be clockwise,
the current in the loop on the left is +10.0 A. Defining ξ = B · ds for a given path, we
find that the ratio ξdashed /ξsolid = [01]
. Determine the current (magnitude
and sign) in the right-hand loop. Hint: Draw a top-view diagram of the figure, which
should make the looped paths and current directions more apparent. [−90.0, 90.0 A]
13
21-2. In the cross-sectional view of a coaxial cable below, the
center conductor is surrounded by a rubber layer,
which is surrounded by an outer conductor, which is
surrounded by another rubber layer. In a particular
application, the current in the inner conductor is
mA, directed out of the page,
Iinner = [02]
while the current in the outer conductor is
mA, directed into the page.
Iouter = [03]
Determine magnitude and sign of the vertical (up = +)
component of (a) the magnetic field at point a and
(b) the magnetic field at point b. [(a) −40.0, 40.0 µT
(b) −40.0, 40.0 µT]
21-3. A superconducting solenoid with 2000 turns/m is meant to generate a magnetic field of
[04]
T. (a) Calculate the current required. (b) Determine the force per unit
length exerted on the windings by this magnetic field. Note that while an individual
current-carrying wire segment experiences no force due to the B-field that it creates, that
wire segment does experience a force due to the collective field produced by all of the
current-carrying coils around the solenoid. [(a) 3.00, 6.00 kA (b) 30.0, 90.0 kN/m]
22-1. An ideal solenoid 7.20 cm in diameter and 38.0 cm long has
N = [01]
turns and carries 12.0 A of current.
Calculate the magnetic flux through the surface of a disk of
radius 5.00 cm that is positioned perpendicular to and centered
on the axis of the solenoid. [1.00, 5.00 mT·m2 ]
22-2. Consider the hemispherical closed surface with radius
R = 3.00 cm shown below, which is in a uniform magnetic field
◦
of 0.250 T that makes an angle θ = [02]
with the
vertical. (a) Calculate the magnetic flux entering the circular
face of the closed surface. (b) Calculate the magnetic flux
entering through the hemispherical surface.
[(a) −0.700, 0.700 mT·m2 (b) −0.700, 0.700 mT·m2 ]
22-3. The magnetic field due to a magnetic dipole located at the origin, can be described as a
function of position ~r = rr̂, via the expression
B=
~ · r̂)r̂ − m
~
µ0 3(m
,
3
4π
r
A·m2 be
where m is the dipole moment vector. Let a dipole moment of [03]
oriented along the +z direction and imagine a Gaussian sphere of radius 0.750 m
centered on the dipole. (a) Calculate the magnetic flux exiting the upper (+z)
hemisphere. (b) What is the magnetic flux exiting the lower (−z) hemisphere? Hint: Try
using spherical coordinates, and don’t panic. The math is easy. [(a) −50.0, 50.0 µT·m2
(b) −50.0, 50.0 µT·m2 ]
14
23-1. When 1.00 g of an unknown material is placed in a north-pointing 50-µT magnetic field,
it is found to exhibit a magnetic moment that points roughly 25◦ east of north. How
many of the following statements are true of this material? (1) The material is
diamagnetic. (2) The moment will grow with decreasing temperature. (3) The material
exhibits magnetic hysteresis. (4) The material is paramagnetic. (5) Removing the
applied field would eliminate the moment. (6) The moment is permanent. (7) The
moment is induced by the present field. (8) The material is ferromagnetic. (9) The
material has a magnetic domain structure. (10) The material would be weakly repelled
by a strong magnet. (11) The material would be weakly attracted by a strong magnet.
(12) The material could be strongly attracted to a strong magnet. (13) The material
would be attracted to a steel paper clip. (14) The material would not be attracted to a
steel paper clip. (15) χ < 0. (16) µ/µ0 > 1. (17) This is impossible behavior for any
known material.
23-2. A toroid with N = 500 turns, a mean radius of R = 20.0 cm, a coil radius of r = 1.00 cm,
, is carrying 2.55 A of
and a powdered steel core with susceptibility χ = [01]
current. Assume that the field is uniform inside the toroid (i.e. R r). (a) Calculate the
magnetic permeability µ of the steel core. (b) Calculate the magnetic field strength µ0 H
inside the toroid. (The factor µ0 makes the units the same as those of B.) (c) Calculate
the magnetization µ0 M inside the toroid. (d) Calculate the magnetic field B inside the
toroid. [(a) 0.100, 0.300 mT·m/A (b) 1.00, 2.00 mT (c) 0.100, 0.300 T
(d) 0.100, 0.300 T]
23-3. At room temperature (T = 300 K), a paramagnetic gas of density
ρ = 5.00 × 1019 molecules/cm3 is subjected to a [02]
T magnetic field. The
gas responds with a magnetic moment of 0.01µB per molecule. (a) Determine the
magnetization (magnetic moment per unit volume) of the gas. (b) Determine the
magnetic susceptibility of the gas. (c) Determine the Curie constant of the gas.
[(a) 3.00, 6.00 A/m (b) 1.00 × 10−6 , 3.00 × 10−6 (c) 300, 700 A·K/T·m]
24-1. A uniform magnetic field oscillates in time as B = B0 cos(ωt),
where B0 = [01]
T, within a circular region of radius
a = 2.50 cm. A loop of wire containing a single 1.20 V light bulb
surrounds the field-containing region. Determine the oscillation
frequency needed to light the bulb (i.e. to match the emf amplitude
with the light bulb voltage specification). Note: do NOT use the
more appropriate rms quantities if you know about them.
[400, 990 Hz]
24-2. A coil of N2 = 15 turns and radius a = 10.0 cm surrounds a long solenoid of radius
r = 2.00 cm and N1 = 1000 turns/m. If the current in the solenoid varies as
I = I0 cos(ωt), where I0 = [02]
A and ω = 120 s−1 , determine the maximum
induced emf in the coil. [5.00, 9.00 mV]
15
24-3. A square coil that consists of 100 turns of wire rotates about a
vertical axis at 1500 rev/s. The horizontal component of the
Earth’s magnetic field at the location of the coil is
µT. Determine the maximum emf induced in the
[03]
coil by this field. [30.0, 80.0 mV]
25-1. Use Lenz’s law and Figures (a)–(d) below to answer the following questions concerning
the direction of induced currents.
(a) What is the direction of the induced current in resistor R in Fig. (a) when the bar
magnet is moved to the left? (1) left (2) right (3) zero current
(b) What is the direction of the current induced in the resistor R right after the switch S
in Fig. (b) is closed? (1) left (2) right (3) zero current
(c) What is the direction of the induced current in R when the current I in Fig. (c)
decreases rapidly to zero? (1) left (2) right (3) zero current
(d) A copper bar is moved to the right while its axis is maintained in a direction
perpendicular to a magnetic field, as shown in Fig. (d). If the top of the bar becomes
positive relative to the bottom, what is the direction of the magnetic field? (1) left
(2) right (3) up (4) down (5) into page (6) out of page.
16
25-2. The square loop shown is made of wires with total
series resistance of 12.6 Ω. It is placed in a uniform
0.117-T magnetic field directed into the plane of the
paper. The loop, which is hinged at each corner, is
pulled as shown until the separation between points A
and B is 3.00 m. If this process takes
seconds, what is the average
t = [01]
current generated in the loop (magnitude and sign).
Let “+” indicate clockwise current and “−” indicate
counterclockwise current. [2.00, 3.00 mA]
25-3. A circular loop of wire is moved at constant speed through regions where uniform
magnetic fields of the same magnitude are directed into or out of the paper, as indicated.
The instantaneous location of the loop, as it moves to the right, is indicated at seven
positions.
(a) At how many of the seven positions will there be no induced emf in the loop?
(b) At how many of the seven positions will there be a CW induced emf in the loop?
(c) At how many of the seven positions will there be a CCW induced emf in the loop?
(d) At which position will the magnitude of the induced emf be maximum?
25-4. An electric motor consists of a rectangular coil (2.50 cm × 4.00 cm) with 80 turns of wire
that draws I = [02]
A of current as it rotates at 3600 rev/min in a uniform
B = 0.800 T magnetic field. (a) Determine the maximum torque delivered by the motor.
(b) Determine the peak power produced by the motor. [(a) 0.100, 0.300 J
(b) 40.0, 99.0 W]
26-1. A helicopter has blades with a length of 3.00 m extending outward from a central hub
and rotating at f = [01]
rev/s. If the vertical component of the Earth’s
magnetic field is 50.0 µT, what is the emf induced between the blade tip and the center
hub? [1.00, 3.00 mV]
17
26-2. A conducting axle with mass m = [02]
kg and length L = 1.50 m long rolls at
constant velocity along a pair of conducting rails that are inclined 30◦ from the
horizontal. A resistive load R = 100 Ω connects the rails, which are immersed in a
uniform 0.800 T magnetic field that points downward. (a) Determine the magnitude of
the magnetic force on the axle. (b) Determine the speed of the rolling axle. Hints: Draw
a free-body diagram. Separate forces into components, parallel and perpendicular to the
rail. Take the inclination angle into account when computing the induced emf.
[(a) 50.0, 99.0 N (b) 4.00, 8.00 km/s]
26-3. A closed rectangular wire loop has dimensions
w = 0.80 m, ` = 1.50 m, mass m = [03]
g,
and resistance R = 0.750 Ω. The rectangle is allowed to
fall through a region of uniform magnetic field, directed
out of the page as shown, and accelerates downward as
it approaches a terminal speed of 2.00 m/s with its top
not yet in the region of the field. Calculate the
magnitude of the magnetic field. [0.400, 0.700 T]
27-1. A 10.0-mH inductor carries a current of I = Imax sin ωt with Imax = 5.00 A and
ω/2π = 60.0 Hz. What is the magnitude of the back emf at t = [01]
s?
[0.0, +20.0 V]
27-2. For the RL circuit shown, let L = 3.00 H, R = 8.00 Ω, and
V. The switch is closed at t = 0.
E = [02]
(a) Calculate the ratio of the potential difference across the
resistor to that across the inductor when I = 2.00 A.
(b) Calculate the voltage across the inductor [03]
s
after the switch is closed. [(a) 0.60, 1.20 (b) 0.100, 0.800 V]
18
27-3. Two coils, held in fixed positions, have a mutual inductance of 130 µH. What is the peak
voltage in one when a sinusoidal current given by I(t) = Imax sin(ωt) flows in the other?
s−1 . [1.00, 1.50 V]
Imax = 12.0 A and ω = [04]
27-4. A [05]
-V battery, a 5.00-Ω resistor, and a 12.0-H inductor are connected in
series. After the current in the circuit has reached its maximum value, calculate (a) the
power being supplied by the battery, (b) the power being delivered to the resistor, (c) the
power being delivered to the inductor, and (d) the energy stored in the magnetic field of
the inductor. [(a) 20.0, 99.0 W (b) 20.0, 99.0 W (c) 0.0, 99.0 W (d) 20.0, 99.0 J]
28-1. The switch in the circuit shown is connected to
point a for a long time. R = 14.0 Ω,
L = 0.110 H, C = [01]
µF, and
E = 12 V. After the switch is thrown to point b,
what are (a) the frequency of oscillation of the
LC circuit, (b) the maximum charge that
appears on the capacitor, (c) the maximum
current in the inductor, and (d) the total
energy the circuit possesses at t = 3.00 s?
[(a) 400, 500 Hz (b) 10.0, 20.0 µC
(c) 30.0, 50.0 mA
(d) 7.00 × 10−5 , 9.90 × 10−5 J]
28-2. In the figure, let R = 7.60 Ω, L = [02]
mH, and
C = 1.80 µF. (a) Calculate the frequency of the damped
oscillation of the circuit. (b) What is the critical resistance?
[(a) 2.00 × 103 , 3.00 × 103 Hz (b) 60.0, 90.0 Ω]
28-3. The switch in the figure is thrown closed at t = 0.
R = 75 Ω, E = [03]
V, C = 1.80 µF, and
L = 2.20 mH. Before the switch is closed, the capacitor is
uncharged and all currents are zero. The instant after the
switch is closed, determine the currents in (a) L, (b) C,
and (c) R. Also determine the potential differences across
(d) L, (e) C, and (f) R. A long time after the switch is
closed, determine the potential differences across (g) L,
(h) C, and (i) R. [(a) 0.000, 0.500 A (b) 0.000, 0.500 A
(c) 0.000, 0.500 A (d) 0.0, 40.0 V (e) 0.0, 40.0 V
(f) 0.0, 40.0 V (g) 0.0, 40.0 V (h) 0.0, 40.0 V
(i) 0.0, 40.0 V]
19
29-1. An inductor is connected to a 20.0-Hz power supply that produces a 50.0-V peak voltage.
What inductance is needed to keep the instantaneous current in the circuit below
mA? [4.00, 7.00 H]
[01]
29-2. What maximum current flows through a [02]
-µF capacitor when it is
connected across (a) a North American outlet having Vrms = 120 V and f = 60.0 Hz?
(b) a European outlet having Vrms = 240 V and f = 50.0 Hz? [(a) 0.100, 0.400 A
(b) 0.100, 0.400 A]
29-3. (a) Draw to scale a phasor diagram showing Z, XL , XC , and φ for an AC series circuit
with R = [03]
Ω, C = 11.0 µF, L = 0.200 H, and f = (500/π) Hz. Submit
this part of the problem to the 220 homework bins on a single sheet of paper before class.
Include your CID!!! (b) What is Z? (c) What is the phase angle φ? [(b) 200, 500 Ω
(c) 10.0, 30.0◦ ]
30-1. A series RLC circuit is used in a radio to tune in to an FM station broadcasting at
99.7 MHz. The resistance in the circuit is 12.0 Ω, and the inductance is
[01]
µH. What capacitance should be used? [1.00, 3.00 pF]
30-2. In a certain series RLC circuit, Irms = 9.00 A, Vrms = 180 V, and the current leads the
◦
voltage by [02]
. (a) What is the resistance R of the circuit? (b) What is the
reactance of the circuit (XL − XC )? [(a) 5.0, 20.0 Ω (b) 5.0, 20.0 Ω]
30-3. In a series RLC circuit, R = [03]
Ω, XC = 150 Ω, XL = 100 Ω,
E = 100 V (rms), and f = [04]
Hz. (a) Find L. (b) Find C. (c) Find the rms
current flowing in the circuit. (d) Find the phase shift φ. (e) Find the power dissipated.
(f) Find the ratio of VCmax /VRmax . [(a) 0.100, 0.400 H (b) 10.0, 25.0 µF
(c) 0.300, 0.700 A (d) −90.0, +90.0◦ (e) 30.0, 70.0 W (f) 0.50, 2.00]
31-1. A step down transformer is used for recharging the batteries of a portable device such as
a tape player. The turns ratio inside the transformer is 13:1, and it is used with 120 V
(rms) household service. If a particular ideal transformer draws [01]
A (rms)
from the house outlet, (a) what (rms) voltage is supplied to the tape player from the
transformer? (b) What (rms) current is supplied to the tape player from the transformer?
(c) How much power is delivered? [(a) 5.00, 9.50 V (b) 3.00, 6.00 A (c) 30.0, 50.0 W]
32-1. An air-filled circular parallel plate capacitor with radius a = 5.00 cm and plate
separation d = 2.00 mm, is driven by a 60 Hz alternating voltage with amplitude
V = [01]
V. Naturally, the magnitude of the current is greatest at the instant
when the voltage is zero. At such an instant, determine the magnitude of the (a) rate of
change of electric flux in the capacitor, (b) displacement current in the capacitor, and
(c) magnetic field near the edge of the capacitor. [(a) 100, 300 kV·m/s (b) 1.00, 3.00 µA
(c) 5.00, 9.99 pT]
20
32-2. Which of the following laws or principles are required to solve the problems described
below. In each case, choose only one answer. If more than one response seems
appropriate, choose the one most fundamental to the problem at hand. Possible
responses are: (1) Gauss’s law of electrostatics, (2) Gauss’s law of magnetism,
(3) Faraday’s law, (4) Ampere-Maxwell law, (5) Lorentz force law.
(a) Determine the magnetic field near a current carrying wire.
(b) Determine the trajectory of a proton in a uniform magnetic field.
(c) Determine the electric field inside a charged capacitor.
(d) Determine the magnetic field inside a charging capacitor.
(e) Determine the power delivered by a wind-turbine generator.
(f) Determine the electric field near the surface of a conductor.
(g) Determine the voltage difference between the ends of a metal bar moving in a
magnetic field.
(h) Determine the total magnetic flux through a closed surface.
(i) Determine the voltage in the secondary winding of a transformer.
(j) The magnetic field produced by a moving charged particle.
32-3. Determine the validity of each of the following statements. Possible responses are
(1) True or (2) False.
(a) Ampere’s law is physically equivalent to the Lorentz force law.
(b) Gauss’s law of electrostatics is physically equivalent to Gauss’s law of magnetism.
(c) Coulomb’s law is physically equivalent to Gauss’s law of electrostatics.
(d) The Biot-Savart law is physically equivalent to Faraday’s law.
(e) Lenz’s law is a corollary of Faraday’s law.
(f) Gauss’s law of electrostatics relates electric charge to electric flux.
(g) Gauss’s law of magnetism relates magnetic charge to magnetic flux.
(h) The Ampere-Maxwell law relates magnetic circulation to changing electric flux.
(i) The Ampere-Maxwell law relates magnetic circulation to electric current.
(j) Faraday’s law relates electric charge to changing magnetic flux.
32-4. Complete this problem on a separate sheet of paper and submit it with your CID#
prominently displayed.
Name and state each of Maxwell’s equations and the Lorentz force law in plain English
with no reference to symbols or acronyms.
21
33-1. A transverse wave on a string is described by the wave function y = y0 sin(kx + ωt),
where y0 = [01]
m, k = [02]
m−1 , and ω = [03]
s−1 . At
time t = 0.200 s and string position x = 1.6 m, determine the following quantities:
(a) Wavelength.
(b) Wavenumber.
(c) Wave frequency (cyclic).
(d) Wave period. (e) Wave velocity (magnitude and sign).
(f) Transverse string position (magnitude and sign).
(g) Peak transverse string position (magnitude).
(h) Average transverse string position (magnitude).
(i) Transverse string velocity (magnitude and sign).
(j) Transverse string acceleration (magnitude and sign).
[ (a) 10.0, 25.0 m (b) 0.200, 0.600 m−1 (c) 1.00, 3.00 Hz (d) 0.400, 0.700 s
(e) −60.0, +60.0 m/s (f) −0.150, 0.150 m (g) 0.000, 0.150 m (h) −0.150, 0.150 m
(i) −3.00, +3.00 m/s (j) −40.0, +40.0 m/s2 ]
33-2. The speed of an electromagnetic wave traveling in a transparent nonmagnetic substance
√
is 1/ µ0 κ0 , where κ is the dielectric constant of the substance, which depends on
frequency. Determine the speed of light in a liquid with a dielectric constant of
κ = [04]
at optical frequencies. FYI, water has a dielectric constant of 1.78 in
this range. [2.00 × 108 , 3.00 × 108 m/s]
33-3. A standing-wave interference pattern is set up by radio waves between two metal sheets
d = [05]
m apart. This is the shortest distance between the plates that will
produce a standing-wave pattern. What is the fundamental frequency of the radio waves?
[50.0, 95.0 MHz]
33-4. Match the following object sizes to the wavelength of the appropriate electromagnetic
radiation. Possible responses are (1) gamma rays, (2) x-rays, (3) ultraviolet rays,
(4) visible light, (5) infrared, (6) microwaves, (7) FM radio waves, (8) AM radio wave,
(9) long-wavelength radiation.
(a) An atom.
(b) Your finger.
(c) Your height.
(d) The thickness of a human hair.
(e) A bacterium
(f) A virus.
(g) An atomic nucleus.
(h) Your campus.
(i) Your world (which may also be your campus).
22
34-1. Neldon the Nerd went to see Star Wars and was fascinated by the red light pulses from
the laser blasters. He decides to make such a weapon. He chooses a pulsed laser with a
wavelength of 580 nm so that the light will be red.
m long and lasted
(a) The pulses in the movie appeared to be L = [01]
roughly 0.2 seconds. But Neldon is annoyed to discover that a light pulse this long must
have a temporal duration of only
.
(b) Neldon can’t make such a pulse, but does manage to build a gun with a
T = [02]
µs pulse. At t = 0, when the pulse begins, E is exactly zero at the
muzzle of the gun. During the length of the pulse, E will be zero again
more
times.
(c) Neldon decides to blast the white clock on the wall across the room since its white
reflective surface resembles that of a storm trooper uniform. A short time after the small
spot of light strikes near the center of the clock face, the electric field points toward
M = [03]
minutes after 12 o’clock. At this same instant, the magnetic field
points toward
minutes after 12 o’clock.
[(a) 1.00, 4.00 ns (b) 1.00 × 109 , 3.00 × 109 (c) 0.0, 59.9 min]
34-2. Neldon then adjusts the pulse length of his laser blaster to 2.00 µs and the beam
mm. Though he finds that his laser pulse has an
diameter to D = [04]
impressive total energy of E = [05]
kJ, he is again annoyed when the clock
doesn’t shatter. (a) So he computes the momentum delivered by the pulse assuming
complete reflection, and finds it to be a mere
. He then calculates (b) the average
beam intensity, (c) the peak beam intensity, (d) the peak E-field magnitude, and (e) the
peak B-field magnitude. [(a) 2.00 × 10−5 , 4.00 × 10−5 kg·m/s (b) 5.00 × 1014 , 9.00 × 1014
W/m2 (c) 1.00 × 1015 , 2.00 × 1015 W/m2 (d) 6.00 × 108 , 9.00 × 108 N/C (e) 2.00, 3.00 T]
35-1. An AM radio station broadcasts isotropically (equally in all directions) with an average
power of 4.00 kW. An optimally-oriented λ/2 dipole antenna 65.0 cm long is located
d = [01]
km from the transmitter. (a) Compute the maximum E-field at the
receiving antenna. (b) Compute the maximum B-field at the receiving antenna.
Compare this to the magnetic field of the earth, which is roughly 50 µT. (c) Compute the
maximum emf induced by this signal between the two ends of receiving antenna.
[(a) 0.300, 0.500 N/C (b) 1.00, 2.00 nT (c) 0.200, 0.400 V]
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