Physics 220 Homework Problems, Spring Term, 2008 1-1. A cat slides down a rubber rod and falls from the rod into a metal pail A resting on a non-conducting shelfwith two other metal pails, B and C, which are in contact, but neither is in contact with A. The shelfbreaks 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. Consi der vecto rs R = (2.10,y = [01] , 1.00) and S = (3.30, 4.00, 0.90). (a) Calculate the magnitude ofR. (b) Calculate the z component of unit vector ˆ R. (c) Calculate the angle between vectors R and S. (d) Calculate the z component ofR × 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 iden tical 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 ◦ ]
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1-1. A cat slides down a rubber rod and falls from the rodinto 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 toA, and all pails fall separated to the non-conductingfloor. The cat then runs away.
(a) At the end of this process the charge on pail A1. is positive.2. is negative.3. is zero.
(b) At the end of this process the charge on pail B1. 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 C1. 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 R.
(c) Calculate the angle between vectors R and S. (d) Calculate the z component of
2-1. A charged particle with a charge of −7.5 pC is placed at the origin where the electricfield (SI units) is E = (3.75 i− 2.90 j). This force is directed toward which quadrant oraxis of the xy plane?
1. I2. II
3. III4. IV5. +x6. −x7. +y8. −y
2-2. The sketch in the square frame represents two negative pointcharges and one positive point charge, all of the same magnitude.The letters “a” and “b” simply designate two positions within theframe. 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”?
2-3. In the lab, an object having a net charge of Q = [01] 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]
3-1. Find the area of region bound by the curve y = b− x2 and the x axis, where
b = [01] . [1.00, 7.00]
3-2. 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 isan appropriate differential volume for determining the totalvolume of the cup? The radius r of the cup varies with theheight z according to (r/a)2 = z/L.
3-3. Consider a cone of height L and base radius a. What is anappropriate differential area for determining the total outersurface area?
1. 2πa√
a2 + L2z dz/L2
2. 2πaz dz/L
3. 2πa dz/L4. πa2 dz/L2
5. π√
a2 + L2 dz
3-4. A charged hemispherical bowl with radius 13.7 cm and charge
density σ = [02] 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 vectorelectric 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 fieldlines 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.
4-2. Consider the pattern of electric field lines in the figure.
(a) By counting field lines, rank the left-hand (L) andright-hand (R) charges in order of decreasing magnitude.1. L > R2. R > L
3. L = R(b) Rank the points in the figure according to decreasingelectric field magnitude.1. A = B > C 2. C > A = B3. A > C = B4. C > B > A5. A > B > C
(c) The direction of the electric field at point C is1. up
2. down3. left4. right5. 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
speed of v = [01] m/s in a region where an upward electric field has a uniform
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.
5-2. Four closed surfaces, S 1 through S 4, are drawn together with threecharges, −2Q, +Q, and −Q. Rank the four surfaces according to theamount of electric flux exiting each one. In answering this problemwe are asking about NET flux. [Exiting flux (field lines going out) iscanceled by field lines coming in.] That is, summing the net charge
enclosed is important.1. S 4 > S 2 > S 1 > S 32. S 3 > S 1 > S 2 > S 43. S 4 = S 2 > S 1 > S 34. S 3 > S 1 > S 2 = S 45. S 2 = S 3 > S 1 = S 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]
7-1. An electron is placed half way between two parallel plates (A and B). Plate A is held at0 V and plate B is held at 100 V. The electron will:
1. Hit plate A with 0 J of energy.2. Hit plate B with 0 J of energy.3. Hit plate A with 8 × 10−18 J of energy.4. Hit plate B with 8 × 10−18 J of energy.5. Hit plate A with 1.6× 10−17 J of energy.6. Hit plate B with 1.6× 10−17 J of energy.
7-2. An electron is released from rest in a uniform electric field of magnitude
E = [01] V/m. (a) Through what potential difference will it have passed after
moving 1.24 cm? (b) How fast will the electron be moving after having traveled that
8-2. 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 thefigure. Their potential values are shown. Anumber of locations are labeled with dots. Wealso 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 fieldpointing?(c) Which point has the lowest electric field?(d) What direction is that lowest electric fieldpointing?
9-1. A uniformly charged insulating rod of length 60.0 cm is bent into the shape of a
semicircle. If the rod has a total charge of Q = [01] pC. Find the electricpotential at the center of the semicircle. [−2.50, 2.50 V]
9-2. A hollow spherical metallic shell of radius of R = 25 cm holds a net surface charge of
Q = [02] 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,
separated by a distance of [01] mm. If a 20-V potential difference is applied
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
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,
C 1 = [03] µF, C 2 = 10.0 µF,
and C 3 = 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 C 3?
[(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 thecorrect answers.
1. Add a larger capacitor in series with the first.2. Add a smaller capacitor in series with the first.3. Add a larger capacitor in parallel with the first.4. Add a smaller capacitor in parallel with the first.
11-1. Two capacitors C 1 = 25.0 µF and C 2 = [01] µF are connected in parallel and
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]
11-2. A parallel plate air gap capacitor is connected across a 12.0 V potential. At this point it
stores [03] µC of charge. It is then disconnected from the source while still
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 thecapacitor? (d) What is the charge on the capacitor? [(a) 2.00, 6.00 µF (b) 5.0, 15.0 µF
11-4. You have a square parallel plate capacitor (edge length a and separation d). It howeverdoes 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. half the edge length, and half the separation.2. half the edge length, half the separation, and add a dielectric of constant 2.3. half the edge length and a dielectric of constant of 2.5.4. one fourth the edge length and four times the separation.5. one fourth the edge length, twice the separation, and a dielectric of 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.
13-1. When the voltage across a certain conducting filament is doubled, the current flowingthrough it is observed to increase by a factor greater than two. What type of materialcould the conductor be made of? Hint: Consider the effects of heating.
1. copper2. quartz3. lead4. silicon
13-2. The resistance of a platinum wire is to be calibrated for low-temperature measurements.
A platinum wire with a resistance of [01] Ω at 20C is immersed in liquid
nitrogen at 77 K (−196C). 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
14-3. You have a resistor connected across a battery. If you wish to increase the current drawnfrom the battery, which of the following options will work? Choose all of the correctanswers.
1. Add a larger resistor in series with the first.
2. Add a smaller resistor in series with the first.3. Add a larger resistor in parallel with the first.4. Add a smaller resistor in parallel with the first.
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
ρ = 3.52× 105 Ω·m, L is 4.00 cm, ra = 0.50 cm and rb = [03] cm. (a) The
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
(a) If at some instant the capacitor in this circuit has no charge,what is the current in the resistors?
1. 02. E/2R
3. E/R4. 2E/R
(b) If at some instant the capacitor in this circuit has charge Q = C E, what is thecurrent in the resistors?
1. 02. E/2R3. E/R4. 2E/R
(c) If at some instant the capacitor in this circuit has charge Q = 2C E, what is thecurrent in the resistors?
1. 02. E/2R3. E/R4. 2E/R
17-1. Consider an electron moving near the earth’s equator. It experiences a Lorentz force dueto the earth’s magnetic field. Possible directions for this force include (1) up or outward,(2) down or inward, (3) east, (4) west, (5) north, (6) south, and (7) zero force. What willbe the direction of the force if the electron is moving
(a) upward?
(b) downward?(c) east?(d) west?(e) north?
17-2. An electron is projected at a speed of 3.70× 106 m/s in the i + j + k direction into a
uniform magnetic field B = 6.43 i + By j− 8.29 k (Tesla), where By = [01] T.
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
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]
19-3. A long metallic conductor oriented along the z axis has anoblong cross section in the xy plane as shown and carries currentin the −z direction. There is a uniform external magnetic fieldpresent with field lines lying parallel to the xy plane. We labelseveral directions as follows: (1) ↑, (2) , (3) →, (4) , (5) ↓,(6) , (7) ←, (8) , (9) magnitude is zero, (10) none of theabove. What is the direction of the external magnetic field if the
most negative potential occurs at(a) point A?(b) point B?(c) point C?(d) point D?
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 thehorizontal 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
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 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]
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
I inner = [02] mA, directed out of the page,
while the current in the outer conductor is
I outer = [03] mA, directed into the page.
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 thecurrent-carrying coils around the solenoid. [(a) 3.00, 6.00 kA (b) 30.0, 90.0 kN/m]
23-3. A coil of N 2 = 15 turns and radius a = 10.0 cm surrounds a long solenoid of radius
r = 2.00 cm and N 1 = 1000 turns/m. If the current in the solenoid varies as
I = I 0 cos(ωt), where I 0 = [03] A and ω = 120 s−1, determine the maximum
induced emf in the coil. [5.00, 9.00 mV]
24-1. Use Lenz’s law and Figures (a)–(d) below to answer the following questions concerningthe direction of induced currents.
(a) What is the direction of the induced current in resistor R in Fig. (a) when the barmagnet 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 Sin 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 directionperpendicular to a magnetic field, as shown in Fig. (d). If the top of the bar becomespositive 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.
25-4. 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]
26-1. A 10.0-mH inductor carries a current of I = I max sin ωt with I max = 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]
26-2. For the RL circuit shown, let L = 3.00 H, R = 8.00 Ω, and
E = [02] V. The switch is closed at t = 0.
(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]
26-3. 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) = I max sin(ωt) flows in the other?
I max = 12.0 A and ω = [04] s−1. [1.00, 1.50 V]
26-4. 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) thepower 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]
30-1. 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]
30-2. Which of the following laws or principles are required to solve the problems describedbelow. In each case, choose only one answer. If more than one response seemsappropriate, choose the one most fundamental to the problem at hand. Possibleresponses 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 amagnetic 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.
30-3. 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.
30-4. 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 Englishwith no reference to symbols or acronyms.
31-4. Match the following object sizes to the wavelength of the appropriate electromagneticradiation. 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).
32-1. 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 awavelength of 580 nm so that the light will be red.
(a) The pulses in the movie appeared to be L = [01] m long and lasted
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
32-3. 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 = [06] 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.