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Fundamentals of Ethics for Scientists and Engineers 1st Edition Edmund G. Seebauer, Robert L. Barry - Solutions

Instead of sending power by a 750-kV, 1000-A transmission line, one desires to beam this energy via an electromagnetic wave. The beam has a uniform intensity within a cross-sectional area of 50 m2. What are the rms values of the electric and the magnetic fields?
A laser pulse has an energy of 20 J and a beam radius of 2 mm. The pulse duration is 10 ns and the energy density is constant within the pulse.(a) What is the spatial length of the pulse?(b) What is the energy density within the pulse?(c) Find the electric and magnetic amplitudes of the laser pulse.
The electric field of an electromagnetic wave oscillates in the y direction and the Poynting vector is given byS(x , t) = (100 W / m2) cos2 [10x - (3 ×109)t]iwhere x is in meters and t is in seconds.(a) What is the direction of propagation of the wave? (b) Find the
A pulsed laser fires a 1000-MW pulse of 200-ns duration at a small object of mass 10 mg suspended by a fine fiber 4 cm long. If the radiation is completely absorbed without other effects, what is the maximum angle of deflection of this pendulum?
A 10- by 15-cm card has a mass of 2 g and is perfectly reflecting. The card hangs in a vertical plane and is free to rotate about a horizontal axis through the top edge. The card is illuminated uniformly by an intense light that causes the card to make an angle of 1o with the vertical. Find the
A valuable 0.08-kg gem and a 105-kg spaceperson are separated by 95 m. Both objects are initially at rest. The spaceperson has a 1.5-kW laser that can be used as a photon rocket motor to propel the person toward the diamond. How long would it take the spaceperson to move 95 m using the laser rocket
It has been suggested that spacecraft could be propelled by the radiation pressure from the sun. What must be the surface mass density (kg/m2) of a perfectly reflecting sheet so that at a distance of one astronomical unit the force due to radiation pressure is twice that due to the gravitational
Suppose a mass of 50 kg is attached to a perfectly reflecting sheet whose surface mass density is that obtained in Problem 43. What must be the surface area of the sheet so that at a distance of one astronomical unit the acceleration of the system away from the sun is 0.4 mm/s2? How does the
A very long wire of radius 4 mm is heated to 1000 K. The surface of the wire is an ideal blackbody radiator.(a) What is the total power radiated per unit length? Find(b) The magnitude of the Poynting vector S,(c) Erms, and(d) Brms at a distance of 25 cm from the wire.
A blackbody sphere of radius R is a distance 2 × 1011 m from the sun. The effective area of the body for absorption of energy from the sun is πR2, but the area for radiation by the object is 4πR2. The power output of the sun is 3.83 × 1026 W. What is the temperature of the sphere?
Show by direct substitution that Equation 32-17a is satisfied by the wave functionEy = E0 sin (kx – ωt) = E0 sin k(x – ct)where c = ω/k.
(a) Using arguments similar to those given in the text, show that for a plane wave, in which E and B are independent of y and z,(b) Show that Ez and By also satisfy the wave equation.
(a) Show that if E is in volts per meter and B is in teslas, the units of the Poynting vector S = E × B/μ0 are watts per square meter.(b) Show that if the intensity I is in watts per square meter, the units of radiation pressure Pr = I/c are newtons per square meter.
A loop antenna that may be rotated about a vertical axis is used to locate an unlicensed amateur radio transmitter. If the output of the receiver is proportional to the intensity of the received signal, how does the output of the receiver vary with the orientation of the loop antenna?
An electromagnetic wave has a frequency of 100 MHz and is traveling in a vacuum. The magnetic field is given by B(z, t) = (10–8 T) cos (kz – ωt)i.(a) Find the wavelength, and the direction of propagation of this wave.(b) Find the electric vector E(z, t).(c) Give Poynting's vector, and
A circular loop of wire can be used to detect electromagnetic waves. Suppose a 100-MHz FM station radiates 50 kW uniformly in all directions. What is the maximum rms voltage induced in a loop of radius 30 cm at a distance of 105 m from the station?
The electric field from a radio station some distance from the transmitter is given by E = (10+ N/C) × cos 106t, where t is in seconds.(a) What voltage is picked up on a 50-cm wire oriented along the electric field direction?(b) What voltage can be induced in a loop of radius 20 cm?
A circular capacitor of radius a has a thin wire of resistance R connecting the centers of the two plates. A voltage V0 sin ωt is applied between the plates.(a) What is the current drawn by this capacitor?(b) What is the magnetic field as a function of radial distance r from the centerline within
A 20-kW beam of radiation is incident normally on a surface that reflects half of the radiation. What is the force on this surface?
The electric fields of two harmonic waves of angular frequency ω1 and ω2 are given by E1 = E1,0 cos (k1x – ω1t)j and E2 = E2,0 cos (k2x – ω2t + δ)j. Find(a) The instantaneous Poynting vector for the resultant wave motion and(b) The time-average Poynting vector. If E2 =
Suppose one has an excellent radio capable of detecting a signal as weak as 10–14 W/m2. This radio has a 2000-turn coil antenna having a radius of 1 cm wound on an iron core that increases the magnetic field by a factor of 200. The radio frequency is 140 KHz.(a) What is the amplitude of the
A 654-nm laser whose beam diameter is 0.4 mm points upward. A small, perfectly reflecting spherical particle having a diameter of 10 μm and a density of 0.2 g/cm3 is supported against gravity by the radiation pressure from the laser beam. Determine the power output of this laser.
A long, cylindrical conductor of length L, radius a, and resitivity ρ carries a steady current I that is uniformly distributed over its cross-sectional area.(a) Use Ohm's law to relate the electric field E in the conductor to I, ρ, and a.(b) Find the magnetic field B just outside the
A long solenoid of n turns per unit length has a current that slowly increases with time. The solenoid has radius R, and the current in the windings has the form I(t) = at.(a) Find the induced electric field at a distance r < R from the solenoid axis.(b) Find the magnitude and direction of the
Small particles might be blown out of solar systems by the radiation pressure of sunlight. Assume that the particles are spherical with a radius r and a density of 1 g/cm3 and that they absorb all the radiation in a crosssectional area of πr2. They are a distance R from the sun, which
Some science fiction writers have used solar sails to propel interstellar spaceships. Imagine a giant sail erected on a spacecraft subjected to the solar radiation pressure.(a) Show that the spacecraft's acceleration is given byWhere PS is the power output of the sun and is equal to 3.8 × 1026 W,
Novelty stores sell a device called a radiometer (Figure), in which a balanced vane spins rapidly. A card is mounted on each arm of the vane. One side of each card is white and the other is black. Assume that the mass of each card is 2 g, that the light-collecting area for each card is 1 cm2, and
When an electromagnetic wave is reflected at normal incidence on a perfectly conducting surface, the electric field vector of the reflected wave at the reflecting surface is the negative of that of the incident wave.(a) Explain why this should be.(b) Show that the superposition of incident and
An intense point source of light radiates 1 MW isotropically. The source is located 1.0 m above an infinite perfectly reflecting plane. Determine the force that acts on the plane.
(Multiple choice)(1)Which waves have greater frequencies, light waves or X rays?(2)Are the frequencies of ultraviolet radiation greater or less than those of infrared radiation?(3) True or false:(a) Maxwell's equations apply only to fields that are constant over time.(b) The wave equation can
1. What kind of waves have wavelengths of the order of a few meters?2. What is the frequency of a 3-cm microwave?3. Show that the units of E = cB are consistent; that is, show that when B is in teslas and c is in meters per second, the units of cB are volts per meter or newtons per coulomb.
1. The detection of radio waves can be accomplished with either a dipole antenna or a loop antenna. The dipole antenna detects the (pick one) [electric] [magnetic] field of the wave, and the loop antenna detects the [electric] [magnetic] field of the wave.2. A transmitter uses a loop antenna with
1. Use the known values of μ0 and Є0 in SI units to compute c = 1 / √Є0μ0 and show that it is approximately 3 × 108 m/s.2. At the surface of the earth, there is an approximate average solar flux of 0.75 kW/m2. A family wishes to construct a solar energy conversion system to power their
1. Show that the relation between the momentum carried by an electromagnetic wave and the energy, Equation 32-13, can also be derived using the Einstein–Planck relation, E = hf; the de Broglie equation, p = h/λ; and c = fλ.2. Find the force exerted by the electromagnetic wave on the reflecting
A 200-turn coil has an area of 4 cm2 and rotates in a magnetic field of 0.5 T.(a) What frequency will generate a maximum emf of 10 V?(b) If the coil rotates at 60 Hz, what is the maximum emf?
In what magnetic field must the coil of Problem 1 be rotating to generate a maximum emf of 10 V at 60 Hz?
A 2-cm by 1.5-cm rectangular coil has 300 turns and rotates in a magnetic field of 4000 G.(a) What is the maximum emf generated when the coil rotates at 60 Hz?(b) What must its frequency be to generate a maximum emf of 110 V?
The coil of Problem 3 rotates at 60 Hz in a magnetic field B. What value of B will generate a maximum emf of 24 V?
A 100-W light bulb is plugged into a standard 120-V (rms) outlet. Find(a) Irms,(b) Imax, and(c) The maximum power.
A 3-Ω resistor is placed across a generator having a frequency of 60 Hz and a maximum emf of 12.0 V.(a) What is the angular frequency ω of the current?(b) Find Imax and Irms. What is(c) The maximum power into the resistor,(d) The minimum power, and(e) The average power?
A circuit breaker is rated for a current of 15 A rms at a voltage of 120 V rms.(a) What is the largest value of Imax that the breaker can carry?(b) What average power can be supplied by this circuit?
What is the reactance of a 1.0-mH inductor at(a) 60 Hz,(b) 600 Hz, and(c) 6 kHz ?
An inductor has a reactance of 100 Ω at 80 Hz.(a) What is its inductance?(b) What is its reactance at 160 Hz?
What is the reactance of a 1.0-nF capacitor at(a) 60 Hz,(b) 6 kHz, and(c) 6 MHz?
An emf of 10.0 V maximum and frequency 20 Hz is applied to a 20-μF capacitor. Find (a) Imax and(b) Irms.
At what frequency is the reactance of a 10-μF capacitor(a) 1 Ω,(b) 100 Ω, and(c) 0.01 Ω?
Draw the resultant phasor diagram for a series RLC circuit when VL < VC. Show on your diagram that the emf will lag the current by the phase angle δ given by tan δ = VC – VL/VR
Two ac voltage sources are connected in series with a resistor R = 25 Ω. One source is given by V1 = (5.0 V) cos (ωt – a), and the other source is V2 = (5.0 V) cos (ωt + a), with a = π/6.(a) Find the current in R using a trigonometric identity for the sum of two cosines.(b) Use phasor
Show from the definitions of the henry and the farad that 1 / √LC has the unit s–1.
(a) What is the period of oscillation of an LC circuit consisting of a 2-mH coil and a 20-μF capacitor?(b) What inductance is needed with an 80-μF capacitor to construct an LC circuit that oscillates with a frequency of 60 Hz?
An LC circuit has capacitance C1 and inductance L1. A second circuit has C2 = ½C1 and L2 = 2L1, and a third circuit has C3 = 2C1 and L3 = ½ L1.(a) Show that each circuit oscillates with the same frequency.(b) In which circuit would the maximum current be greatest if the capacitor in
A 5-μF capacitor is charged to 30 V and is then connected across a 10-mH inductor.(a) How much energy is stored in the system?(b) What is the frequency of oscillation of the circuit?(c) What is the maximum current in the circuit?
A coil can be considered to be a resistance and an inductance in series. Assume that R = 100 Ω and L = 0.4 H. The coil is connected across a 120-V-rms, 60-Hz line. Find(a) The power factor,(b) The rms current, and(c) The average power supplied.
A resistance R and a 1.4-H inductance are in series across a 60-Hz ac voltage. The voltage across the resistor is 30 V and the voltage across the inductor is 40 V.(a) What is the resistance R?(b) What is the ac input voltage?
A coil has a dc resistance of 80 Ω and an impedance of 200 Ω at a frequency of 1 kHz. One may neglect the wiring capacitance of the coil at this frequency. What is the inductance of the coil?
A single transmission line carries two voltage signals given by V1 = (10V) cos 100t and V2 = (10 V) cos 10,000t, where t is in seconds. A series inductor of 1H and a shunting resistor of 1 kΩ is inserted into the transmission line as indicated in Figure.(a) What is the voltage signal observed
A coil with resistance and inductance is connected to a 120-V-rms, 60-Hz line. The average power supplied to the coil is 60 W, and the rms current is 1.5 A. Find(a) The power factor,(b) The resistance of the coil, and(c) The inductance of the coil.(d) Does the current lag or lead the voltage? What
A 36-mH inductor with a resistance of 40 Ω is connected to a source whose voltage is ← = (345 V) cos (150πt), where t is in seconds. Determine the maximum current in the circuit, the maximum and rms voltages across the inductor, the average power dissipation, and the maximum and average energy
A coil of resistance R, inductance L, and negligible capacitance has a power factor of 0.866 at a frequency of 60 Hz. What is the power factor for a frequency of 240 Hz?
A resistor and an inductor are connected in parallel across an emf ← = Emax as shown in Figure. Show that(a) The current in the resistor is IR = (←max /R) cos ωt,(b) The current in the inductor is IL = (←max /XL) cos (ωt – 90°), and(c) I = IR + IL = Imax cos (ωt –
Figure shows a load resistor RL = 20Ω connected to a high-pass filter consisting of an inductor L = 3.2 mH and a resistor R = 4Ω. The input voltage is ← = (100 V) cos (2πft). Find the rms currents in R, L, and RL if(a) f = 500 Hz and(b) f = 2000 Hz.(c) What fraction of the total
An ac source ←1 = (20 V) cos (2πft) in series with a battery ←2 = 16 V is connected to a circuit consisting of resistors R1 = 10Ω and R2 = 8Ω and an inductor L = 6 mH (Figure). Find the power dissipated in R1 and R2 if(a) f = 100 Hz,(b) f = 200 Hz, and(c) f = 800Hz.
A 100-V-rms voltage is applied to a series RC circuit. The rms voltage across the capacitor is 80 V. What is the voltage across the resistor?
The circuit shown in Figure is called an RC high-pass filter because high input frequencies are transmitted with greater amplitude than low input frequencies.(a) If the input voltage is Vin = V0 cos Ï‰t, show that the output voltage is(b) At what angular frequency is the output voltage half the
A coil draws 15 A when connected to a 220-V 60-Hz ac line. When it is in series with a 4-Ω resistor and the combination is connected to a 100-V battery, the battery current after a long time is observed to be 10 A.(a) What is the resistance in the coil?(b) What is the inductance of the coil?
Figure shows a load resistor RL = 20 Ω connected to a low-pass filter consisting of a capacitor C = 8 μF and resistor R = 4 Ω. The input voltage is ← = (100 V) cos (2πft). Find the rms currents in R, C, and RL if(a) f = 500 Hz and(b) f = 2000 Hz.
The generator voltage in Figure is given by ← = (100 V) cos (2πft).(a) For each branch, what is the amplitude of the current and what is its phase relative to the applied voltage?(b) What is the angular frequency ω such that the current in the generator vanishes?(c) At this resonance, what is
The charge on the capacitor of a series LC circuit is given by Q = (15 μC) cos (1250t + π/4) where t is in seconds.(a) Find the current as a function of time.(b) Find C if L = 28 mH.(c) Write expressions for the electrical energy Ue, the magnetic energy Um, and the total energy U.
One method for measuring the compressibility of a dielectric material uses an LC circuit with a parallel-plate capacitor. The dielectric is inserted between the plates and the change in resonance frequency is determined as the capacitor plates are subjected to a compressive stress. In such an
Figure shows an inductance L and a parallel plate capacitor of width w = 20 cm and thickness 0.2 cm. A dielectric with dielectric constant κ = 4.8 that can completely fill the space between the capacitor plates can be slid between the plates. The inductor has an inductance L = 2 mH. When half the
A series RLC circuit in a radio receiver is tuned by a variable capacitor so that it can resonate at frequencies from 500 to 1600 kHz. If L = 1.0 μH, find the range of capacitances necessary to cover this range of frequencie s.
(a) Find the power factor for the circuit in Example 31-5 when ω = 400 rad/s.(b) At what angular frequency is the power factor 0.5?
An ac generator with a maximum emf of 20 V is connected in series with a 20-μF capacitor and an 80-Ω resistor. There is no inductance in the circuit. Find(a) The power factor,(b) The rms current, and(c) The average power if the angular frequency of the generator is 400 rad/s.
Show that the formula Pav = RErms2/Z2 gives the correct result for a circuit containing only a generator and(a) A resistor,(b) A capacitor, and(c) An inductor.
A series RLC circuit with L = 10 mH, C = 2 μF, and R = 5 Ω is driven by a generator with a maximum emf of 100 V and a variable angular frequency ω. Find(a) The resonant frequency ω0 and(b) Irms at resonance. When ω = 8000 rad/s, find(c) XC and XL,(d) Z and Irms, and(e) The phase angle δ.
Find the power factor and the phase angle d for the circuit in Problem 55 when the generator frequency is(a) 900 Hz,(b) 1.1 kHz, and(c) 1.3 kHz.
FM radio stations have carrier frequencies that are separated by 0.20 MHz. When the radio is tuned to a station, such as 100.1 MHz, the resonance width of the receiver circuit should be much smaller than 0.2 MHz so that adjacent stations are not received. If f0 = 100.1 MHz and ∆f = 0.05 MHz, what
A coil is connected to a 60-Hz, 100-V ac generator. At this frequency the coil has an impedance of 10Ω and a reactance of 8Ω.(a) What is the current in the coil?(b) What is the phase angle between the current and the applied voltage?(c) What series capacitance is required so that the current and
A 0.25-H inductor and a capacitor C are connected in series with a 60-Hz ac generator. An ac voltmeter is used to measure the rms voltages across the inductor and capacitor separately. The rms voltage across the capacitor is 75 V and that across the inductor is 50 V.(a) Find the capacitance C and
(a) Show that Equation 31-51 can be written asFind δ approximately at(b) Very low frequencies and(c) Very highfrequencies.
(a) Show that in a series RC circuit with no inductance, the power factor is given by (b) Sketch a graph of the power factor versus ω.
In the circuit in Figure, the ac generator produces an rms voltage of 115 V when operated at 60 Hz. What is the rms voltage across points(a) AB,(b) BC,(c) CD,(d) AC, and(e) BD?
A variable -frequency ac generator is connected to a series RLC circuit for which R = 1 kΩ, L = 50 mH, and C = 2.5 μF.(a) What is the resonance frequency of the circuit?(b) What is the Q value?(c) At what frequencies is the value of the average power delivered by the generator half of its maximum
An experimental physicist wishes to design a series RLC circuit with a Q value of 10 and a resonance frequency of 33 kHz. She has a 45-mH inductor with negligible resistance. What values for the resistance R and capacitance C should she use?
When an RLC series circuit is connected to a 120-V-rms, 60-Hz line, the current is Irms = 11.0 A and the current leads the voltage by 45°.(a) Find the power supplied to the circuit.(b) What is the resistance?(c) If the inductance L = 0.05 H, find the capacitance C.(d) What capacitance or
A series RLC circuit is driven at a frequency of 500 Hz. The phase angle between the applied voltage and current is determined from an oscilloscope measurement to be δ = 75o. If the total resistance is known to be 35 Ω and the inductance is 0.15 H, what is the capacitance of the circuit?
A series RLC circuit with R = 400 Ω, L = 0.35 H, and C = 5 μF is driven by a generator of variable frequency f.(a) What is the resonance frequency f0? Find f and f/f0 when the phase angle δ is(b) 60°, and(c) –60°.
Sketch the impedance Z versus ω for(a) A series LR circuit,(b) A series RC circuit, and(c) A series RLC circuit.
Given the circuit shown in Figure,(a) Find the power loss in the inductor.(b) Find the resistance r of the inductor.(c) Find the inductanceL.
In a series RLC circuit, XC = 16 Ω and XL = 4Ω at some frequency. The resonance frequency is ω0 = 104 rad/s.(a) Find L and C. If R = 5Ω and (max = 26 V, find(b) The Q factor and(c) The maximum current.
In a series RLC circuit connected to an ac generator whose maximum emf is 200 V, the resistance is 60 Ω and the capacitance is 8.0 μF. The inductance can be varied from 8.0 mH to 40.0 mH by the insertion of an iron core in the solenoid. The angular frequency of the generator is 2500 rad/s. If the
A certain electrical device draws 10 A rms and has an average power of 720 W when connected to a 120-V-rms, 60-Hz power line.(a) What is the impedance of the device?(b) What series combination of resistance and reactance is this device equivalent to?(c) If the current leads the emf, is the
A method for measuring inductance is to connect the inductor in series with a known capacitance, a known resistance, an ac ammeter, and a variable -frequency signal generator. The frequency of the signal generator is varied and the emf is kept constant until the current is maximum.(a) If C = 10
A resistor and a capacitor are connected in parallel across a sinusoidal emf ← = Emax cos ωt as shown in Figure.(a) Show that the current in the resistor is IR = (←max/R) cos ωt.(b) Show that the current in the capacitor branch is IC = (←max/XC) cos (ωt + 90°).(c) Show
The impedances of motors, transformers, and electromagnets have inductive reactance. Suppose that the phase angle of the total impedance of a large industrial plant is 25o when the plant is under full operation and using 2.3 MW of power. The power is supplied to the plant from a substation 4.5 km
In the circuit shown in Figure, R = 10 Ω, RL = 30 Ω, L = 150 mH, and C = 8 μF; the frequency of the ac source is 10 Hz and its amplitude is 100 V.(a) Using phasor diagrams, determine the impedance of the circuit when switch S is closed.(b) Determine the impedance of the circuit
In the circuit shown in Figure, R1 = 2Ω, R2 = 4Ω, L = 12 mH, C = 30 μF, and ← = (40 V) cos (ωt).(a) Find the resonance frequency.(b) At the resonance frequency, what are the rms currents in each resistor and the rms current supplied by the source emf?
For the circuit in Figure, derive an expression for the Q of the circuit, assuming the resonance issharp.
For the circuit in Figure, L = 4 mH.(a) What capacitance C will result in a resonance frequency of 4 kHz?(b) When C has the value found in (a), what should be the resistance R so that the Q of the circuit is8?
If the capacitance of C in Problem 82 is reduced to half the value found in Problem 82, what then are the resonance frequency and the Q of the circuit? What should be the resistance R to give Q = 8?

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