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physics
physics scientists and engineers

Questions and Answers of Physics Scientists and Engineers

What electric field strength and direction will allow the proton in FIGURE P31.30 to pass through this region of space without being deflected? B= 0.010 T- v = 2.0 x 107 m/s FIGURE P31.30 +
What is the force (magnitude and direction) on the proton in FIGURE P31.29? Give the direction as an angle cw or ccw from vertical. E= 1.0 x 10 V/m x / x v = 1.0 x 10' m/s B= 0.10 T FIGURE P31.29
What are the electric field strength and direction at the position of the electron in FIGURE P31.28 ? 3.2 x 10-13 N F 30° B=0.10 T Moving out of page at 1.0 x 10' m/s FIGURE P31.28
A 200 mW vertically polarized laser beam passes through a polarizing filter whose axis is 35° from horizontal. What is the power of the laser beam as it emerges from the filter?
Unpolarized light with intensity 350 W/m2 passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity
FIGURE EX31.25 shows a vertically polarized radio wave of frequency 1.0 × 106Hz traveling into the page.The maximum electric field strength is 1000 V/m. What are a. The maximum magnetic field
Only 25% of the intensity of a polarized light wave passes through a polarizing filter. What is the angle between the electric field and the axis of the filter?
At what distance from a 10 W point source of electromagnetic waves is the magnetic field amplitude 1.0 μT?
A 1000 W carbon-dioxide laser emits light with a wavelength of 10 μm into a 3.0-mm-diameter laser beam. What force does the laser beam exert on a completely absorbing target?
A 200 MW laser pulse is focused with a lens to a diameter of 2.0 μm.a. What is the laser beam’s electric field amplitude at the focal point?b. What is the ratio of the laser beam’s electric
A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of power. Assume that the radiation is emitted uniformly in all directions.a. What is the wave’s intensity 30 km from the antenna?b. What
A helium-neon laser emits a 1.0-mm-diameter laser beam with a power of 1.0 mW. What are the amplitudes of the electric and magnetic fields of the light wave?
A radio receiver can detect signals with electric field amplitudes as small as 300 μV/m. What is the intensity of the smallest detectable signal?
A radio wave is traveling in the negative y-direction. What is the direction of E at a point where B is in the positive x direction?
a. What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 100 V/m?b. What is the intensity of the wave?
The electric field of an electromagnetic wave in a vacuum is Ey = (20.0 V/m) cos [(6.28 × 108)x - ωt], where x is in m and t is in s. What are the wave’s(a) Wavelength,(b) Frequency,(c) Magnetic
The magnetic field of an electromagnetic wave in a vacuum is Bz = (3.00 μT) sin [( 1.00 × 107)x - ωt], where x is in m and t is in s. What are the wave’s(a) Wavelength,(b) Frequency,(c) Electric
What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 2.0 mT?
What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 10 V/m?
A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. The electric field between the plates is increasing at the rate 1.0 × 106 V/m s. What is the magnetic field strength (a) On the
A 5.0-cm-diameter parallel-plate capacitor has a 0.50 mm gap. What is the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500,000 V/s?
A vertically polarized electromagnetic wave passes through the five polarizers in FIGURE Q31.10. Rank in order, from largest to smallest, the transmitted intensities Iato Ie. P
Older televisions used a loop antenna like the one in FIGURE Q31.9. How does this antenna work?
Show that the displacement current inside a parallel-plate capacitor can be written C(dVC/dt).
Show that the quantity є0(dΦe/dt) has units of current.
In what directions are the electromagnetic waves traveling in FIGURE Q31.7 ? a. b. L Le L Li
The magnetic field is uniform over each face of the box shown in FIGURE EX31.6. What are the magnetic field strength and direction on the front surface? 2T 2T 3 T 3T 1 cm 2 cm FIGURE EX31.6 1 cm 1T
Do the situations in FIGURE Q31.6 represent possible electromagnetic waves? If not, why not? a. b. 3000 V/m Vem 10 μΤy
A rocket zooms past the earth at v = 2.0 × 106m/s. Scientists on the rocket have created the electric and magnetic fields shown in FIGURE EX31.5. What are the fields measured by an earthbound
Scientists in the laboratory create a uniform electric field E =1.0 × 106 kn V/m in a region of space where B = 0. What are the fields in the reference frame of a rocket traveling in the
What is the current through surface S in FIGURE Q31.4 if you curl your right fingers in the direction of the arrow? 2 A S 2A FIGURE Q31.4
Laboratory scientists have created the electric and magnetic fields shown in FIGURE EX31.3. These fields are also seen by scientists who zoom past in a rocket traveling in the x-direction at 1.0 ×
If you curl the fingers of your right hand as shown, are the electric fluxes in FIGURE Q31.3 positive or negative? a. b. x x x x x х х x x
A rocket cruises past a laboratory at 1.00 × 106 m/s in the positive x-direction just as a proton is launched with velocity (in the laboratory frame) v = (1.41 × 106î + 1.41 × 106ĵ) m/s. What
Sharon drives her rocket through the magnetic field of FIGURE Q31.2 traveling to the right at a speed of 1000 m/s as measured by Bill. As she passes Bill, she shoots a positive charge backward at a
FIGURE EX31.1 shows the electric and magnetic field in frame A. A rocket in frame B travels parallel to one of the axes of the A coordinate system. Along which axis must the rocket travel, and in
Andre is flying his spaceship to the left through the laboratory magnetic field of FIGURE Q31.1. a. Does Andre see a magnetic field? If so, in which direction does it point?b. Does Andre see an
Let’s look at the details of eddy-current braking. A square loop, length l on each side, is shot with velocity v0 into a uniform magnetic field B. The field is perpendicular to the plane of the
A 10 cm × 10 cm square loop lies in the xy-plane. The magnetic field in this region of space is B = (0.30tî + 0.50t2 k̂) T, where t is in s. What is the emf induced in the loop at(a) T = 0.5 s(b)
FIGURE EX30.18 shows the current as a function of time through a 20-cm-long, 4.0-cm-diameter solenoid with 400 turns. Draw a graph of the induced electric field strength as a function of time at a
A 5.0-cm-diameter coil has 20 turns and a resistance of 0.50 Ω. A magnetic field perpendicular to the coil is B = 0.020t + 0.010t2, where B is in tesla and t is in seconds.a. Find an expression for
The current in the solenoid of FIGURE EX30.12 is increasing. The solenoid is surrounded by a conducting loop. Is there a current in the loop? If so, is the loop current cw or ccw? FIGURE EX30.12
An electron travels with v = 5.0 × 106î m/s through a point in space where E = (2.0 × 105î - 2.0 × 105ĵ) V/m and B = -0.10k̂ T. What is the force on the electron?
In FIGURE P31.33, a circular loop of radius r travels with speed v along a charged wire having linear charge density λ. The wire is at rest in the laboratory frame, and it passes through the center
The magnetic field inside a 4.0-cm-diameter superconducting solenoid varies sinusoidally between 8.0 T and 12.0 T at a frequency of 10 Hz.a. What is the maximum electric field strength at a point 1.5
A simple series circuit consists of a 150 Ω resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0
A wire with conductivity σ carries current I. The current is increasing at the rate dI/dt.a. Show that there is a displacement current in the wire equal to (є0/σ)(dI/dt).b. Evaluate the
A 10 A current is charging a 1.0-cm-diameter parallel-plate capacitor.a. What is the magnetic field strength at a point 2.0 mm radially from the center of the wire leading to the capacitor?b. What is
FIGURE P31.38 shows the voltage across a 0.10 μF capacitor. Draw a graph showing the displacement current through the capacitor as a function of time. AVe (V) 100 50- 0+ t (us) FIGURE P31.38 1 3 4
FIGURE P31.39 shows the electric field inside a cylinder of radius R = 3.0 mm. The field strength is increasing with time as E = 1.0 × 108t2V/m, where t is in s. The electric field outside the
A long, thin superconducting wire carrying a 15 A current passes through the center of a thin, 2.0-cm-diameter ring. A uniform electric field of increasing strength also passes through the ring,
A 1.0 μF capacitor is discharged, starting at t = 0 s. The displacement current through the plates is Idisp = (10 A)exp(-t/2.0 μs). What was the capacitor’s initial voltage (ΔVC)0?
At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E = (200î + 300ĵ - 50k̂) V/m and B = B0(7.3î - 7.3 ĵ + ak̂) μT.a. What are the values of a and
a. Show that uE and uB, the energy densities of the electric and magnetic fields, are equal to each other in an electromagnetic wave. In other words, show that the wave’s energy is divided equally
The intensity of sunlight reaching the earth is 1360 W/m2.a. What is the power output of the sun?b. What is the intensity of sunlight reaching Mars?
Assume that a 7.0-cm-diameter, 100 W lightbulb radiates all its energy as a single wavelength of visible light. Estimate the electric and magnetic field strengths at the surface of the bulb.
The electric field of a 450 MHz radio wave has a maximum rate of change of 4.5 × 1011 (V/m)/s. What is the wave’s magnetic field amplitude?
When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5 × 109 km from the earth. Its radio transmitter, with which it sent back data and images, broadcast with a mere 21 W of power.
In reading the instruction manual that came with your garage-door opener, you see that the transmitter unit in your car produces a 250 mW, 350 MHz signal and that the receiver unit is supposed to
The maximum electric field strength in air is 3.0 MV/m. Stronger electric fields ionize the air and create a spark. What is the maximum power that can be delivered by a 1.0 cm-diameter laser beam
A LASIK vision-correction system uses a laser that emits 10 ns-long pulses of light, each with 2.5 mJ of energy. The laser beam is focused to a 0.85-mm-diameter circle on the cornea.What is the
The intensity of sunlight reaching the earth is 1360 W/m2. Assuming all the sunlight is absorbed, what is the radiation-pressure force on the earth? Give your answer(a) In newtons(b) As a fraction of
For radio and microwaves, the depth of penetration into the human body is proportional to λ1/2. If 27 MHz radio waves penetrate to a depth of 14 cm, how far do 2.4 GHz microwaves penetrate?
A laser beam shines straight up onto a flat, black foil of mass m.a. Find an expression for the laser power P needed to levitate the foil.b. Evaluate P for a foil with a mass of 25 μg.
For a science project, you would like to horizontally suspend an 8.5 by 11 inch sheet of black paper in a vertical beam of light whose dimensions exactly match the paper. If the mass of the sheet is
You’ve recently read about a chemical laser that generates a 20-cm-diameter, 25 MW laser beam. One day, after physics class, you start to wonder if you could use the radiation pressure from this
Unpolarized light of intensity I0 is incident on three polarizing filters. The axis of the first is vertical, that of the second is 45° from vertical, and that of the third is horizontal. What light
Unpolarized light of intensity I0 is incident on two polarizing filters. The transmitted light intensity is I0/10. What is the angle between the axes of the two filters?
Unpolarized light of intensity I0 is incident on a stack of 7 polarizing filters, each with its axis rotated 15° cw with respect to the previous filter. What light intensity emerges from the last
A cube of water 10 cm on a side is placed in a microwave beam having E0 = 11 kV/m. The microwaves illuminate one face of the cube, and the water absorbs 80% of the incident energy. How long will it
An 80 kg astronaut has gone outside his space capsule to do some repair work. Unfortunately, he forgot to lock his safety tether in place, and he has drifted 5.0 m away from the capsule.Fortunately,
An electron travels with v = 5.0 × 106 in m/s through a point in space where B = 0.10 ĵ T. The force on the electron at this point is F = (9.6 × 10-14î - 9.6 × 10-14k̂) N. What is the
The radar system at an airport broadcasts 11 GHz microwaves with 150 kW of power. An approaching airplane with a 31 m2 cross section is 30 km away. Assume that the radar broadcasts uniformly in all
Large quantities of dust should have been left behind after the creation of the solar system. Larger dust particles, comparable in size to soot and sand grains, are common. They create shooting stars
Consider current I passing through a resistor of radius r, length L, and resistance R.a. Determine the electric and magnetic fields at the surface of the resistor. Assume that the electric field is
FIGURE Q32.1 shows emf phasors a, b, and c. a. For each, what is the instantaneous value of the emf?b. At this instant, is the magnitude of each emf increasing, decreasing, or holding constant? 100 V
The emf phasor in FIGURE EX32.1 is shown at t = 2.0 ms. a. What is the angular frequency ω? Assume this is the first rotation.b. What is the peak value of the emf? 135° at t= 2.0 ms -So V -50 V
A resistor is connected across an oscillating emf. The peak current through the resistor is 2.0 A. What is the peak current if:a. The resistance R is doubled?b. The peak emf Ԑ0 is doubled?c. The
The emf phasor in FIGURE EX32.2 is shown at t = 15 ms. a. What is the angular frequency ω? Assume this is the first rotation.b. What is the instantaneous value of the emf? 30° Phasor at E = 12 V
A capacitor is connected across an oscillating emf. The peak current through the capacitor is 2.0 A. What is the peak current if:a. The capacitance C is doubled?b. The peak emf Ԑ0 is doubled?c. The
A 110 Hz source of emf has a peak voltage of 50 V. Draw the emf phasor at t = 3.0 ms.
A low-pass RC filter has a crossover frequency fc = 200 Hz. What is fc if:a. The resistance R is doubled?b. The capacitance C is doubled?c. The peak emf Ԑ0 is doubled?
Draw the phasor for the emf Ԑ = (170 V) cos((2π × 60 Hz)t) at t = 60 ms.
An inductor is connected across an oscillating emf. The peak current through the inductor is 2.0 A. What is the peak current if:a. The inductance L is doubled?b. The peak emf Ԑ0 is doubled?c. The
FIGURE EX32.5 shows voltage and current graphs for a resistor. a. What is the emf frequency f ?b. What is the value of the resistance R?c. Draw the resistor??s voltage and current phasors at t = 15
The resonance frequency of a series RLC circuit is 1000 Hz. What is the resonance frequency if:a. The resistance R is doubled?b. The inductance L is doubled?c. The capacitance C is doubled?d. The
A 200 Ω resistor is connected to an AC source with Ԑ0 = 10 V. What is the peak current through the resistor if the emf frequency is(a) 100 Hz?(b) 100 kHz?
In the series RLC circuit represented by the phasors of FIGURE Q32.7, is the emf frequency less than, equal to, or greater than the resonance frequency ω0? Explain. FIGURE Q32.7
The peak current to and from a capacitor is 10 mA. What is the peak current ifa. The emf frequency is doubled?b. The emf peak voltage is doubled (at the original frequency)?
The resonance frequency of a series RLC circuit is less than the emf frequency. Does the current lead or lag the emf? Explain.
A 0.30 μF capacitor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current to and from the capacitor if the emf frequency is(a) 100 Hz?(b) 100 kHz?
The current in a series RLC circuit lags the emf by 20°. You cannot change the emf. What two different things could you do to the circuit that would increase the power delivered to the circuit by
FIGURE EX32.9 shows voltage and current graphs for a capacitor. a. What is the emf frequency f?b. What is the value of the capacitance C? Vc ic Voltage 10 V- 15 mA 0- 0.00 s 0.01 s 0.02 s F-15 mA
A 20 nF capacitor is connected across an AC generator that produces a peak voltage of 5.0 V.a. At what frequency f is the peak current 50 mA?b. What is the instantaneous value of the emf at the
The average power dissipated by a resistor is 4.0 W. What is PR if:a. The resistance R is doubled while Ԑ0 is held fixed?b. The peak emf Ԑ0 is doubled while R is held fixed?c. Both are doubled
capacitor is connected to a 15 kHz oscillator. The peak current is 65 mA when the rms voltage is 6.0 V. What is the value of the capacitance C?
A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V.a. What is the capacitance?b. If the peak voltage is held constant, what is the peak current at 500 kHz?
a. Evaluate VCin FIGURE EX32.13 at emf frequencies 1, 3, 10, 30, and 100 kHz.b. Graph VCversus frequency.Draw a smooth curve through your five points. ww 16 N (10 V) cos ot F1.0 µF FIGURE EX32.13
a. Evaluate VRin FIGURE EX32.14 at emf frequencies 100, 300, 1000, 3000, and 10,000 Hz.b. Graph VRversus frequency.Draw a smooth curve through your five points. 1.6 μF (10 V) cos o 100 0 FIGURE
A high-pass RC filter is connected to an AC source with a peak voltage of 10.0 V. The peak capacitor voltage is 6.0 V. What is the resistor voltage?

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