A single loop of steel wire, lying flat in a plane, has an area of 8.20 cm2 and a resistance of 1.80 Ω. A uniform magnetic field points perpendicular to the plane of the loop. The field initially has a magnitude of 0.500 T, and the magnitude increases linearly to 2.00 T in a time of 1.08 s. What is the induced current (in mA) in the loop of wire over this time? mA
Respiration monitor belts are sometimes used in hospitals to monitor the breathing of patients. One particular model consists of a 200-turn coil of wire that wraps around a patient's chest. When the patient inhales, the area bounded by the coil increases by 38.0 cm2. The magnitude of the Earth's magnetic field is 50.0 μT and makes an angle of 28.0∘ with the plane of the coil. If the patient takes 1.68 s to inhale, what is the magnitude of the average induced emf in the coil (in μV) during this time interval? μV
(a) A 13.0 m long, thin, uniform metal rod slides north at a speed of 30.0 m/s. The length of the rod maintains an east-west orientation while sliding. The vertical component of the Earth's magnetic field at this location has a magnitude of 46.0 μT. What is the magnitude of the induced emf between the ends of the rod (in mV)? mV (b) What If? The east end of the rod impacts and sticks to a pylon, causing the rod to rotate clockwise as viewed from above. While the rod rotates, what is the magnitude of the induced emf between the ends of the rod (in mV)? (Hint: use conservation of angular momentum to find the speed of the rod after the collision.) mV
In the figure below, a steel bar sitting on two parallel metal rails, connected to each other by a resistor, is pulled to the right at a constant speed. The resistance R = 7.00 Ω, the distance between the rails is ℓ = 1.20 m, and a uniform 3.50 T magnetic field is directed into the page. At what speed (in m/s) should the bar be moved to produce a current of 0.500 A in the resistor? m/s
The figure below shows a rectangular coil of length ℓ and width w consisting of N turns of conducting wire, moving to the right with a constant velocity v→. The coil moves into a region of uniform magnetic field B→, pointing into the page and perpendicular to the plane of the coil. The total resistance of the coil is R. Find the magnitude and direction of the total magnetic force on the coil for the following situations. (Use the following as necessary: N, B, w, l, v, and R. ) (a) as it enters the magnetic field magnitude F = direction (b) as it moves within the field magnitude F = direction (c) as it leaves the field magnitude F = direction
A long solenoid with 6.00×102 turns per meter and radius 2.00 cm carries an oscillating current I = 8.00 sin90πt, where I is in amperes and t is in seconds. (a) What is the electric field induced at a radius r = 1.00 cm from the axis of the solenoid? (Use the following as necessary: t. Let E be measured in millivolts/meter and t be measured in seconds.) E = (b) What is the direction of this electric field when the current is increasing counterclockwise in the solenoid? clockwise counterclockwise
You are working in a factory that uses many motors. Your supervisor is pointing out a motor to you that shows signs of weakness and may suddenly seize, so that the rotor suddenly stops rotating. The motor in normal operation carries a direct current of 0.300 A when connected to a 120 V power supply. The resistance of the motor windings is 18.4 Ω. Your supervisor asks you to determine by what factor the rate of change of internal energy in the windings will increase if the rotor seizes while it is operating and the supply voltage is not cut off. Pseized Pnormal =
The figure represents an electromagnetic brake that uses eddy currents. An electromagnet hangs from a railroad car near one rail. To stop the car, a large current is sent through the coils of the electromagnet. The moving electromagnet induces eddy currents in the rails, whose fields oppose the change in the field of the electromagnet. The magnetic fields of the eddy currents exert force on the current in the electromagnet, thereby slowing the car. The direction of the car's motion and the direction of the current in the electromagnet are shown correctly in the picture. Determine which of the eddy currents shown on the rails is correct. Explain your answer.
As shown in the circuit diagram below, an AC source delivers an alternating voltage at audio frequencies to a speaker connected to the source through a resistor. The source voltage has an amplitude of 13.0 V, the resistance R = 7.00 Ω, and the speaker is equivalent to a resistance of 10.4 Ω. Determine the time-averaged power (in W ) transferred to the speaker. W
When an inductor is connected to a 60.0 Hz source it has an inductive reactance of 59.8 Ω. Determine the maximum current in the inductor (in A) if it is connected to a 48.0 Hz source that produces a 120 V rms voltage. A
What maximum current is delivered by an AC source with ΔVmax = 54.0 V and f = 110.0 Hz when connected across a 3.70−μF capacitor? mA
A student has a 82.0 μH inductor, a 82.0 μF capacitor, and a variable frequency AC source. Determine the source frequency (in kHz ) at which the inductor and capacitor have the same reactance. kHz
An inductor (L = 420 mH), a capacitor (C = 4.43 μF), and a resistor (R = 440 Ω) are connected in series. A 50.0−Hz AC source produces a peak current of 250 mA in the circuit. (a) Calculate the required peak voltage ΔVmax . V (b) Determine the phase angle by which the current leads or lags the applied voltage. magnitude direction
An AC voltage of the form Δv = 100 sin1000 t, where Δv is in volts and t is in seconds, is applied to a series RLC circuit. Assume the resistance is 460 Ω, the capacitance is 5.40 μF, and the inductance is 0.500 H. Find the average power delivered to the circuit. W
You wish to build a series RLC circuit for a project you are working on. Looking in your electronics parts box, you are disappointed to find that you have only two resistors, each of resistance 54.0 Ω, two capacitors, each of capacitance 9.00 nF, and one inductor of inductance 4.00 mH. You need to determine the lowest possible angular frequency (in rad/s) at resonance that you can obtain from all five components by connecting the inductor in series with a combination of the two resistors and a combination of the two capacitors. rad/s
The primary coil of a transformer has N1 = 400 turns, and the secondary coil has N2 = 2560 turns. If the input voltage across the primary coil is Δv(t) = 170 cosωt, where Δv is in volts and t is in seconds, what rms voltage is developed across the secondary coil? V
(a) What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60.0 Hz power source having a maximum voltage of 160 V? Ω (b) What is the resistance of a 110 W bulb? Ω
In the AC circuit shown in the figure below, R = 70.0 Ω and the output voltage of the AC source is ΔVmaxsin(ωt). (a) If ΔvR = 0.265 Δvmax for the first time at t = 0.0080 s, what is the angular frequency of the source? rad/s (b) What is the next value of t for which ΔvR = 0.265 Δvmax? s
An AC source operating at a frequency of 370 Hz has a maximum output voltage of 2.00 V. What is the smallest inductor that can be connected across the source and the rms current remain less than 1.40 mA ? (Enter the inductance in H.) H
A 46.0-mH inductor is connected to a North American electrical outlet ( ΔVrms = 120 V, f = 60.0 Hz). Assuming the energy stored in the inductor is zero at t = 0, determine the energy stored at t = 1 175 s.
A student has a 26.0 μF capacitor and a variable frequency AC source. Determine the following. (a) frequencies (in Hz) for which the capacitor has a reactance below 380 Ω f ≥ Hz (b) reactances (in Ω ) of a 37.0 μF capacitor over this same frequency range xC ≤ Ω
A 1.23−mF capacitor is connected to a North American electrical outlet (ΔVrms = 120 V, f = 60.0 Hz). Assuming the energy stored in the capacitor is zero at t = 0, determine the magnitude of the current in the wires at t = 1 170 s. A
An engineering intern builds an RLC series circuit which includes an AC source that operates at a fixed frequency and voltage. At the operating frequency, the resistance R is equal to the inductive reactance XL. The intern notices that when the plate separation of the parallel-plate capacitor is reduced to one-half its original value, the current in the circuit doubles. Determine the initial capacitive reactance in terms of the resistance R. R
A series RLC circuit has a resistance of 46.0 Ω and an impedance of 67.0 Ω. What average power is delivered to this circuit when ΔVrms = 210 V? W
A series RLC circuit has a resistance of 12 Ω and an impedance of 80 Ω. If the rms voltage applied to the circuit is 140 V, what average power is delivered to the circuit? W
A 14.0−Ω resistor, 5.50−mH inductor, and 50.0−μF capacitor are connected in series to a 55.0−V (rms) source having variable frequency. If the operating frequency is twice the resonance frequency, find the energy delivered to the circuit during one period. mJ
A resistor R, inductor L, and capacitor C are connected in series to an AC source of rms voltage ΔV and variable frequency. If the operating frequency is twice the resonance frequency, find the energy delivered to the circuit during one period. (Use the following as necessary: the rms voltage ΔV, R, L, and C.) E =
The figure below shows an AC source, a transformer with a turns ratio of N1/N2 = 2.40, a source resistor RS, and a load resistor RL. A voltmeter across the load resistor measures an rms voltage of 24.0 V when the load resistor RL is 49.0 Ω and the rms source voltage is ΔVS = 86.0 V. (a) Determine the value of the source resistor RS (in Ω). Ω (b) What If? If the turns ratio is increased to 3.00, determine the source resistance (in Ω) required to deliver the same amount of power to the load. Ω
A 0.170− A current is charging a capacitor that has circular plates 13.5 cm in radius. The plate separation is 4.00 mm. (a) What is the time rate of increase of electric field between the plates? V/(m⋅s) (b) What is the magnetic field between the plates 5.00 cm from the center? T
A proton moves through a region containing a uniform electric field given by E→ = 58.0 j^ V/m and a uniform magnetic field B→ = (0.200 i^ + 0.300 j^ + 0.400 k^) T. Determine the acceleration of the proton when it has a velocity v→ = 230 i^ m/s a→ = m/s2
The wavelength of light emitted by a helium-neon laser is λ = 632.8 nm. What is the frequency of these light waves (in Hz)? Hz
An electromagnetic wave in vacuum has an electric field amplitude of 246 V/m. Calculate the amplitude of the corresponding magnetic field. nT
What is the average magnitude of the Poynting vector 7.00 mi from a radio transmitter broadcasting isotropically (equally in all directions) with an average power of 300 kW? μW/m2
An electromagnetic wave is normally incident on a flat surface. Assuming the power per unit area transmitted is S = 50.5 W/m2, and the surface is a perfect absorber, what is the radiation pressure (in nPa) on the surface? nPa
Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton of mass mp moving in a circular path perpendicular to a magnetic field of magnitude B. (Use any variable or symbol stated above along with the following as necessary: q and c.) λ =
Electromagnetic waves are traveling in the vacuum of space. Calculate the wavelengths of these electromagnetic waves with the following frequencies. (Enter the first wavelength in pm and the second wavelength in cm.) (a) 7.00×1019 Hz pm (a) 9.50×109 Hz cm
A 0.126 -A current is charging a capacitor that has square plates 4.20 cm on each side. The plate separation is 4.00 mm. (a) Find the time rate of change of electric flux between the plates. V⋅m/s (b) Find the displacement current between the plates. A
(a) An electron moves through a uniform electric field E→ = (2.00 i^ + 5.90 j^) V/m and a uniform magnetic field B→ = 0.400 k^ T. Determine the acceleration of the electron when it has a velocity v→ = 12.0 i^ m/s. (Give each component in m/s2.) ax = m/s2 ay = m/s2 az = m/s2 m/s2 (b) What If? For the electron moving along the x-axis in the fields in part (a), what speed (in m/s) would result in the electron also experiencing an acceleration directed along the x-axis? m/s
A woman is listening to her radio, which is 174 m from the radio station transmitter. (a) How many wavelengths of the radio waves are there between the transmitter and radio receiver if the woman is listening to an AM radio station broadcasting at 1260 kHz ? wavelengths (b) How many wavelengths are there between the transmitter and radio if she changes to an FM station broadcasting at 101.7 MHz? wavelengths
For dry air at a temperature of 0∘C and at 1 atm of pressure, electric breakdown occurs when the air is subjected to an electric field with amplitude above about 3.00 MV/m. A high-power laser is shone up into Earth's atmosphere, and the laser's associated electric field ionizes the air and turns it into a conducting plasma. Assume the conditions of the air are such that an electric field of 3.00 MV/m causes the air to ionize. (a) What will be the intensity (in W/m2) of a laser beam that can produce a field of this magnitude? W/m2 (b) Assuming the laser is operating at this maximum intensity, what is the power (in W) delivered in a cylindrical beam with a diameter of d = 4.55 mm? W
A particular star is d = 16.1 light-years (Iy) away, with a power output of P = 3.10×1026 W. Note that one light-year is the distance traveled by the light through a vacuum in one year. (a) Calculate the intensity of the emitted light at distance d (in nW/m2). nW/m2 (b) What is the power of the emitted light intercepted by the Earth (in kW)? (The radius of Earth is 6.37×106 m.) kW What If? Of the more than 150 stars within 20 light-years of Earth, 90 are very dim red dwarf stars each with an average luminosity of 2.00×1025 W, about 5% the luminosity of the Sun. If the average distance of these objects from the Earth is 10.0 ly, find the following. (c) the ratio of the total intensity of starlight from these 90 stars to the intensity of the single bright star found in part (a) Idwarf stars Isingle star = (d) the ratio of the total power the Earth intercepts from these stars to the power intercepted from the bright star in part (b) Pdwarf stars Psingle star =
A 12.0-mW helium-neon laser emits a beam of circular cross section with a diameter of 2.75 mm. (a) Find the maximum electric field in the beam. kN/C (b) What total energy is contained in a 1.00−m length of the beam? pJ (c) Find the momentum carried by a 1.00−m length of the beam. kg⋅m/s
A 26.3−mW laser beam of diameter 2.16 mm is reflected at normal incidence by a perfectly reflecting mirror. Calculate the radiation pressure on the mirror. N/m2
A quarter-wave monopole radio antenna (also called a Marconi antenna) consists of a long conductor of one quarter the length of the transmitted wavelength. The lower end of the antenna is connected to a conducting ground plane (often simply the Earth) which reflects the transmitted signal, creating an effective antenna length of a half wavelength. (a) What must be the height of the antenna (in m ) for a radio station broadcasting at 509 kHz? m (b) What must be the height of the antenna (in m) for radio stations broadcasting at 1,500 kHz? m
A radio station has two antennas. The antennas are a distance d apart, where d equals half the broadcast wavelength. The antennas are driven in phase with each other. Let the x-axis be the line that runs through the two antennas. The angles are all measured counterclockwise from the +x-direction. (For the following, assume an observer is positioned a distance D far from the midpoint of the antennas, so that D≫d. ) (a) In which directions is the strongest signal radiated? 0∘, 180∘ 90∘, 270∘ 0∘, 90∘, 180∘, 270∘ 45∘, 135∘, 225∘, 315∘ (b) In which directions is the weakest signal radiated? 0∘, 180∘ 90∘, 270∘ 0∘, 90∘, 180∘, 270∘ 45∘, 135∘, 225∘, 315∘
Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton in a cyclotron with a magnetic field of 0.500 T. m
Compute an order-of-magnitude estimate for the frequency of an electromagnetic wave with wavelength equal to the following. (a) your height 10−13 10−9 104 108 1010 1012 How is this wave classified on the electromagnetic spectrum? (b) the thickness of a sheet of paper ( ≈ 6.00×10−5 m) 10−13 10−9 104 108 1010 1012 How is this wave classified on the electromagnetic spectrum?
VHF, or very high frequency, refers to radio frequency electromagnetic waves in the range 30 to 300 MHz. In the U.S., television stations broadcast channels 2 through 13 in the VHF range between 54.0 MHz and 216 MHz, with ranges 72.0 to 76.0 MHz and 88.0 to 174 MHz not utilized for TV broadcasting. Each channel has a frequency width of 6.00 MHz. The table below gives the lower and upper frequency of each channel. (a) Calculate the broadcast wavelength range for channel 2. (Enter your answers from smallest to largest, in m.) smallest value m largest value m (b) Calculate the broadcast wavelength range for channel 4. (Enter your answers from smallest to largest, in m. ) smallest value m largest value m (c) Calculate the broadcast wavelength range for channel 5. (Enter your answers from smallest to largest, in m.) smallest value m largest value m