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physics
electricity and magnetism

Questions and Answers of Electricity and Magnetism

The tuning circuit of an AM radio contains an LC combination. The inductance is 0.200 mH, and the capacitor is variable, so that the circuit can resonate at any frequency between 550 kHz and 1 650
A radar transmitter contains an LC circuit oscillating at 1.00 x 1010 Hz. (a) What capacitance will resonate with a one-turn loop of inductance 400 pH at this frequency? (b) If the capacitor has
A series RLC circuit has components with following values: L = 20.0 mH, C = 100 nF, R = 20.0 Ω, and ∆Vmax = 100 V, with ∆v = ∆Vmax sin wt. Find (a) The resonant
A 10.0-Ω resistor, 10.0-mH inductor, and 100-μF capacitor are connected in series to a 50.0-V (rms) source having variable frequency. Find the energy that is delivered to the circuit during
A resistor R, inductor L, and capacitor C are connected in series to an AC source of rms voltage ∆V and variable frequency. Find the energy that is delivered to the circuit during one period if
Compute the quality factor for the circuits described in Problems 22 and 23. Which circuit has the sharper resonance?
A step-down transformer is used for recharging the batteries of portable devices such as tape players. The turn’s ratio inside the transformer is 13:1 and it is used with 120-V (rms) household
A transformer has N1 = 350 turns and N2 = 2 000 turns. If the input voltage is ∆v (t) = (170 V) cos wt, what rms voltage is developed across the secondary coil?
A step-up transformer is designed to have an output voltage of 2 200 V (rms) when the primary is connected across a 110-V (rms) source. (a) If the primary winding has 80 turns, how many turns are
In the transformer shown in Figure P33.47, the load resistor is 50.0 Ω. The turn€™s ratio N1:N2 is 5:2, and the source voltage is 80.0 V (rms). If a voltmeter across the load measures
The secondary voltage of an ignition transformer in a furnace is 10.0 kV. When the primary operates at an rms voltage of 120 V, the primary impedance is 24.0 Ω and the transformer is 90.0%
A transmission line that has a resistance per unit length of 4.50 x 10-4 (/m is to be used to transmit 5.00 MW over 400 miles (6.44 x 105 m). The output voltage of the generator is 4.50 kV. (a)
One particular plug-in power supply for a radio looks similar to the one shown in Figure 33.23 and is marked with the following information: Input 120 V AC 8 W Output 9 V DC 300 mA. Assume that these
Consider the filter circuit shown in Figure 33.25a.(a) Show that the ratio of the output voltage to the input voltage is(b) What value does this ratio approach as the frequency decreases toward zero?
Consider the filter circuit shown in Figure 33.26a. (a) Show that the ratio of the output voltage to the input voltage is (b) What value does this ratio approach as the frequency decreases toward
The RC high-pass filter shown in Figure 33.25 has a resistance R = 0.500 Ω. (a) What capacitance gives an output signal that has half the amplitude of a 300-Hz input signal? (b) What is the
The RC low-pass filter shown in Figure 33.26 has a resistance R = 90.0 Ω and a capacitance C = 8.00 nF. Calculate the ratio (∆V out/∆V in) for an input frequency of (a) 600 Hz and
The resistor in Figure P33.55 represents the midrange speaker in a three-speaker system. Assume its resistance to be constant at 8.00 (. The source represents an audio amplifier producing signals of
Show that the rms value for the saw tooth voltage shown in Figure P33.56 is ∆Vmax / √3.
A series RLC circuit consists of an 8.00-Ω resistor, a 5.00-μF capacitor, and a 50.0-mH inductor. A variable frequency source applies an emf of 400 V (rms) across the combination. Determine
A capacitor, a coil, and two resistors of equal resistance are arranged in an AC circuit, as shown in Figure P33.58. An AC source provides an emf of 20.0 V (rms) at a frequency of 60.0 Hz. When the
To determine the inductance of a coil used in a research project, a student first connects the coil to a 12.0-V battery and measures a current of 0.630 A. The student then connects the coil to a
One insulated conductor from a household extension cord has mass per length 19.0 g/m. A section of this conductor is held under tension between two clamps. A subsection is located in a region of
In Figure P33.61, find the rms current delivered by the 45.0-V (rms) power supply when(a) The frequency is very large and(b) The frequency is very small.
In the circuit shown in Figure P33.62, assume that all parameters except for C are given. (a) Find the current as a function of time.(b) Find the power delivered to the circuit.(c) Find the current
An 80.0-Ω resistor and a 200-mH inductor are connected in parallel across a 100-V (rms), 60.0-Hz source. (a) What is the rms current in the resistor? (b) By what angle does the total current
Make an order-of-magnitude estimate of the electric current that the electric company delivers to a town (Figure P33.64) from a remote generating station. State the data you measure or estimate. If
Consider a series RLC circuit having the following circuit parameters: R = 200 Ω, L = 663 mH, and C = 26.5 μF. The applied voltage has an amplitude of 50.0 V and a frequency of 60.0 Hz.
A voltage ∆v = (100 V) sin wt (in SI units) is applied across a series combination of a 2.00-H inductor, a 10.0-μF capacitor, and a 10.0-Ω resistor. (a) Determine the angular
Impedance matching Example 28.2 showed that maximum power is transferred when the internal resistance of a DC source is equal to the resistance of the load. A transformer may be used to provide
A power supply with ∆Vrms = 120 V is connected between points a and d in Figure P33.26. At what frequency will it deliver a power of 250 W?
Figure P33.69a shows a parallel RLC circuit, and the corresponding phasor diagram is given in Figure P33.69b. The instantaneous voltages (and rms voltages) across each of the three circuit elements
An 80.0-Ω resistor, a 200-mH inductor, and a 0.150-μF capacitor are connected in parallel across a 120-V (rms) source operating at 374 rad/s. (a) What is the resonant frequency of the
A series RLC circuit is operating at 2 000 Hz. At this frequency, XL = XC = 1 884 Ω. The resistance of the circuit is 40.0 Ω. (a) Prepare a table showing the values of XL, XC, and Z for f
A series RLC circuit in which R = 1.00 Ω, L = 1.00 mH, and C = 1.00 nF is connected to an AC source delivering 1.00 V (rms). Make a precise graph of the power delivered to the circuit as a
Suppose the high-pass filter shown in Figure 33.25 has R = 1 000 Ω and C = 0.050 0 μF. (a) At what frequency does ∆Vout/∆Vin = ½? (b) Plot log10 (∆Vout/∆Vin)
A very long, thin rod carries electric charge with the linear density 35.0 nC/m. It lies along the x axis and moves in the x direction at a speed of 15.0 Mm/s. (a) Find the electric field the rod
(a) The distance to the North Star, Polaris, is approximately 6.44 x 1018 m. If Polaris were to burn out today, in what year would we see it disappear? (b) How long does it take for sunlight to
The speed of an electromagnetic wave traveling in a transparent nonmagnetic substance is v = 1 / √kμ0Є0, where 0 is the dielectric constant of the substance. Determine the speed of
An electromagnetic wave in vacuum has an electric field amplitude of 220 V/m. Calculate the amplitude of the corresponding magnetic field.
Figure 34.3 shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose that the wavelength is 50.0 m, and the electric field vibrates in the xy plane with amplitude of 22.0
Write down expressions for the electric and magnetic fields of a sinusoidal plane electromagnetic wave having a frequency of 3.00 GHz and traveling in the positive x direction. The amplitude of the
In SI units, the electric field in an electromagnetic wave is described by Ey = 100 sin (1.00 x 107 x –wt). Find (a) The amplitude of the corresponding magnetic field oscillations, (b) The
Verify by substitution that the following equations are solutions to Equations 34.8 and 34.9, respectively: E =E max cos (kx – wt) B =E max cos (kx – wt)
A very large flat sheet carries a uniformly distributed electric current with current per unit width Js. Example 30.6 demonstrated that the current creates a magnetic field on both sides of the
A standing-wave interference pattern is set up by radio waves between two metal sheets 2.00 m apart. This is the shortest distance between the plates that will produce a standing-wave pattern. What
A microwave oven is powered by an electron tube called a magnetron, which generates electromagnetic waves of frequency 2.45 GHz. The microwaves enter the oven and are reflected by the walls. The
How much electromagnetic energy per cubic meter is contained in sunlight, if the intensity of sunlight at the Earth’s surface under a fairly clear sky is 1 000 W/m2?
An AM radio station broadcasts isotropically (equally in all directions) with an average power of 4.00 kW. A dipole receiving antenna 65.0 cm long is at a location 4.00 miles from the transmitter.
What is the average magnitude of the Poynting vector 5.00 miles from a radio transmitter broadcasting isotropically with an average power of 250 kW?
A monochromatic light source emits 100 W of electromagnetic power uniformly in all directions. (a) Calculate the average electric-field energy density 1.00 m from the source. (b) Calculate the
A community plans to build a facility to convert solar radiation to electrical power. They require 1.00 MW of power, and the system to be installed has an efficiency of 30.0% (that is, 30.0% of the
Assuming that the antenna of a 10.0-kW radio station radiates spherical electromagnetic waves, compute the maximum value of the magnetic field 5.00 km from the antenna, and compare this value with
The filament of an incandescent lamp has a 150-2 resistance and carries a direct current of 1.00 A. The filament is 8.00 cm long and 0.900 mm in radius. (a) Calculate the Poynting vector at the
One of the weapons being considered for the “Star Wars” antimissile system is a laser that could destroy ballistic missiles. When a high-power laser is used in the Earth’s atmosphere, the
In a region of free space the electric field at an instant of time is E = (80.0i + 32.0j) 64.0k) N/C and the magnetic field is B = (0.200i + 0.080 0j + 0.290k) μT. (a) Show that the two fields
Let us model the electromagnetic wave in a microwave oven as a plane traveling wave moving to the left, with an intensity of 25.0 kW/m2. An oven contains two cubical containers of small mass, each
A lightbulb filament has a resistance of 110 2. The bulb is plugged into a standard 120-V (rms) outlet, and emits 1.00% of the electric power delivered to it by electromagnetic radiation of frequency
A certain microwave oven contains a magnetron that has an output of 700 W of microwave power for an electrical input power of 1.40 kW. The microwaves are entirely transferred from the magnetron into
High-power lasers in factories are used to cut through cloth and metal (Fig. P34.23). One such laser has a beam diameter of 1.00 mm and generates an electric field having amplitude of 0.700 MV/m at
A 10.0-mW laser has a beam diameter of 1.60 mm. (a) What is the intensity of the light, assuming it is uniform across the circular beam? (b) What is the average energy density of the beam?
At one location on the Earth, the rms value of the magnetic field caused by solar radiation is 1.80 μT. From this value calculate (a) The rms electric field due to solar radiation, (b) The
A 100-mW laser beam is reflected back upon itself by a mirror. Calculate the force on the mirror..
A radio wave transmits 25.0 W/m2 of power per unit area. A flat surface of area A is perpendicular to the direction of propagation of the wave. Calculate the radiation pressure on it, assuming the
A possible means of space flight is to place a perfectly reflecting aluminized sheet into orbit around the Earth and then use the light from the Sun to push this “solar sail.” Suppose a sail of
A 15.0-mW helium–neon laser (A = 632.8 nm) emits a beam of circular cross section with a diameter of 2.00 mm. (a) Find the maximum electric field in the beam. (b) What total energy is contained
Given that the intensity of solar radiation incident on the upper atmosphere of the Earth is 1 340 W/m2, determine (a) The intensity of solar radiation incident on Mars, (b) The total power
A plane electromagnetic wave has an intensity of 750 W/m2. A flat, rectangular surface of dimensions 50 cm x 100 cm is placed perpendicular to the direction of the wave. The surface absorbs half of
A uniform circular disk of mass 24.0 g and radius 40.0 cm hangs vertically from a fixed, frictionless, horizontal hinge at a point on its circumference. A horizontal beam of electromagnetic radiation
Figure 34.10 shows a Hertz antenna (also known as a half wave antenna, because its length is A/2). The antenna is located far enough from the ground that reflections do not significantly affect its
Two hand-held radio transceivers with dipole antennas are separated by a large fixed distance. If the transmitting antenna is vertical, what fraction of the maximum received power will appear in the
Two radio-transmitting antennas are separated by half the broadcast wavelength and are driven in phase with each other. In which directions are (a) The strongest and (b) The weakest signals
Accelerating charges radiate electromagnetic waves. Calculate the wavelength of radiation produced by a proton moving in a circle of radius R perpendicular to a magnetic field of magnitude B.
A coil has an inductance of 3.00 mH, and the current in it changes from 0.200 A to 1.50 A in a time of 0.200 s. Find the magnitude of the average induced emf in the coil during this time.
A coiled telephone cord forms a spiral with 70 turns, a diameter of 1.30 cm, and an unstretched length of 60.0 cm. Determine the self-inductance of one conductor in the unstretched cord.
A 2.00-H inductor carries a steady current of 0.500 A. When the switch in the circuit is opened, the current is effectively zero after 10.0 ms. What is the average induced emf in the inductor
Calculate the magnetic flux through the area enclosed by a 300-turn, 7.20-mH coil when the current in the coil is 10.0 mA.
A 10.0-mH inductor carries a current I = I max sin 1t, with I max = 5.00 A and 1/2) = 60.0 Hz. What is the back emf as a function of time?
An emf of 24.0 mV is induced in a 500-turn coil at an instant when the current is 4.00 A and is changing at the rate of 10.0 A/s. What is the magnetic flux through each turn of the coil?
An inductor in the form of a solenoid contains 420 turns, is 16.0 cm in length, and has a cross-sectional area of 3.00 cm2. What uniform rate of decrease of current through the inductor induces an
The current in a 90.0-mH inductor changes with time as I = 1.00t2 + 6.00t (in SI units). Find the magnitude of the induced emf at (a) T = 1.00 s and (b) T = 4.00 s. (c) At what time is the emf
A 40.0-mA current is carried by a uniformly wound air-core solenoid with 450 turns, a 15.0-mm diameter, and 12.0-cm length. Compute (a) The magnetic field inside the solenoid, (b) The magnetic
A solenoid has 120 turns uniformly wrapped around a wooden core, which has a diameter of 10.0 mm and a length of 9.00 cm. (a) Calculate the inductance of the solenoid. (b) What If? The wooden
A piece of copper wire with thin insulation, 200 m long and 1.00 mm in diameter, is wound onto a plastic tube to form a long solenoid. This coil has a circular cross section and consists of tightly
A toroid has a major radius R and a minor radius r, and is tightly wound with N turns of wire, as shown in Figure P32.12. If R >> r, the magnetic field in the region enclosed by the wire of the
A self-induced emf in a solenoid of inductance L changes in time as Є = Є0 e-kt. Find the total charge that passes through the solenoid, assuming the charge is finite.
Calculate the resistance in an RL circuit in which L = 2.50 H and the current increases to 90.0% of its final value in 3.00 s.
A 12.0-V battery is connected into a series circuit containing a 10.0-. Resistor and a 2.00-H inductor, how long will it take the current to reach? (a) 50.0% and (b) 90.0% of its final value?
Show that I = I 0 e-t/+ is a solution of the differential equation IR + L dl/ dt = 0 where r = L/R and I0 is the current at t = 0.
Consider the circuit in Figure P32.17, taking Є = 6.00 V, L = 8.00 mH, and R = 4.00 Ω.(a) What is the inductive time constant of the circuit?(b) Calculate the current in the circuit
In the circuit shown in Figure P32.17, let L = 7.00 H, R = 9.00Ω, and Є = 120 V. What is the self-induced emf 0.200 s after the switch is closed?
For the RL circuit shown in Figure P32.17, let the inductance be 3.00 H, the resistance 8.00 Ω, and the battery emf 36.0 V. (a) Calculate the ratio of the potential difference across the
A 12.0-V battery is connected in series with a resistor and an inductor. The circuit has a time constant of 500 μs, and the maximum current is 200 mA. What is the value of the inductance?
An inductor that has an inductance of 15.0 H and a resistance of 30.0 Ω is connected across a 100-V battery. What is the rate of increase of the current? (a) At t = 0 and (b) At t = 1.50 s?
When the switch in Figure P32.17 is closed, the current takes 3.00 ms to reach 98.0% of its final value. If R 10.0Ω, what is the inductance?
The switch in Figure P32.23 is open for t
A series RL circuit with L = 3.00 H and a series RC circuit with C = 3.00 'F have equal time constants. If the two circuits contain the same resistance R, (a) What is the value of R and (b) What
A current pulse is fed to the partial circuit shown in Figure P32.25. The current begins at zero, then becomes 10.0 A between t = 0 and t = 200 μs, and then is zero once again. Determine the
One application of an RL circuit is the generation of time varying high voltage from a low-voltage source, as shown in Figure P32.26.(a) What is the current in the circuit a long time after the
A 140-mH inductor and a 4.90-Ω resistor are connected with a switch to a 6.00-V battery as shown in Figure P32.27.(a) If the switch is thrown to the left (connecting the battery), how much time

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