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physics
electricity and magnetism

College Physics 7th Edition Raymond A. Serway, Jerry S. Faughn, Chris Vuille, Charles A. Bennett - Solutions

One very long wire carries current 30.0 A to the left along the x axis. A second very long wire carries current 50.0 A to the right along the line (y = 0.280 m, z= 0). (a) Where in the plane of the two wires is the total magnetic field equal to zero? (b) A particle with a charge of -2.00
Consider the current-carrying loop shown in Figure P30.12, formed of radial lines and segments of circles whose centers are at point P. Find the magnitude and direction of B at P.
A wire carrying a current I is bent into the shape of an equilateral triangle of side L. (a) Find the magnitude of the magnetic field at the center of the triangle. (b) At a point halfway between the center and any vertex, is the field stronger or weaker than at the center?
Determine the magnetic field (in terms of I, a, and d) at the origin due to the current loop in Figure P30.14.
Two long, parallel conductors carry currents I1 = 3.00 A and I2 = 3.00 A, both directed into the page in Figure P30.15. Determine the magnitude and direction of the resultant magnetic field at P.
Two long, parallel conductors, separated by 10.0 cm, carry currents in the same direction. The first wire carries current I1 = 5.00 A and the second carries I 2 = 8.00 A. (a) What is the magnitude of the magnetic field created by I1 at the location of I 2? (b) What is the force per unit length
In Figure P30.17, the current in the long, straight wire is I1 = 5.00 A and the wire lies in the plane of the rectangular loop, which carries the current I2 = 10.0 A. The dimensions are c = 0.100 m, a = 0.150 m, and ℓ = 0.450 m. Find the magnitude and direction of the net force exerted on the
Two long, parallel wires are attracted to each other by a force per unit length of 320 μN/m when they are separated by a vertical distance of 0.500 m. The current in the upper wire is 20.0 A to the right. Determine the location of the line in the plane of the two wires along which the total
Three long wires (wire 1, wire 2, and wire 3) hang vertically. The distance between wire 1 and wire 2 is 20.0 cm. On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries a downward current of 4.00 A. Wire 3 is located such that when it carries a certain current, each
The unit of magnetic flux is named for Wilhelm Weber. The practical-size unit of magnetic field is named for Johann Karl Friedrich Gauss. Both were scientists at GÃ¶ttingen, Germany. Along with their individual accomplishments, together they built a telegraph in 1833. It consisted of a
Four long, parallel conductors carry equal currents of I = 5.00 A. Figure P30.21 is an end view of the conductors. The current direction is into the page at points A and B (indicated by the crosses) and out of the page at C and D (indicated by the dots). Calculate the magnitude and direction of the
A long straight wire lies on a horizontal table and carries a current of 1.20 μA. In a vacuum, a proton moves parallel to the wire (opposite the current) with a constant speed of 2.30 x 104 m/s at a distance d above the wire. Determine the value of d. You may ignore the magnetic field due to
Figure P30.23 is a cross-sectional view of a coaxial cable. 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 1.00 A out of the page and the
The magnetic field 40.0 cm away from a long straight wire carrying current 2.00 A is 1.00 μT. (a) At what distance is it 0.100 μT? (b) What If? At one instant, the two conductors in a long household extension cord carry equal 2.00-A currents in opposite directions. The two wires are
A packed bundle of 100 long, straight, insulated wires forms a cylinder of radius R = 0.500 cm. (a) If each wire carries 2.00 A, what are the magnitude and direction of the magnetic force per unit length acting on a wire located 0.200 cm from the center of the bundle? (b) What If? Would a wire
The magnetic coils of a tokomak fusion reactor are in the shape of a toroid having an inner radius of 0.700 m and an outer radius of 1.30 m. The toroid has 900 turns of large diameter wire, each of which carries a current of 14.0 kA. Find the magnitude of the magnetic field inside the toroid along
Consider a column of electric current passing through plasma (ionized gas). Filaments of current within the column are magnetically attracted to one another. They can crowd together to yield a very great current density and a very strong magnetic field in a small region. Sometimes the current can
Niobium metal becomes a superconductor when cooled below 9 K. Its superconductivity is destroyed when the surface magnetic field exceeds 0.100 T. Determine the maximum current a 2.00-mm-diameter niobium wire can carry and remain superconducting, in the absence of any external magnetic field.
A long cylindrical conductor of radius R carries a current I as shown in Figure P30.29. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to J = br, where b is a constant. Find an expression for the magnetic field B(a)
In Figure P30.30, both currents in the infinitely long wires are in the negative x direction. (a) Sketch the magnetic field pattern in the yz plane.(b) At what distance d along the z axis is the magnetic field a maximum?
What current is required in the windings of a long solenoid that has 1 000 turns uniformly distributed over a length of 0.400 m, to produce at the center of the solenoid a magnetic field of magnitude 1.00 x 10-4 T?
Consider a solenoid of length ℓ and radius R, containing N closely spaced turns and carrying a steady current I. (a) In terms of these parameters, find the magnetic field at a point along the axis as a function of distance a from the end of the solenoid. (b) Show that as ℓ becomes
A single-turn square loop of wire, 2.00 cm on each edge, carries a clockwise current of 0.200 A. The loop is inside a solenoid, with the plane of the loop perpendicular to the magnetic field of the solenoid. The solenoid has 30 turns/cm and carries a clockwise current of 15.0 A. Find the force on
Consider the hemispherical closed surface in Figure P30.34. The hemisphere is in a uniform magnetic field that makes an angle θ with the vertical. Calculate the magnetic flux through(a) The flat surface S1 and(b) The hemispherical surface S2.
A cube of edge length ℓ = 2.50 cm is positioned as shown in Figure P30.35. A uniform magnetic field given by B = (5i + 4j + 3k) T exists throughout the region.(a) Calculate the flux through the shaded face.(b) What is the total flux through the six faces?
A solenoid 2.50 cm in diameter and 30.0 cm long has 300 turns and carries 12.0 A.(a) Calculate the flux through the surface of a disk of radius 5.00 cm that is positioned perpendicular to and centered on the axis of the solenoid, as shown in Figure P30.36a.(b) Figure P30.36b shows an enlarged end
A 0.100-A current is charging a capacitor that has square plates 5.00 cm on each side. The plate separation is 4.00 mm. Find (a) The time rate of change of electric flux between the plates and (b) The displacement current between the plates.
A 0.200-A current is charging a capacitor that has circular plates 10.0 cm in radius. If the plate separation is 4.00 mm, (a) What is the time rate of increase of electric field between the plates? (b) What is the magnetic field between the plates 5.00 cm from the center?
In Bohr’s 1913 model of the hydrogen atom, the electron is in a circular orbit of radius 5.29 x 10-11 m and its speed is 2.19 x 106 m/s. (a) What is the magnitude of the magnetic moment due to the electron’s motion? (b) If the electron moves in a horizontal circle, counterclockwise as seen
A magnetic field of 1.30 T is to be set up in an iron-core toroid. The toroid has a mean radius of 10.0 cm, and magnetic permeability of 5 000 μ0. What current is required if the winding has 470 turns of wire? The thickness of the iron ring is small compared to 10 cm, so the field in the
A toroid with a mean radius of 20.0 cm and 630 turns (see Fig. 30.30) is filled with powdered steel whose magnetic susceptibility X is 100. The current in the windings is 3.00 A. Find B (assumed uniform) inside the toroid.
A particular paramagnetic substance achieves 10.0% of its saturation magnetization when placed in a magnetic field of 5.00 T at a temperature of 4.00 K. The density of magnetic atoms in the sample is 8.00 x 1027 atoms/m3, and the magnetic moment per atom is 5.00 Bohr magnetons. Calculate the Curie
Calculate the magnetic field strength H of a magnetized substance in which the magnetization is 0.880 x 106 A/m and the magnetic field has magnitude 4.40 T.
At saturation, when nearly all of the atoms have their magnetic moments aligned, the magnetic field in a sample of iron can be 2.00 T. If each electron contributes a magnetic moment of 9.27 x 10-24 A (m2 (one Bohr magneton), how many electrons per atom contribute to the saturated field of iron?
(a) Show that Curie’s law can be stated in the following way: The magnetic susceptibility of a paramagnetic substance is inversely proportional to the absolute temperature, according to 8 = Cμ0/T, where C is Curie’s constant. (b) Evaluate Curie’s constant for chromium
A circular coil of 5 turns and a diameter of 30.0 cm is oriented in a vertical plane with its axis perpendicular to the horizontal component of the Earth’s magnetic field. A horizontal compass placed at the center of the coil is made to deflect 45.0° from magnetic north by a current of 0.600 A
The magnetic moment of the Earth is approximately 8.00 x 1022 A (m2. (a) If this were caused by the complete magnetization of a huge iron deposit, how many unpaired electrons would this correspond to? (b) At two unpaired electrons per iron atom, how many kilograms of iron would this correspond
The magnitude of the Earth’s magnetic field at either pole is approximately 7.00 x 10-5 T. Suppose that the field fades away, before its next reversal. Scouts, sailors, and conservative politicians around the world join together in a program to replace the field. One plan is to use a current loop
A very long, thin strip of metal of width w carries a current I along its length as shown in Figure P30.49. Find the magnetic field at the point P in the diagram. The point P is in the plane of the strip at distance b away from it.
Suppose you install a compass on the center of the dashboard of a car. Compute an order-of-magnitude estimate for the magnetic field at this location produced by the current when you switch on the headlights. How does it compare with the Earth’s magnetic field? You may suppose the dashboard is
For a research project, a student needs a solenoid that produces an interior magnetic field of 0.030 0 T. She decides to use a current of 1.00 A and a wire 0.500 mm in diameter. She winds the solenoid in layers on an insulating form 1.00 cm in diameter and 10.0 cm long. Determine the number of
A thin copper bar of length ℓ = 10.0 cm is supported horizontally by two (nonmagnetic) contacts. The bar carries current I1 = 100 A in the -x direction, as shown in Figure P30.52. At a distance h = 0.500 cm below one end of the bar, a long straight wire carries a current I2 = 200 A in the z
A non-conducting ring of radius 10.0 cm is uniformly charged with a total positive charge 10.0 μC. The ring rotates at a constant angular speed 20.0 rad/s about axis through its center, perpendicular to the plane of the ring. What is the magnitude of the magnetic field on the axis of the ring
A non-conducting ring of radius R is uniformly charged with a total positive charge q. The ring rotates at a constant angular speed 4 about an axis through its center, perpendicular to the plane of the ring. What is the magnitude of the magnetic field on the axis of the ring a distance R/2 from its
Two circular coils of radius R, each with N turns, are perpendicular to a common axis. The coil centers are a distance R apart. Each coil carries a steady current I in the same direction, as shown in Figure P30.55.(a) Show that the magnetic field on the axis at a distance x from the center of one
Two identical, flat, circular coils of wire each have 100 turns and a radius of 0.500 m. The coils are arranged as a set of Helmholtz coils (see Fig. P30.55), parallel and with separation 0.500 m. Each coil carries a current of 10.0 A. Determine the magnitude of the magnetic field at a point on the
We have seen that a long solenoid produces a uniform magnetic field directed along the axis of a cylindrical region. However, to produce a uniform magnetic field directed parallel to a diameter of a cylindrical region, one can use the saddle coils illustrated in Figure P30.57. The loops are wrapped
A very large parallel-plate capacitor carries charge with uniform charge per unit area +/σ on the upper plate and -/σ on the lower plate. The plates are horizontal and both move horizontally with speed v to the right. (a) What is the magnetic field between the plates? (b) What is the
Two circular loops are parallel, coaxial, and almost in contact, 1.00 mm apart (Fig. P30.59). Each loop is 10.0 cm in radius. The top loop carries a clockwise current of 140 A. The bottom loop carries a counterclockwise current of 140 A.(a) Calculate the magnetic force exerted by the bottom loop on
What objects experience a force in an electric field? Chapter 23 gives the answer: any electric charge, stationary or moving, other than the charge that created the field. What creates an electric field? Any electric charge, stationary or moving, as you studied in Chapter 23 What objects experience
Rail guns have been suggested for launching projectiles into space without chemical rockets, and for ground-to-air antimissile weapons of war. A tabletop model rail gun (Fig. P30.61) consists of two long parallel horizontal rails 3.50 cm apart, bridged by a bar BD of mass 3.00 g. The bar is
Fifty turns of insulated wire 0.100 cm in diameter are tightly wound to form a flat spiral. The spiral fills a disk surrounding a circle of radius 5.00 cm and extending to a radius 10.00 cm at the outer edge. Assume the wire carries current I at the center of its cross section. Approximate each
Two long, parallel conductors carry currents in the same direction as shown in Figure P30.63. Conductor A carries a current of 150 A and is held firmly in position. Conductor B carries a current IB and is allowed to slide freely up and down (parallel to A) between a set of non-conducting guides. If
Charge is sprayed onto a large non-conducting belt above the left-hand roller in Figure P30.64. The belt carries the charge with a uniform surface charge density / as it moves with a speed v between the rollers as shown. The charge is removed by a wiper at the right-hand roller. Consider a point
An infinitely long straight wire carrying a current I1 is partially surrounded by a loop as shown in Figure P30.65. The loop has a length L, radius R, and carries a current I2. The axis of the loop coincides with the wire. Calculate the force exerted on the loop.
Measurements of the magnetic field of a large tornado were made at the Geophysical Observatory in Tulsa, Oklahoma, in 1962. The tornado’s field was measured to be B = 1.50 x 10-8 T pointing north when the tornado was 9.00 km east of the observatory. What current was carried up or down the funnel
A wire is formed into the shape of a square of edge length L (Fig. P30.67). Show that when the current in the loop is I, the magnetic field at point P, a distance x from the center of the square along its axis is
The force on a magnetic dipole aligned with a non-uniform magnetic field in the x direction is given by Fx = |μ|dB/dx. Suppose that two flat loops of wire each have radius R and carry current I. (a) The loops are arranged coaxially and separated by a variable distance x, large compared to R.
A wire carrying a current I is bent into the shape of an exponential spiral, r = eθ, from θ = 0 to θ = 2π as suggested in Figure P30.69. To complete a loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude and direction of B at the
Table P30.70 contains data taken for a ferromagnetic material.(a) Construct a magnetization curve from the data. Remember that B = B0 + μ0M.(b) Determine the ratio B/B0 for each pair of values of B and B0, and construct a graph of B/B0 versus B0. (The fraction B/B0 is called the relative
A sphere of radius R has a uniform volume charge density P Determine the magnetic field at the center of the sphere when it rotates as a rigid object with angular speed w about an axis through its center (Fig. P30.71)
A sphere of radius R has a uniform volume charge density P Determine the magnetic dipole moment of the sphere when it rotates as a rigid body with angular speed 4 about an axis through its center (Fig. P30.71)
A long cylindrical conductor of radius a has two cylindrical cavities of diameter a through its entire length, as shown in Figure P30.73. A current I is directed out of the page and is uniform through a cross section of the conductor. Find the magnitude and direction of the magnetic field in terms
The rms output voltage of an AC source is 200 V and the operating frequency is 100 Hz. Write the equation giving the output voltage as a function of time.
(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 170 V? (b) What If? What is the resistance of a 100-W bulb?
An AC power supply produces a maximum voltage ∆Vmax = 100 V. This power supply is connected to a 24.0-Ω resistor, and the current and resistor voltage are measured with an ideal AC ammeter and voltmeter, as shown in Figure P33.3. What does each meter read? Note that an ideal ammeter has
In the simple AC circuit shown in Figure 33.2, R = 70.0 Ω and ∆v = ∆Vmax sin wt. (a) If ∆vR = 0.250 ∆Vmax for the first time at t = 0.010 0 s, what is the angular frequency of the source? (b) What is the next value of t for which ∆vR = 0.250 ∆Vmax?
The current in the circuit shown in Figure 33.2 equals 60.0% of the peak current at t = 7.00 ms. What is the smallest frequency of the source that gives this current?
Figure P33.6 shows three lamps connected to a 120-V AC (rms) household supply voltage. Lamps 1 and 2 have 150-W bulbs; lamp 3 has a 100-W bulb. Find the rms current and resistance of each bulb.
An audio amplifier, represented by the AC source and resistor in Figure P33.7, delivers to the speaker alternating voltage at audio frequencies. If the source voltage has an amplitude of 15.0 V, R = 8.20 Ω, and the speaker is equivalent to a resistance of 10.4 Ω, what is the time
An inductor is connected to a 20.0-Hz power supply that produces a 50.0-V rms voltage. What inductance is needed to keep the instantaneous current in the circuit below 80.0 mA?
In a purely inductive AC circuit, as shown in Figure 33.6, ∆Vmax = 100 V. (a) The maximum current is 7.50 A at 50.0 Hz. Calculate the inductance L. (b) What If? At what angular frequency w is the maximum current 2.50 A?
An inductor has a 54.0-Ω reactance at 60.0 Hz. What is the maximum current if this inductor is connected to a 50.0-Hz source that produces a 100-V rms voltage?
For the circuit shown in Figure 33.6, ∆Vmax = 80.0 V, w = 65.0π rad/s, and L = 70.0 mH. Calculate the current in the inductor at t = 15.5 ms.
A 20.0-mH inductor is connected to a standard electrical outlet (∆Vrms = 120 V; f = 60.0 Hz). Determine the energy stored in the inductor at t = (1/180) s, assuming that this energy is zero at t = 0.
Determine the maximum magnetic flux through an inductor connected to a standard electrical outlet (∆Vrms = 120 V, f = 60.0 Hz).
(a) For what frequencies does a 22.0-μF capacitor have a reactance below 175 Ω? (b) What If? Over this same frequency range, what is the reactance of a 44.0-μF capacitor?
What is the maximum current in a 2.20-μF capacitor when it is connected across? (a) A North American electrical outlet having ∆Vrms = 120 V, f = 60.0 Hz, and (b) What If? A European electrical outlet having ∆Vrms = 240 V, f = 50.0 Hz?
A capacitor C is connected to a power supply that operates at a frequency f and produces an rms voltage ∆V. What is the maximum charge that appears on either of the capacitor plates?
What maximum current is delivered by an AC source with ∆Vmax = 48.0 V and f = 90.0 Hz when connected across a 3.70-μF capacitor?
A 1.00-mF capacitor is connected to a standard electrical outlet (∆Vrms = 120 V; f = 60.0 Hz). Determine the current in the capacitor at t = (1/180) s, assuming that at t = 0, the energy stored in the capacitor is zero.
An inductor (L = 400 mH), a capacitor (C = 4.43μF), and a resistor (R = 500Ω 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 ∆Vmax. (b) Determine the phase angle by which the current leads or
At what frequency does the inductive reactance of a 57.0-μH inductor equal the capacitive reactance of a 57.0-μF capacitor?
A series AC circuit contains the following components: R = 150 Ω, L = 250 mH, C = 2.00 μF and a source with ∆Vmax = 210 V operating at 50.0 Hz. Calculate the (a) Inductive reactance, (b) Capacitive reactance, (c) Impedance, (d) Maximum current, and (e) Phase angle between
A sinusoidal voltage ∆v (t) = (40.0 V) sin(100t) is applied to a series RLC circuit with L = 160 mH, C = 99.0 μF, and R = 68.0 Ω. (a) What is the impedance of the circuit? (b) What is the maximum current? (c) Determine the numerical values for Imax, w, and ǿ in the
An RLC circuit consists of a 150-Ω resistor, a 21.0-μF capacitor, and a 460-mH inductor, connected in series with a 120-V, 60.0-Hz power supply. (a) What is the phase angle between the current and the applied voltage? (b) Which reaches its maximum earlier, the current or the voltage?
Four circuit elements—a capacitor, an inductor, a resistor, and an AC source—are connected together in various ways. First the capacitor is connected to the source, and the rms current is found to be 25.1 mA. The capacitor series with the inductor and the source, making the rms current 68.2 mA,
A person is working near the secondary of a transformer, as shown in Figure P33.25. The primary voltage is 120 V at 60.0 Hz. The capacitance Cs, which is the stray capacitance between the hand and the secondary winding, is 20.0 μF. Assuming the person has a body resistance to ground Rb = 50.0
An AC source with∆ Vmax = 150 V and f = 50.0 Hz is connected between points a and d in Figure P33.26. Calculate the maximum voltages between points (a) A and b, (b) B and c, (c) C and d, and (d) B and d.
Draw to scale a phasor diagram showing Z, XL, XC, and - for an AC series circuit for which R = 300 (, C = 11.0 μF, L = 0.200 H, and f = (500/π) Hz.
In an RLC series circuit that includes a source of alternating current operating at fixed frequency and voltage, the resistance R is equal to the inductive reactance. If the plate separation of the capacitor is reduced to half of its original value, the current in the circuit doubles. Find the
A coil of resistance 35.0 Ω and inductance 20.5 H is in series with a capacitor and a 200-V (rms), 100-Hz source. The rms current in the circuit is 4.00 A. (a) Calculate the capacitance in the circuit. (b) What is ∆Vrms across the coil?
The voltage source in Figure P33.30 has an output of μVrms = 100 V at an angular frequency of w= 1 000 rad/s. Determine(a) The current in the circuit and(b) The power supplied by the source.(c) Show that the power delivered to the resistor is equal to the power supplied by the source.
An AC voltage of the form ∆v = (100 V) sin (1 000t) is applied to a series RLC circuit. Assume the resistance is 400 Ω, the capacitance is 5.00 μF, and the inductance is 0.500 H. Find the average power delivered to the circuit
A series RLC circuit has a resistance of 45.0 Ω and an impedance of 75.0 Ω. What average power is delivered to this circuit when ∆Vrms = 210 V?
In a certain series RLC circuit, Irms = 9.00 A, ∆Vrms = 180 V, and the current leads the voltage by 37.0°. (a) What is the total resistance of the circuit? (b) Calculate the reactance of the circuit (XL − XC).
Suppose you manage a factory that uses many electric motors. The motors create a large inductive load to the electric power line, as well as a resistive load. The electric company builds an extra-heavy distribution line to supply you with a component of current that is 90° out of phase with the
Suppose power ∆ is to be transmitted over a distance d at a voltage ∆ V with only 1.00% loss. Copper wire of what diameter should be used for each of the two conductors of the transmission line? Assume the current density in the conductors is uniform.
A diode is a device that allows current to be carried in only one direction (the direction indicated by the arrowhead in its circuit symbol). Find in terms of ∆V and R the average power delivered to the diode circuit of Figure P33.36.
An RLC circuit is used in a radio to tune into an FM station broadcasting at 99.7 MHz. The resistance in the circuit is 12.0 Ω, and the inductance is 1.40 μH. What capacitance should be used?

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