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physics
electricity and magnetism

University Physics with Modern Physics 12th Edition Hugh D. Young, Roger A. Freedman, Lewis Ford - Solutions

A uniform rectangular coil of total mass 210 g and dimensions 0.500 m X 1.00 m is oriented perpendicular to a uniform 3.00-T magnetic field (Fig). A current of 2.00 A is suddenly started in the coil.(a) About which axis (A, or A2) will the coil begin to rotate? Why?(b) Find the initial angular
A circular coil with area A and N turns is free to rotate about a diameter that coincides with the x-axis. Current I is circulating in the coil. There is a uniform magnetic field B in the positive y-direction. Calculate the magnitude and direction of the torque T and the value of the potential
A coil with magnetic moment 1.45 A. m2 is oriented initially with its magnetic moment antiparallel to a uniform 0.835-T magnetic field. What is the change in potential energy of the coil when it is rotated 1800 so that its magnetic moment is parallel to the field?
A dc motor with its rotor and field coils connected in series has an internal resistance of 3.2.n. When the motor is running at full load on a 120-V line, the emf in the rotor is 105 V. (a) What is the current drawn by the motor from the line? (b) What is the power delivered to the motor? (c) What
(a) What is the current in the field coils?(b) What is the current in the rotor?(c) What is the induced emf developed by the motor?(d) How much mechanical power is developed by this motor?
A shunt-wound dc motor with the field coils and rotor connected in parallel (Fig) operates from a 120-V dc power line. The resistance of the field windings, RI , is 218 .n. The resistance of the rotor, R" is 5.9 .n. When the motor is running, the rotor develops an emf E. The motor draws a current
Figure shows a portion of a silver ribbon with z1 = 11.8 mm and y1 = 0.23 mm, carrying a current of 120 A in the +x-direction. The ribbon lies in a uniform magnetic field, in the y-direction, with magnitude 0.95 T. Apply the simplified model of the Hall Effect presented in Section 27.9. If there
Let Fig. represent a strip of an unknown metal of the same dimensions as those of the silver ribbon in Exercise 27.51. When the magnetic field is 2.29 T and the current is 78.0 A, the Hall emf is found to be 131 µV. What does the simplified model of the Hall effect presented in Section 27.9 give
When a particle of charge q > 0 moves with a velocity of U1 at 45.0o from the +x-axis in the xy-plane a uniform magnetic field exerts a force F, along the -z-axis (Fig). When the same particle moves with a velocity U2 with the same magnitude as u1 but along the +z-axis, a force u2 of magnitude F2
A particle with charge 9.45 X 10-8 e is moving in a region where there is a uniform magnetic field of 0.450 T in the + x direction. At a particular instant of time the velocity of the particle has components Ux = -1.68 X 104 m/s, Uy = -3.11 X 104 m/s, and Uz = 5.85 X 104 m/s. What are the
You wish to hit a target from several meters away with a charged coin having a mass of 5.0 g and a charge of +2500 µc. The coin is given an initial velocity of 12.8 m/s, and a downward, uniform electric field with field strength 27.5 N/c exists throughout the region. If you aim directly at the
A cyclotron is to accelerate protons to an energy of 5.4 MeV. The superconducting electromagnet of the cyclotron produces a 3.5-T magnetic field perpendicular to the proton orbits. (a) When the protons have achieved a kinetic energy of 2.7 MeV, what is the radius of their circular orbit and what is
The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.85 T. The poles have a radius of 0.40 m, which is the maximum radius of the orbits of the accelerated particles. (a) What is the maximum energy to which protons (q = 1.60 X 10-19C, m = 1.67 X l0-27kg) can be
The force on a charged particle moving in a magnetic field can be computed as the vector sum of the forces due to each separate component of the magnetic field. As an example, a particle with charge q is moving with speed v in the -y-direction. It is moving in a uniform magnetic field B = Bxi + Byj
Auniform, 458-gmetal bar 75.0cm long carries a current I in a uniform, horizontal, 1.55-T magnetic field as shown in Fig. The bar is hinged at b but rests unattached at a. What is the largest current that can flow from a to b without the electrical contact at a?
In the electron gun of a TV picture tube the electrons (charge -e, mass m) are accelerated by a voltageV. After leaving the electron gun, the electron beam travels a distance D to the screen; in this region there is a transverse magnetic field of magnitude B and no electric field.(a) Sketch the
A particle with negative charge q and mass m = 2.58 X 10-15 kg is travelling through a region containing a uniform magnetic field B = - (0.120 T) k. At. a particular instant of time the velocity of the particle is v = (1.05 X 106 m/s)( -3i + 4j + 12k) and the force F on the particle has a magnitude
A long, straight wire containing a semicircular region of radius 0.95 m is placed in a uniform magnetic field of magnitude 2.20 T as shown in Fig. What is the net magnetic force acting on the wire when it carries a current of 3.40 A?
A magnetic field exerts a torque T on a round current carrying loop of wire. What will be the torque on this loop (in terms of T) if its diameter is tripled?
A particle of charge q > 0 is moving at speed v in the +z-direction through a region of uniform magnetic field B. The magnetic force on the particle is F = F0 (3i + 4j), where F0 is a positive constant. (a) Determine the components Bx By, and Bz or at least as many of the three components as is
Suppose the electric field between the plates P and P' in Fig is 1.88 X 104 V/m and the magnetic field in both regions is 0.701 T. If the source contains the three isotopes of krypton, 82 Kr, 84 Kr, and 86Kr, and the ions are singly charged, find the distance between the lines formed by the three
Mass Spectrograph A mass spectrograph is used to measure the masses of ions, or to separate ions of different masses (see Section 27.5). In one design for such an instrument, ions with mass m and charge q are accelerated through a potential difference V. They then enter a uniform magnetic field
A straight piece of conducting wire with mass M and length L is placed on a frictionless incline tilted at an angle θ from the horizontal (Fig). There is a uniform, vertical magnetic field B at all points (produced by an arrangement of magnets not shown in the figure). To keep the wire from
A 3.00-N metal bar, 1.50 m long and having a resistance of 10.0 Ω, rests horizontally on conducting wires connecting it to the circuit shown in Fig. The bar is in a uniform, horizontal, 1.60-T magnetic field and is not attached to the wires in the circuit. What is the acceleration of the bar
Two positive ions having the same charge q but different masses m1 and m2 are accelerated horizontally from rest through a potential difference V. They then enter a region where there is a uniform magnetic field B normal to the plane of the trajectory.(a) Show that if the beam entered the magnetic
A plastic circular loop of radius R and a positive charge q is distributed uniformly around the circumference of the loop. The loop is then rotated around its central axis, perpendicular to the plane of the loop, with angular speed w. If the loop is in a region where there is a uniform magnetic
Determining Diet One method for determining the amount of com in early Native American diets is the stable isotope ratio analysis (SIRA) technique. As com photosynthesizes, it concentrates the isotope carbon-l3. Where as most other plants concentrate carbon-12. Over reliance on com consumption can
An Electromagnetic Rail Gun A conducting bar with mass m and length L slides over horizontal rails that are connected to a voltage source. The voltage source maintains a constant current I in the rails and bar, and a constant, uniform, vertical magnetic field B fills the region between the rails
A long wire carrying a 6.00-A current reverses direction by means of two right-angle bends, as shown in Fig. The part of the wire where the bend occurs is in a magnetic field of 0.666 T confined to the circular region of diameter 75 cm, as shown. Find the magnitude and direction of the net force
A wire 25.0 cm long lies along the z-axis and carries a current of 9.00 A in the +z-direction. The magnetic field is uniform and bas components Bx = -0.242 T, By = -0.985 T, and Bz = -0.336 T. (a) Find the components of the magnetic force on the wire. (b) What is the magnitude of the net magnetic
The rectangular loop of Wire shown in fig. bas a mass of 0.15 g per centimetre of length and is pivoted about side ab on a frictionless axis. The current in the wire is 8.2 A in the direction shown. Find the magnitude and direction of the magnetic field parallel to the y-axis that will cause the
The rectangular loop shown in Fig. is pivoted about the y-axis and carries a current of 15.0 A in the direction indicated.(a) If the loop is in a uniform magnetic field with magnitude 0.48 T in the + x direction, find the magnitude and direction of the torque required to hold the loop in the
A thin, uniform rod with negligible mass and length 0.200 m is attached to the floor by a frictionless hinge at point P (Fig). A horizontal spring with force constant k = 4.80 N/m connects the other end of the rod to a vertical wall. The rod is in a uniform magnetic field B = 0.340 T directed into
The triangular loop of wire shown in Fig. carries a current I = 5.00 A in the direction shown. The loop is in a uniform magnetic field that bas magnitude B = 3.00 T and the same direction as the current in side PQ of the loop.(a) Find the force exerted by the magnetic field on each side of the
A Voice Coil It was shown in Section 27.7 that the net force on a current loop in a uniform magnetic field is zero. The magnetic force on the voice coil of a loudspeaker (see Fig) is nonzero because the magnetic field at the coil is not uniform. A voice coil in a loudspeaker bas 50 turns of wire
Paleoclimate. Climatologists can determine the past temperature of the earth by comparing the ratio of the isotope oxygen-18 to the isotope oxygen-16 in air trapped in ancient ice sheets, such as those in Greenland. In one method for separating these isotopes, a sample containing both of them is
Force on a Current Loop in a Nonuniform Magnetic Field, It was shown in Section 21.7 that the net force on a cur rent loop in a uniform magnetic field is zero. But what if B is not uniform Figure shows a square loop of wire that lies in the xy-plane. The loop has corners at (0, 0), (0, L), (L, 0),
Torque on a Current Loop in a Nonuniform Magnetic Field. In Section 27.7 the expression for the torque on a current loop was derived assuming that the magnetic field B was uniform. But what if B is not uniform? Figure shows a square loop of wire that lies in the xy-plane. The loop has comers at (0,
An insulated wire with mass m = 5.40 X 10-5 kg is bent into the shape of an inverted U such that the horizontal part has a length I = 15.0 cm. The bent ends of the wire are partially immersed in two pools of mercury, with 2.5 cm of each end below the mercury's surface. The entire structure is in a
Derivation of Eq. (27.26) for a Circular Current Loop A wire ring lies in the xy-plane with its center at the origin. The ring carries a counter clockwise current I (Fig). A uniform magnetic field B is in the. + x-direction, B = Bxi (The result is easily extended to B in an arbitrary direction.)(a)
A circular loop of wire with area A lies in the xy-plane. As viewed along the z-axis looking in the - z-direction toward the origin, a current I is circulating clockwise around the loop. The torque produced by an external magnetic field B is given by T= D (4i - 3j), where D is a positive constant,
Quark Model of the Neutron The neutron is a particle with zero charge. Nonetheless, it has a nonzero magnetic moment with z component 9.66 X 10-27 A. m2. This can be explained by the internal structure of the neutron. A substantial body of evidence indicates that a neutron is composed of three
Using Gauss's Law for Magnetism In a certain region of space, the magnetic field B is not uniform. The magnetic field has both a z component and a component that points radially away from or toward the z-axis. The z-component is given by Bz (z) = βz, where β is a positive constant. The
A circular ring with area 4.45 cm2 is carrying a current of 12.5 A the ring is free to rotate about a diameter. The ring, initially at rest, is immersed in a region of uniform magnetic field given by B = (1.15 X 10-2 T) (12i + 3j - 4k). The ring is positioned initially such that its rnagne1ic
A particle with charge 2.15µC and mass 3.20 X 10-11 kg is initially travelling in the +y-direc1ion with a speed U0 = 1.45 X 105 m/s. It then enters a region containing a uniform magnetic field that is directed into and perpendicular to, the page in Fig. The magnitude of the field is 0.420 T.
The Electromagnetic Pump Magnetic forces acting on conducting fluids provide a convenient means of pumping these fluids. For example, this method can be used to pump blood without the damage to the cells that can be caused by a mechanical pump. A horizontal tube with rectangular cross section
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin shown in Fig. There is a uniform electric field E in the +y-direction and a uniform magnetic field B directed out of the page. It is shown in more advanced books that the path is a cycloid whose radius of
(See Problem)(a) What Figure is the potential of point a with respect to point b in when switch S is open?(b) Which point, a or b, is at the higher potential?(c) What is the 1inaI potential of point b with respect to ground when switch S is closed? (d) How much does the charge on each capacitor
A Multirange Ammeter The resistance of the moving coil of the galvanometer G in Fig. is 48.0 Ω, and the galvanometer deflects full scale with a current of 0.0200 A. When the meter is connected to the circuit being measured, one connection is made to the post marked +and the other to the post
A Multirange Voltmeter Figure shows the internal wiring of a €œthree-scale€ voltmeter whose binding posts are marked +, 3.00 v, 15.0 V, and 150 V, When the meter is connected to the circuit being measured, one connection is made to the post marked + and the other to the post
Point a in Fig is maintained at a constant potential of 400 V. above ground. (See Problem)(a) What is the reading of a voltmeter with the proper range and with resistance 5.00 X 104 Ω when connected between point b and ground?(b) What is the reading of a voltmeter with resistance 5.00 X 1O6
A 150-V voltmeter has a resistance of 30,000 Ω. When connected in series with a large resistance R across a 110-V line, the meter reads 68 V. Find the resistance R.
The Wheatstone Bridge The circuit shown in Fig called a Wheatstone bridge. is used to determine !he value of an unknown resistor X by comparison with three resistors M, N, and P whose resistances can be varied. For each setting, the resistance of each resistor is precisely known. With switches K1
A certain galvanometer has a resistance of 65.0 Ω and deflects full scale with a current of 1.50 mA in its coil. This is to be replaced with a second galvanometer that has a resistance of 38.0 Ω and deflects full scale with a current of 3.60 µA in its coil. Devise a circuit incorporating
A 224- Ω resistor and a 589-Ω resistor are connected in series across a 90.0-V line. (a) What is the voltage across each resistor? (b) A voltmeter connected across the 224- Ω resistor reads 23.8 V. find the voltmeter resistance. (c) Find the reading of the same voltmeter if it
A .2.36-µ.F capacitor that is initially uncharged is connected in series with a 4.26- Ω resistor and an emf source with E = 120 V and negligible internal resistance. (a) Just after the connection is made, what are (i) the rate at which electrical energy is being dissipated in the resistor;
A capacitor that is initially uncharged is connected in series with a resistor and an emf source with E = 110 V and negligible internal resistance. Just after the circuit is completed, the current through the resistor is 6.5 X 10-5 A. The time constant for the circuit is 6.2 s. What are the
A resistor with R = 850 Ω is connected to the plates of a charged capacitor with capacitance C = 4.62 µF. Just before the connection is made, the charge on the capacitor is 8.10 mC. (a) What is the energy initially stored in the capacitor? (b) What is the electrical power dissipated in
Strictly speaking, Eq. (26.16) implies that an infinite amount of time is required to discharge a capacitor completely. Yet for practical purposes, a capacitor may be considered to be fully discharged after a finite length of time. To be specific, consider a capacitor with capacitance C connected
An R-C circuit has a time constant RC. (a) If the circuit is discharging, how long will it take for its stored energy to be reduced to 1/e of its initial value? (b) If it is charging, how long will it take for the stored energy to reach 1/e of its maximum value?
The current in a charging capacitor is given by Eq. (26.13). (a) The instantaneous power supplied by the battery is Ei. Integrate this to find the total energy supplied by the battery. (b) The instantaneous power dissipated in the resistor is i2R. Integrate this to find the total energy dissipated
(a) Using Eq. (26.17) for the current in a discharging capacitor, derive an expression for the instantaneous power P = i2R dissipated in the resistor. (b) Integrate the expression for P to find the total energy dissipated in the resistor, and show that this is equal to the total energy initially
According to the theorem of superposition, the response (current) in a circuit is proportional to the stimulus (voltage) that causes it. This is true even if there are multiple sources in a circuit. This theorem can be used to analyze a circuit without resorting to Kirchhoff's rules by considering
A Capacitor Burglar Alarm The capacitance of a capacitor can be affected by dielectric material that, although not inside the capacitor, is near enough to the capacitor to be polarized by the fringing electric field that exists near a charged capacitor. This effect is usually of the order of
An Infinite Network As shown in Fig. a network of resistors of resistances R. and R2 extends to infinity toward the right. Prove that the total resistance RT of the infinite network is equal to
Suppose a resistor R lies along each edge of a cube (12 resistors in all) with connections at the corners. Find the equivalent resistance between two diagonally opposite corners of the cube (points a and b in Fig).
Attenuator Chains and Axons The infinite network of resistors shown in Fig. is known as an attenuator chain, since this chain of resistors causes the potential difference between the upper and lower wires to decrease, or attenuate, along the length of the chain.(a) Show that if the potential
Explain what is meant by the term “a neutral atom.’’ Explain what “a negatively charged atom’’ means.
A charged comb often attracts small bits of dry paper that then fly away when they touch the comb. Explain.
Sparks are often seen or heard on a dry day when fabrics are removed from a clothes dryer in dim light. Explain.
Hospital personnel must wear special conducting shoes while working around oxygen in an operating room. Why? Contrast with what might happen if people wore rubber soled shoes.
Explain from an atomic viewpoint why charge is usually transferred by electrons.
A light, uncharged metallic sphere suspended from a thread is attracted to a charged rubber rod. After it touches the rod, the sphere is repelled by the rod. Explain.
A foreign student who grew up in a tropical country but is studying in the United States may have had no experience with static electricity sparks or shocks until he or she first experiences an American winter. Explain.
Explain the similarities and differences between Newton’s law of universal gravitation and Coulomb’s law.
A balloon is negatively charged by rubbing and then clings to a wall. Does this mean that the wall is positively charged? Why does the balloon eventually fall?
A light strip of aluminum foil is draped over a horizontal wooden pencil. When a rod carrying a positive charge is brought close to the foil, the two parts of the foil stand apart. Why? What kind of charge is on the foil?
When defining the electric field, why is it necessary to specify that the magnitude of the test charge be very small?
How could you experimentally distinguish an electric field from a gravitational field?
A large metallic sphere insulated from ground is charged with an electrostatic generator while a student standing on an insulating stool holds the sphere. Why is it safe to do this? Why would it not be safe for another person to touch the sphere after it had been charged?
Is it possible for an electric field to exist in empty space? Explain. Consider point A in Figure 23.23(a). Does charge exist at this point? Does a force exist at this point? Does a field exist at this point?
When is it valid to approximate a charge distribution by a point charge?
Explain why electric field lines never cross. Suggestion: Begin by explaining why the electric field at a particular point must have only one direction.
Figures 23.14 and 23.15 show three electric field vectors at the same point with a little extrapolation, Figure 23.21 would show many electric field lines at the same point. Is it really true that “no two field lines can cross’’? Are the diagrams drawn correctly? Explain your answers.
A free electron and a free proton are released in identical electric fields. Compare the electric forces on the two particles. Compare their accelerations.
Explain what happens to the magnitude of the electric field created by a point charge as r approaches zero.
An object with negative charge is placed in a region of space where the electric field is directed vertically upward. What is the direction of the electric force exerted on this charge?
A charge 4q is at a distance r from a charge "q. Compare the number of electric field lines leaving the charge 4q with the number entering the charge "q. Where do the extra lines beginning on 4q end?
Consider two equal point charges separated by some distance d. At what point (other than 4) would a third test charge experience no net force?
Explain the differences between linear, surface, and volume charge densities, and give examples of when each would be used.
If the electron in Figure 23.26 is projected into the electric field with an arbitrary velocity vi (at an arbitrary angle to E), will its trajectory still be parabolic? Explain.
Would life be different if the electron were positively charged and the proton were negatively charged? Does the choice of signs have any bearing on physical and chemical interactions? Explain.
Why should a ground wire be connected to the metal support rod for a television antenna?
Suppose someone proposes the idea that people are bound to the Earth by electric forces rather than by gravity. How could you prove this idea is wrong?
Consider two electric dipoles in empty space. Each dipole has zero net charge. Does an electric force exist between the dipoles—that is, can two objects with zero net charge exert electric forces on each other? If so, is the force one of attraction or of repulsion?
The Sun is lower in the sky during the winter months than it is in the summer. How does this change the flux of sunlight hitting a given area on the surface of the Earth? How does this affect the weather?
If the electric field in a region of space is zero, can you conclude that no electric charges are in that region? Explain.
If more electric field lines leave a Gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?
A uniform electric field exists in a region of space in which there are no charges. What can you conclude about the net electric flux through a Gaussian surface placed in this region of space?
If the total charge inside a closed surface is known but the distribution of the charge is unspecified, can you use Gauss’s law to find the electric field? Explain.

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