An insulated copper wire is wrapped around an iron nail.

Problem 1CQ The north pole of a bar magnet is brought near the center of another bar magnet, as shown in Figure. Will the force between the magnets be attractive, repulsive, or zero? Why? FIGURE

Problem 1P What currents are needed to generate the magnetic field strengths of Table 24.1 at a point 1.0 cm from a long, straight wire?

Problem 2CQ You have a bar magnet whose poles are not marked. How can you find which pole is north and which is south by using only a piece of string?

Problem 2P At what distances from a very thin, straight wire carrying a 10 A current would the magnetic field strengths of Table 24.1 be generated?

Problem 3CQ When you are in the southern hemisphere, does a compass point north or south?

Problem 3P The magnetic field at the center of a 1.0-cm-diameter loop is 2.5 mT. a. What is the current in the loop? b. A long, straight wire carries the same current you found in part a. At what distance from the wire is the magnetic field 2.5 mT?

Problem 4CQ Green turtles use the earth’s magnetic field to navigate. They seem to use the field to tell them their latitude—how far north or south of the equator they are. Explain how knowing the direction of the earth’s field could give this information.

Problem 4P For a particular scientific experiment, it is important to be completely isolated from any magnetic field, including the earth’s field. A 1.00-m-diameter current loop with 200 turns of wire is set up so that the field at the center is exactly equal to the earth’s field in magnitude but opposite in direction. What is the current in the current loop?

Problem 5CQ A horseshoe magnet consists of a bar magnet bent into a U-shape, as shown in Figure. Sketch the magnetic field lines for a horseshoe magnet. FIGURE

Problem 5P What are the magnetic field strength and direction at points 1, 2, and 3 in Figure P24.6?

Problem 6CQ What is the current direction in the wire of Figure Q24.7? Explain.

Problem 6P Although the evidence is weak, there has been concern in recent years over possible health effects from the magnetic fields generated by transmission lines. A typical high-voltage transmission line is 20 m off the ground and carries a current of 200 A. Estimate the magnetic field strength on the ground underneath such a line. What percentage of the earth’s magnetic field does this represent?

Problem 7CQ What is the current direction in the wire of Figure Q24.8?

Problem 7P Some consumer groups urge pregnant women not to use electric blankets, in case there is a health risk from the magnetic fields from the approximately 1 A current in the heater wires. a. Estimate, stating any assumptions you make, the magnetic field strength a fetus might experience. What percentage of the earth’s magnetic field is this? b. It is becoming standard practice to make electric blankets with minimal external magnetic field. Each wire is paired with another wire that carries current in the opposite direction. How does this reduce the external magnetic field?

Problem 8CQ Since the wires in the walls of your house carry current, you might expect that you could use a compass to detect the positions of the wires. In fact, a compass will experience no deflection when brought near a current-carrying wire because the current is AC (meaning “alternating current”—the current switches direction 120 times each second). Explain why a compass doesn’t react to an AC current.

Problem 8P A long wire carrying a 5.0 A current perpendicular to the xy-plane intersects the x-axis at x = -2.0 cm. A second, parallel wire carrying a 3.0 A current intersects the x-axis at x = +2.0 cm. At what point or points on the x-axis is the magnetic field zero if (a) the two currents are in the same direction and (b) the two currents are in opposite directions?

Problem 9CQ Two wires carry currents in opposite directions, as in Figure. The field is 2.0 mT at a point below the lower wire. What are the strength and direction of the field at point 1 (midway between the two wires) and at point 2 (the same distance above the upper wire as the 2.0 m T point is below the lower wire)? FIGURE

Problem 9P The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below 9 K. However, the superconductivity is destroyed if the magnetic field at the surface of the wire of the metal reaches or exceeds 0.10 T. What is the maximum current in a straight, 3.0-mm-diameter superconducting niobium wire? Hint: You can assume that all the current flows in the center of the wire.

Problem 10CQ As shown in Figure Q24.10, a uniform magnetic field points upward, in the plane of the paper. A long wire perpendicular to the paper initially carries no current. When a current is turned on in the wire in the direction shown, the magnetic field at point 1 is found to be zero. Draw the magnetic field vector at point 2 when the current is on.

Problem 10P The small currents in axons corresponding to nerve impulses produce measurable magnetic fields. A typical axon carries a peak current of 0.040 mA. What is the strength of the field at a distance of 1.0 ?m?

Two long wires carry currents in the directions shown in Figure Q24.11. One wire is 10 cm above the other. In which direction is the magnetic field at a point halfway between them?

Problem11P If an electron is not moving, is it possible to set it in motion using a magnetic field? Explain.

Problem 12P Two concentric current loops lie in the same plane. The smaller loop has a radius of 3.0 cm and a current of 12 A. The bigger loop has a current of 20 A. The magnetic field at the center of the loops is found to be zero. What is the radius of the bigger loop?

Problem 13CQ Figure shows a solenoid as seen in cross section. Compasses are placed at points 1 and 2. In which direction will each compass point when there is a large current in the direction shown? Explain. FIGURE

Problem 13P The magnetic field of the brain has been measured to be approximately . Although the currents that cause this field are quite complicated, we can get a rough estimate of their size by modeling them as a single circular current loop 16 cm (the width of a typical head) in diameter. What current is needed to produce such a field at the center of the loop?

Problem 14CQ One long solenoid is placed inside another solenoid with twice the diameter but the same length. Each solenoid carries the same current but in opposite directions, as shown in Figure. If they also have the same number of turns, in which direction does the magnetic field in the center point? Explain. FIGURE

Problem 14P A researcher would like to perform an experiment in zero magnetic field, which means that the field of the earth must be canceled. Suppose the experiment is done inside a solenoid of diameter 1.0 m, length 4.0 m, with a total of 5000 turns of wire. The solenoid is oriented to produce a field that opposes and exactly cancels the 52 ?T local value of the earth’s field. What current is needed in the solenoid’s wire?

Problem 15CQ A researcher would like to perform an experiment in zero magnetic field, which means that the field of the earth must be canceled. Suppose the experiment is done inside a solenoid of diameter 1.0 m, length 4.0 m, with a total of 5000 turns of wire. The solenoid is oriented to produce a field that opposes and exactly cancels the 52 ?T local value of the earth’s field. What current is needed in the solenoid’s wire?

Problem 15P What is the magnetic field at the center of the loop in Figure P24.17?

Problem 16CQ What is the initial direction of deflection for the charge particles entering the magnatic fields shown in Figure? (a) (b) FIGURE

Problem 16P Experimental tests have shown that hammerhead sharks can detect magnetic fields. In one such test, 100 turns of wire were wrapped around a 7.0-m-diameter cylindrical shark tank. A magnetic field was created inside the tank when this coil of wire carried a current of 1.5 A. Sharks trained by getting a food reward when the field was present would later unambiguously respond when the field was turned on. a. What was the magnetic field strength in the center of the tank due to the current in the coil? b. Is the strength of the coil’s field at the center of the tank larger or smaller than that of the earth?

Problem 17CQ Determine the magnetic field direction that causes the charged particles shown in Figure Q24.17 to experience the indicated magnetic forces.

Problem 17P We have seen that the heart produces a magnetic field that can be used to diagnose problems with the heart. The magnetic field of the heart is a dipole field produced by a loop current in the outer layers of the heart. Suppose that the field at the center of the heart is and that the heart has a diameter of approximately 12 cm. What current circulates around the heart to produce this field?

Problem 18CQ Determine the magnetic field direction that causes the charged particles shown in Figure Q24.18 to experience the indicated magnetic forces.

Problem 18P You have a 1.0-m-long copper wire. You want to make an N-turn current loop that generates a 1.0 mT magnetic field at the center when the current is 1.0 A. You must use the entire wire. What will be the diameter of your coil?

Problem 19CQ An electron is moving near a long, current-carrying wire, as shown in Figure Q24.19. What is the direction of the magnetic force on the electron?

Problem 20CQ Two positive charges are moving in a uniform magnetic field with velocities as shown in Figure Q24.20. The magnetic force on each charge is also shown. In which direction does the magnetic field point?

Problem 20P A proton moves with a speed of in the directions shown in Figure P24.22. A 0.50 T magnetic field points in the positive x-direction. For each, what is the magnetic force on the proton? Give your answers as a magnitude and a direction.

Problem 21CQ An electron is moving in a circular orbit in the earth’s magnetic field directly above the north magnetic pole. Viewed from above, is the rotation clockwise or counterclockwise?

Problem 21P An electron moves with a speed of in the directions shown in Figure P24.23. A 0.50 T magnetic field points in the positive x-direction. For each, what is the magnetic force on the electron? Give your answers as a magnitude and a direction.

Problem 22CQ A proton moves in a region of uniform magnetic field, as shown in Figure Q24.23. The velocity at one instant is shown. Will the subsequent motion be a clockwise or counterclockwise orbit?

Problem 22P An electromagnetic flowmeter applies a magnetic field of 0.20 T to blood flowing through a coronary artery at a speed of 15 cm/s. What force is felt by a chlorine ion with a single negative charge?

Problem 23CQ The detector in a mass spectrometer records the number of ions measured at a fixed position as the field is varied. For a sample consisting of a single atomic species, two peaks were found where one was expected, as shown in Figure. The most likely explanation is that the atoms received different charges when ionized. If the two peaks correspond to ions with charges +eand +2e, which peak is which? Explain. FIGURE

Problem 23P The aurora is caused when electrons and protons, moving in the earth’s magnetic field of

Problem 24CQ A proton is moving near a long, current-carrying wire. When the proton is at the point shown in Figure Q24.24, in which direction is the force on it?

Problem 24P Problem 24.25 describes two particles that orbit the earth’s magnetic field lines. What is the frequency of the circular orbit for Reference: Problem 24.25: The aurora is caused when electrons and protons, moving in the earth’s magnetic field of

Problem 25 CQ A proton is moving near a long, current-carrying wire. When the proton is at the point shown in Figure Q24.25, in which direction is the force on it?

Problem 25P The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit in a magnetic field at a frequency of 2.4 GHz, and as they do so they emit 2.4 GHz electromagnetic waves. What is the strength of the magnetic field?

Problem 26CQ A long wire and a square loop lie in the plane of the paper. Both carry a current in the direction shown in Figure Q24.26. In which direction is the net force on the loop? Explain.

Problem 26P A mass spectrometer similar to the one in Figure 24.36 is designed to separate protein fragments. The fragments are ionized by the removal of a single electron, then they enter a 0.80 T uniform magnetic field at a speed of 2.3 × 105 m/s. If a fragment has a mass 85 times the mass of the proton, what will be the distance between the points where the ion enters and exits the magnetic field?

Problem 27CQ The computers that control MRI machines cannot have CRT monitors. Explain why this is so.

Problem 27P In a certain mass spectrometer, particles with a charge of +e are sent into the spectrometer with a velocity of 2.5 × 105 m/s. They are found to move in a circular path with a radius of 0.21 m. If the magnetic field of the spectrometer is 0.050 T, what kind of particles are these likely to be?

Problem 28CQ A Slinky is a child’s toy that is a long coil spring. Suppose you take a Slinky and let it hang down and stretch out so that the coils do not touch each other, as in Figure. Now you connect the Slinky to a power supply and pass a large DC current through it. Think about the current in the coils. Will the Slinky expand or contract? FIGURE

Problem 28P At t = 0 s, a proton is moving with a speed of 5.5 × 105 m/s at an angle of 30° from the x-axis, as shown in Figure. A uniform magnetic field of magnitude 1.50 T is pointing in the positive y-direction. What will be the y-coordinate of the proton 10 µs later? FIGURE

Problem 29CQ A solenoid carries a current that produces a field inside it. A wire carrying a current lies inside the solenoid, at the center, carrying a current along the solenoid’s axis. Is there a force on this wire due to the field of the solenoid? Explain.

Problem 29P Early black-and-white television sets used an electron beam to draw a picture on the screen. The electrons in the beam were accelerated by a voltage of 3.0 kV; the beam was then steered to different points on the screen by coils of wire that produced a magnetic field of up to 0.65 T. a. What is the speed of electrons in the beam? b. What acceleration do they experience due to the magnetic field, assuming that it is perpendicular to their path? What is this acceleration in units of g? c. If the electrons were to complete a full circular orbit, what would be the radius? d. A magnetic field can be used to redirect the beam, but the electrons are brought to high speed by an electric field. Why can’t we use a magnetic field for this task?

Problem 30CQ You want to make an electromagnet by wrapping wire around a nail. Should you use bare copper wire or wire coated with insulating plastic? Explain

Problem 30P What magnetic field strength and direction will levitate the 2.0 g wire in Figure P24.33?

Problem 31CQ The moon does not have a molten iron core like the earth, but the moon does have a small magnetic field. What might be the source of this field?

Problem 31P What is net force (magnitude and direction) on each wire in Figure P24.34?

Problem 32CQ Archaeologists can use instruments that measure small variations in magnetic field to locate buried walls made of fired brick, as shown in Figure Q24.28. When fired, the magnetic moments in the clay become randomly aligned; as the clay cools, the magnetic moments line up with the earth’s field and retain this alignment even if the bricks are subsequently moved. Explain how this leads to a measurable magnetic field variation over a buried wall.

Problem 32P The unit of current, the ampere, is defined in terms of the force between currents. If two 1.0-meter-long sections of very long wires a distance 1.0 m apart each carry a current of 1.0 A, what is the force between them? (If the force between two actual wires has this value, the current is defined to be exactly 1 A.)

Problem 33MCQ An unmagnetized metal sphere hangs by a thread. When the north pole of a bar magnet is brought near, the sphere is strongly attracted to the magnet, as shown in Figure Q24.29. Then the magnet is reversed and its south pole is brought near the sphere. How does the sphere respond? A. It is strongly attracted to the magnet. B. It is weakly attracted to the magnet. C. It does not respond. D. It is weakly repelled by the magnet. E. It is strongly repelled by the magnet.

Problem 33P A uniform 2.5 T magnetic field points to the right. A 3.0-m-long wire, carrying 15 A, is placed at an angle of 30° to the field, as shown in Figure P24.36. What is the force (magnitude and direction) on the wire?

Problem 34MCQ If a compass is placed above a current-carrying wire, as in Figure Q24.30, the needle will line up with the field of the wire. Which of the views shows the correct orientation of the needle for the noted current direction?

Problem 34P The four wires in Figure are tilted at 20° with respect to a uniform 0.35 T field. If each carries 4.5 A and is 0.35 m long, what is the force (direction and magnitude) on each? FIGURE

Problem 35MCQ Two wires carry equal and opposite currents, as shown in Figure Q24.31. At a point directly between the two wires, the field is A. Directed up, toward the top of the page. B. Directed down, toward the bottom of the page. C. Directed to the left. D. Directed to the right. E. Zero.

Problem 35P Magnetic information on hard drives is accessed by a read head that must move rapidly back and forth across the disk. The force to move the head is generally created with a voice coil actuator, a flat coil of fine wire that moves between the poles of a strong magnet, as in Figure P24.37. Assume that the coil is a square 1.0 cm on a side made of 200 turns of fine wire with total resistance 1.5 ?. The field between the poles of the magnet is 0.30 T; assume that the field does not extend beyond the edge of the magnet. The coil and the mount that it rides on have a total mass of 12 g. a. If a voltage of 5.0 V is applied to the coil, what is the current? b. If the current is clockwise viewed from above, what are the magnitude and direction of the net force on the coil? c. What is the magnitude of the acceleration of the coil?

Problem 36MCQ Figure Q24.32 shows four particles moving to the right as they enter a region of uniform magnetic field, directed into the paper as noted. All particles move at the same speed and have the same charge. Which particle has the largest mass?

Problem 36P A current loop in a motor has an area of . It carries a 240 mA current in a uniform field of 0.62 T. What is the magnitude of the maximum torque on the current loop?

Problem 37MCQ Four particles of identical charge and mass enter a region of uniform magnetic field and follow the trajectories shown in Figure Q24.33. Which particle has the highest velocity?

Problem 37P A square current loop 5.0 cm on each side carries a 500 mA current. The loop is in a 1.2 T uniform magnetic field. The axis of the loop, perpendicular to the plane of the loop, is 30° away from the field direction. What is the magnitude of the torque on the current loop?

Problem 38MCQ If all of the particles shown in Figure Q24.33 are electrons, what is the direction of the magnetic field that produced the indicated deflection? A. Up (toward the top of the page). B. Down (toward the bottom of the page). C. Out of the plane of the paper. D. Into the plane of the paper.

Problem 38P Figure shows two square current loops. The loops are far apart and do not interact with each other. a. Use force diagrams to show that both loops are in equilibrium, having a net force of zero and no torque. b. One of the loop positions is stable. That is, the forces will return it to equilibrium if it is rotated slightly. The other position is unstable, like an upside-down pendulum: If rotated slightly, it will not return to the position shown. Which is which? Explain. FIGURE

Problem 39MCQ If two compasses are brought near enough to each other, the magnetic fields of the compasses themselves will be larger than the field of the earth, and the needles will line up with each other. Which of the arrangements of two compasses shown in Figure Q24.35 is a possible stable arrangement?

Problem 39P The earth’s magnetic dipole moment of 8.0 × 1022 A · m2 is generated by currents within the molten iron of the earth’s outer core. (The inner core is solid iron.) As a simple model, consider the outer core to be a 3000-km-diameter current loop. What is the current in the current loop?

Problem 40P a. What is the magnitude of the torque on the circular current loop in Figure P24.41? b. What is the loop’s stable equilibrium position?

Problem 41P A computer diskette is a plastic disk with a ferromagnetic coating. A single magnetic domain can have its magnetic moment oriented to point either up or down, and these two orientations can be interpreted as a binary 0 (up) or 1 (down). Each 0 or 1 is called a bit of information. A diskette stores roughly 500,000 bytes of data on one side, and each byte contains eight bits. Estimate the width of a magnetic domain, and compare your answer to the typical domain size given in the text. List any assumptions you use in your estimate.

Problem 43GP In Figure, a compass sits 1.0 cm above a wire in a circuit containing a 1.0 F capacitor charged to 5.0 V, a 1.0 ? resistor, and an open switch. The compass is lined up with the earth’s magnetic field. The switch is then closed, so there is a current in the circuit, and the switch remains closed until the capacitor has completely discharged. a. At the position of the compass, what is the magnitude of the magnetic field due to the current in the wire right after the switch is closed? How does this compare with the magnitude of the field of the earth? b. Describe how the compass orientation changes right after the switch is closed, and how the compass orientation changes as time goes on. FIGURE

Problem 42P All ferromagnetic materials have a Curie temperature, a temperature above which they will cease to be magnetic. Explain in some detail why you might expect this to be so.

Problem 44GP The right edge of the circuit in Figure P24.44 extends into a 50 mT uniform magnetic field. What are the magnitude and direction of the net force on the circuit?

Problem 45GP The two 10-cm-long parallel wires in Figure P24.45 are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be ?

Problem The capacitor in Figure is charged to 50 V. The switch closes at t = 0 s. Draw a graph showing the magnetic field strength as a function of time at the position of the dot. On your graph indicate the maximum field strength and provide an appropriate numerical scale on the horizontal axis. FIGURE

Problem 47GP An electron travels with speed between the two parallel charged plates shown in Figure P24.46. The plates are separated by 1.0 cm and are charged by a 200 V battery. What magnetic field strength and direction will allow the electron to pass between the plates without being deflected?

Problem 48GP The two springs in Figure P24.47 each have a spring constant of 10 N/m. They are stretched by 1.0 cm when a current passes through the wire. How big is the current?

Problem 49GP A device called a railgun uses the magnetic force on currents to launch projectiles at very high speeds. An idealized model of a railgun is illustrated in Figure P24.48. A 1.2 V power supply is connected to two conducting rails. A segment of copper wire, in a region of uniform magnetic field, slides freely on the rails. The wire has a 0.85 m? resistance and a mass of 5.0 g. Ignore the resistance of the rails. When the power supply is switched on, a. What is the current? b. What are the magnitude and direction of the force on the wire? c. What will be the wire’s speed after it has slid a distance of 6.0 cm?

Problem 50GP An antiproton (which has the same properties as a proton except that its charge is ? e)is moving in the combined electric and magnetic fields of Figure. a. What are the magnitude and direction of the antiproton’s acceleration at this instant? b. What would be the magnitude and direction of the acceleration if v were reversed? FIGURE

Problem 51GP Typical blood velocities in the coronary arteries range from 10 to 30 cm/s. An electromagnetic flowmeter applies a magnetic field of 0.25 T to a coronary artery with a blood velocity of 15 cm/s. As we saw in Figure 24.36, this field exerts a force on ions in the blood, which will separate. The ions will separate until they make an electric field that exactly balances the magnetic force. This electric field produces a voltage that can be measured. a. What force is felt by a singly ionized (positive) sodium ion? b. Charges in the blood will separate until they produce an electric field that cancels this magnetic force. What will be the resulting electric field? c. What voltage will this electric field produce across an artery with a diameter of 3.0 mm?

Problem 52GP A power line consists of two wires, each carrying a current of 400 A in the same direction. The lines are perpendicular to the earth’s magnetic field and are separated by a distance of 5.0 m. Which is larger: the force of the earth’s magnetic field on each wire or the magnetic force between the wires?

Problem 53GP Bats are capable of navigating using the earth’s field—a plus for an animal that may fly great distances from its roost at night. If, while sleeping during the day, bats are exposed to a field of a similar magnitude but different direction than the earth’s field, they are more likely to lose their way during their next lengthy night flight. Suppose you are a researcher doing such an experiment in a location where the earth’s field is 50 ?T at a 60° angle below horizontal. You make a 50-cm-diameter, 100-turn coil around a roosting box; the sleeping bats are at the center of the coil. You wish to pass a current through the coil to produce a field that, when combined with the earth’s field, creates a net field with the same strength and dip angle (60° below horizontal) as the earth’s field but with a horizontal component that points south rather than north. What are the proper orientation of the coil and the

Problem 54GP At the equator, the earth’s field is essentially horizontal; near the north pole, it is nearly vertical. In between, the angle varies. As you move farther north, the dip angle, the angle of the earth’s field below horizontal, steadily increases. Green turtles seem to use this dip angle to determine their latitude. Suppose you are a researcher wanting to test this idea. You have gathered green turtle hatchlings from a beach where the magnetic field strength is 50 ?T and the dip angle is 56°. You then put the turtles in a 1.2-m-diameter circular tank and monitor the direction in which they swim as you vary the magnetic field in the tank. You change the field by passing a current through a 100-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth. What current should you pass through the coil, and in what direction, to produce a net field in the center of the tank that has a dip angle of 62°?

Problem 55GP Internal components of cathode-ray-tube televisions and computer monitors can become magnetized; the resulting magnetic field can deflect the electron beam and distort the colors on the screen. Demagnetization can be accomplished with a coil of wire whose current switches direction rapidly and gradually decreases in amplitude. Explain what effect this will have on the magnetic moments of the magnetic materials in the device, and how this might eliminate any magnetic ordering.

Problem 56GP A 1.0-m-long, 1.0-mm-diameter copper wire carries a current of 50.0 A to the east. Suppose we create a magnetic field that produces an upward force on the wire exactly equal in magnitude to the wire’s weight, causing the wire to “levitate.” What are the field’s direction and magnitude?

Problem 57GP An insulated copper wire is wrapped around an iron nail. The resulting coil of wire consists of 240 turns of wire that cover 1.8 cm of the nail, as shown in Figure P24.57. A current of 0.60 A passes through the wire. If the ferromagnetic properties of the nail increase the field by a factor of 100, what is the magnetic field strength inside the nail?

Problem 58GP Figure is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to “float” so as to form an equilateral triangle with the lower wires? FIGURE

Problem 60GP A mass spectrometer is designed to separate atoms of carbon to determine the fraction of different isotopes. (Isotopes of an element, as we will see in Chapter 30, have the same atomic number but different atomic mass, due to different numbers of neutrons.) There are three main isotopes of carbon, with the following atomic masses: Atomic masses 12C 1.99 × 10?26 kg 13C 2.16 × 10?26kg 4C 2.33 × 10?26 kg The atoms of carbon are singly ionized and enter a mass spectrometer with magnetic field strength B = 0.200 T at a speed of 1.50 × 105 m/s. The ions move along a semicircular path and exit through an exit slit. How far from the entrance will the beams of the different isotope ions end up?

Problem 59GP long, straight wire with a linear mass density of 50 g/m is suspended by threads, as shown in Figure P24.58. There is a uniform magnetic field pointing vertically downward. A 10 A current in the wire experiences a horizontal magnetic force that deflects it to an equilibrium angle of 10°. What is the strength of the magnetic field ?

Problem 61GP A solenoid is near a piece of iron, as shown in Figure P24.43. When a current is present in the solenoid, a magnetic field is created. This magnetic field will magnetize the iron, and there will be a net force between the solenoid and the iron. a. Make a sketch showing the direction of the magnetic field from the solenoid. On your sketch, label the induced north magnetic pole and the induced south magnetic pole in the iron. b. Will the force on the iron be attractive or repulsive? c. Suppose this force moves the iron. Which way will the iron move?

Problem 62PP The Velocity Selector In experiments where all the charged particles in a beam are required to have the same velocity (for example, when entering a mass spectrometer), scientists use a velocity selector. A velocity selector has a region of uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the motion of the charged particles. Both the electric and magnetic fields exert a force on the charged particles. If a particle has precisely the right velocity, the two forces exactly cancel and the particle is not deflected. Equating the forces due to the electric field and the magnetic field gives the following equation: A particle moving at this velocity will pass through the region of uniform fields with no deflection, as shown in Figure P24.59. For higher or lower velocities than this, the particles will feel a net force and will be deflected. A slit at the end of the region allows only the particles with the correct velocity to pass. Assuming the particle in Figure P24.59 is positively charged, what are the directions of the forces due to the electric field and to the magnetic field? A. The force due to the electric field is directed up (toward the top of the page); the force due to the magnetic field is directed down (toward the bottom of the page). B. The force due to the electric field is directed down (toward the bottom of the page); the force due to the magnetic field is directed up (toward the top of the page). C. The force due to the electric field is directed out of the plane of the paper; the force due to the magnetic field is directed into the plane of the paper. D. The force due to the electric field is directed into the plane of the paper; the force due to the magnetic field is directed out of the plane of the paper.

Problem 63PP The Velocity Selector In experiments where all the charged particles in a beam are required to have the same velocity (for example, when entering a mass spectrometer), scientists use a velocity selector. A velocity selector has a region of uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the motion of the charged particles. Both the electric and magnetic fields exert a force on the charged particles. If a particle has precisely the right velocity, the two forces exactly cancel and the particle is not deflected. Equating the forces due to the electric field and the magnetic field gives the following equation: A particle moving at this velocity will pass through the region of uniform fields with no deflection, as shown in Figure P24.59. For higher or lower velocities than this, the particles will feel a net force and will be deflected. A slit at the end of the region allows only the particles with the correct velocity to pass. How does the kinetic energy of the particle in Figure P24.59 change as it traverses the velocity selector? A. The kinetic energy increases. B. The kinetic energy does not change. C. The kinetic energy decreases.

Problem 64PP The Velocity Selector In experiments where all the charged particles in a beam are required to have the same velocity (for example, when entering a mass spectrometer), scientists use a velocity selector. A velocity selector has a region of uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the motion of the charged particles. Both the electric and magnetic fields exert a force on the charged particles. If a particle has precisely the right velocity, the two forces exactly cancel and the particle is not deflected. Equating the forces due to the electric field and the magnetic field gives the following equation: A particle moving at this velocity will pass through the region of uniform fields with no deflection, as shown in Figure P24.59. For higher or lower velocities than this, the particles will feel a net force and will be deflected. A slit at the end of the region allows only the particles with the correct velocity to pass. Suppose a particle with twice the velocity of the particle in Figure P24.59 enters the velocity selector. The path of this particle will curve A. Upward (toward the top of the page). B. Downward (toward the bottom of the page). C. Out of the plane of the paper. D. Into the plane of the paper.

Problem 65PP The Velocity Selector In experiments where all the charged particles in a beam are required to have the same velocity (for example, when entering a mass spectrometer), scientists use a velocity selector. A velocity selector has a region of uniform electric and magnetic fields that are perpendicular to each other and perpendicular to the motion of the charged particles. Both the electric and magnetic fields exert a force on the charged particles. If a particle has precisely the right velocity, the two forces exactly cancel and the particle is not deflected. Equating the forces due to the electric field and the magnetic field gives the following equation: A particle moving at this velocity will pass through the region of uniform fields with no deflection, as shown in Figure P24.59. For higher or lower velocities than this, the particles will feel a net force and will be deflected. A slit at the end of the region allows only the particles with the correct velocity to pass. Next, a particle with the same mass and velocity as the particle in Figure P24.59 enters the velocity selector. This particle has a charge of 2q—twice the charge of the particle in Figure P24.59. In this case, we can say that A. The force of the electric field on the particle is greater than the force of the magnetic field. B. The force of the magnetic field on the particle is greater than the force of the electric field. C. The forces of the electric and magnetic fields on the particle are still equal.

Problem 66PP Ocean Potentials The ocean is salty because it contains many dissolved ions. As these charged particles move with the water in strong ocean currents, they feel a force from the earth’s magnetic field. Positive and negative charges are separated until an electric field develops that balances this magnetic force. This field produces measurable potential differences that can be monitored by ocean researchers. The Gulf Stream moves northward off the east coast of the United States at a speed of up to 3.5 m/s. Assume that the current flows at this maximum speed and that the earth’s field is 50 ?T tipped 60° below horizontal. What is the direction of the magnetic force on a singly ionized negative chlorine ion moving in this ocean current? A. East B. West C. Up D. Down

Problem 67PP Ocean Potentials The ocean is salty because it contains many dissolved ions. As these charged particles move with the water in strong ocean currents, they feel a force from the earth’s magnetic field. Positive and negative charges are separated until an electric field develops that balances this magnetic force. This field produces measurable potential differences that can be monitored by ocean researchers. The Gulf Stream moves northward off the east coast of the United States at a speed of up to 3.5 m/s. Assume that the current flows at this maximum speed and that the earth’s field is 50 ?T tipped 60° below horizontal. What is the magnitude of the force on this ion?

Problem 68PP Ocean Potentials The ocean is salty because it contains many dissolved ions. As these charged particles move with the water in strong ocean currents, they feel a force from the earth’s magnetic field. Positive and negative charges are separated until an electric field develops that balances this magnetic force. This field produces measurable potential differences that can be monitored by ocean researchers. The Gulf Stream moves northward off the east coast of the United States at a speed of up to 3.5 m/s. Assume that the current flows at this maximum speed and that the earth’s field is 50 ?T tipped 60° below horizontal. What magnitude electric field is necessary to exactly balance this magnetic force?

Problem 69PP Ocean Potentials The ocean is salty because it contains many dissolved ions. As these charged particles move with the water in strong ocean currents, they feel a force from the earth’s magnetic field. Positive and negative charges are separated until an electric field develops that balances this magnetic force. This field produces measurable potential differences that can be monitored by ocean researchers. The Gulf Stream moves northward off the east coast of the United States at a speed of up to 3.5 m/s. Assume that the current flows at this maximum speed and that the earth’s field is 50 ?T tipped 60° below horizontal. The electric field produces a potential difference. If you place one electrode 10 m below the surface of the water, you will measure the greatest potential difference if you place the second electrode A. At the surface. B. At a depth of 20 m. C. At the same depth 10 m to the north. D. At the same depth 10 m to the east.