Figure 21.27 shows two parallel, straight wires that are

A proton in a particle accelerator has a speed of 5.0 106 m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and whose direction makes an angle of  30.0 with respect to the protons velocity (see Figure 21.7c). Find the magnitude and direction of (a) the magnetic force on the proton and (b) the acceleration of the proton. (c) What would be the force and acceleration if the particle were an electron instead of a proton?

Suppose that you accidentally use your left hand, instead of your right hand, to determine the direction of the magnetic force that acts on a positive charge moving in a magnetic field. Do you get the correct answer? (a) Yes, because either hand can be used (b) No, because the direction you get will be perpendicular to the correct direction (c) No, because the direction you get will be opposite to the correct direction

Two particles, having the same charge but different velocities, are moving in a constant magnetic field (see the drawing, where the velocity vectors are drawn to scale). Which particle, if either, experiences the greater magnetic force? (a) Particle 1 experiences the greater force, because it is moving perpendicular to the magnetic field. (b) Particle 2 experiences the greater force, because it has the greater speed. (c) Particle 2 experiences the greater force, because a component of its velocity is parallel to the magnetic field. (d) Both particles experience the same magnetic force, because the component of each velocity that is perpendicular to the magnetic field is the same.

A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant. (a) If it is known that the external magnetic field is zero everywhere in this region, can you conclude that the external electric field is also zero? (b) If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field is also zero?

A velocity selector is a device for measuring the velocity of a charged particle. The device operates by applying electric and magnetic forces to the particle in such a way that these forces balance. Figure 21.10a shows a particle with a positive charge q and a velocity that is perpendicular to a constant magnetic field* . Figure 21.10b illustrates a velocity selector, which is a cylindrical tube that is located within the magnetic field. Inside the tube there is a parallel plate capacitor that produces an electric field (not shown) perpendicular to the magnetic field. The charged particle enters the left end of the tube, moving perpendicular to the magnetic field. If the strengths of and are adjusted properly, the electric and magnetic forces acting on the particle will cancel each other. With no net force acting on the particle, the velocity remains unchanged, according to Newtons first law. As a result, the particle moves in a straight line at a constant speed and exits at the right end of the tube. The magnitude of the velocity that is selected can be determined from a knowledge of the strengths of the electric and magnetic fields. Particles with velocities different from the one selected are deflected and do not exit at the right end of the tube. How should the electric field be directed so that the force it applies to the particle can balance the magnetic force produced by ? The electric field should be directed: (a) in the same direction as the magnetic field; (b) in a direction opposite to that of the magnetic field; (c) from the upper plate of the parallel plate capacitor toward the lower plate; (d) from the lower plate of the parallel plate capacitor toward the upper plate.

A proton is released from rest at point A, which is located next to the positive plate of a parallel plate capacitor (see Figure 21.12). The proton then accelerates toward the negative plate, leaving the capacitor at point B through a small hole in the plate. The electric potential of the positive plate is 2100 V greater than that of the negative plate, so VA VB  2100 V. Once outside the capacitor, the proton travels at a constant velocity until it enters a region of constant magnetic field of magnitude 0.10 T. The velocity is perpendicular to the magnetic field, which is directed out of the page in Figure 21.12. Find (a) the speed vB of the proton when it leaves the negative plate of the capacitor, and (b) the radius r of the circular path on which the proton moves in the magnetic field.

Figure 21.13a shows the bubble-chamber tracks resulting from an event that begins at point A. At this point a gamma ray (emitted by certain radioactive substances), traveling in from the left, spontaneously transforms into two charged particles. There is no track from the gamma ray itself. These particles move away from point A, producing the two spiral tracks. A third charged particle is knocked out of a hydrogen atom and moves forward, producing the long track with the slight upward curvature. Each of the three particles has the same mass and carries a charge of the same magnitude. A uniform magnetic field is directed out of the paper toward you. What is the sign ( or ) of the charge carried by each particle?

Suppose that the positive charge in Figure 21.9a were launched from the negative plate toward the positive plate, in a direction opposite to the electric field . A sufficiently strong electric field would prevent the charge from striking the positive plate. Suppose that the positive charge in Figure 21.9b were launched from the south pole toward the north pole, in a direction opposite to the magnetic field . Would a sufficiently strong magnetic field prevent the charge from reaching the north pole? (a) Yes (b) No, because a magnetic field cannot exert a force on a charged particle that is moving antiparallel to the field (c) No, because the magnetic force would cause the charge to move faster as it moved toward the north pole

Review Conceptual Example 4 and Concept Simulation 21.1 at www.wiley.com/college/ cutnell as background for this question. Three particles move through a constant magnetic field and follow the paths shown in the drawing. Determine whether each particle is positively () charged, negatively ( ) charged, or neutral.

Suppose that the three particles in Figure 21.13a have identical charge magnitudes and masses. Which particle has the greatest speed? Refer to Conceptual Example 4 as needed

A positive charge moves along a circular path under the influence of a magnetic field. The magnetic field is perpendicular to the plane of the circle, as in Figure 21.11. If the velocity of the particle is reversed at some point along the path, will the particle retrace its path? (a) Yes (b) No, because it will move around a different circle in a counterclockwise direction

Refer to Figure 21.11. Assume that the particle in the picture is a proton. If an electron is projected at point 1 with the same velocity , it will not follow exactly the same path as the proton, unless the magnetic field is adjusted in the following manner: the magnitude of the magnetic field must be ___________, and the direction of the magnetic field must be ___________. (a) the same, reversed (b) increased, the same (c) reduced, reversed

The drawing shows a top view of four interconnected chambers. A negative charge is fired into chamber 1. By turning on separate magnetic fields in each chamber, the charge can be made to exit from chamber 4, as shown. How should the magnetic field in each chamber be directed: out of the page or into the page?

The drawing shows a particle carrying a positive charge q at the coordinate origin, as well as a target located in the third quadrant. A uniform magnetic field is directed perpendicularly into the plane of the paper. The charge can be projected in the plane of the paper only, along the positive or negative x or y axis. There are four possible directions (x, x, y, y) for the initial velocity of the particle. The particle can be made to hit the target for only two of the four directions. Which two directions are they? (a) y, y (b) y, x (c) x, y (d)

The voice coil of a speaker has a diameter of d  0.025 m, contains 55 turns of wire, and is placed in a 0.10-T magnetic field. The current in the voice coil is 2.0 A. (a) Determine the magnetic force that acts on the coil and cone. (b) The voice coil and cone have a combined mass of 0.020 kg. Find their acceleration.

Refer to Figure 21.16. (a) What happens to the direction of the magnetic force if the current is reversed? (b) What happens to the direction of the force if both the current and the magnetic poles are reversed?

The same current-carrying wire is placed in the same magnetic field in four different orientations (see the drawing). Rank the orientations according to the magnitude of the magnetic force exerted on the wire, largest to smallest.

A coil of wire has an area of 2.0 104 m2 , consists of 100 loops or turns, and contains a current of 0.045 A. The coil is placed in a uniform magnetic field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil. (b) Find the maximum torque that the magnetic field can exert on the coil.

Figure 21.26 shows a very long, straight wire carrying a current of 3.0 A. A particle has a charge of 6.5  106 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force exerted on the charged particle by the current in the wire.

Figure 21.27 shows two parallel, straight wires that are very long. The wires are separated by a distance of 0.065 m and carry currents of I1 15 A and I2 7.0 A. Find the magnitude and direction of the force that the magnetic field of wire 1 applies to a 1.5-m section of wire 2 when the currents have (a) opposite and (b) the same directions. Ex

Figure 21.28 shows a very long, straight wire carrying a current I1 and a rectangular coil carrying a current I2. The wire and the coil lie in the same plane, with the wire parallel to the long sides of the rectangle. The coil is (a) attracted to the wire, (b) repelled from the wire, (c) neither attracted to nor repelled from the wire.

A long, straight wire carries a current of I1  8.0 A. As Figure 21.30a illustrates, a circular loop of wire lies immediately to the right of the straight wire. The loop has a radius of R  0.030 m and carries a current of I2  2.0 A. Assuming that the thickness of each wire is negligible, find the magnitude and direction of the net magnetic field at the center C of the loop.

The drawing shows a conducting wire wound into a helical shape. The helix acts like a spring and expands back toward its original shape after the coils are squeezed together and released. The bottom end of the wire just barely touches the mercury (a good electrical conductor) in the cup. After the switch is closed, current in the circuit causes the light bulb to glow. Does the bulb (a) repeatedly turn on and off like a turn signal on a car, (b) glow continually, or (c

For each electromagnet at the left in the drawing, will it be attracted to or repelled from the permanent magnet immediately to its right?

For each electromagnet at the left in the drawing, will it be attracted to or repelled from the electromagnet immediately to its right?

Refer to Figure 21.5. If the earths magnetism is assumed to originate from a large circular loop of current within the earth, then the plane of the current loop must be oriented ___________ to the earths magnetic axis, and the direction of the current around the loop (when looking down on the loop from the north magnetic pole) is __________. (a) parallel, clockwise (b) parallel, counterclockwise (c) perpendicular, clockwise (d) perpendicular, counterclockwise

The drawing shows an end-on view of three parallel wires that are perpendicular to the plane of the paper. In two of the wires the current is directed into the paper, while in the remaining wire the current is directed out of the paper. The two outermost wires are held rigidly in place. Which way will the middle wire move? (a) To the left (b) To the right (c) It will not move at all.

In Figure 21.27, assume that the current I1 is larger than the current I2. In parts a and b, decide whether there are places at which the total magnetic field is zero. State whether these places are located to the left of both wires, between the wires, or to the right of both wires.

Each of the four drawings shows the same three concentric loops of wire. The currents in the loops have the same magnitude I and have the directions shown. Rank the magnitude of the net magnetic field produced at the center of each of the four drawings, largest to smallest.

There are four wires viewed end-on in the drawing. They are long, straight, and perpendicular to the plane of the paper. Their cross sections lie at the corners of a square. The magnitude of the current in each wire is the same. What must be the direction of the current in each wire (into or out of the page), so that when any single current is turned off, the total magnetic field at P (the center of the square) is directed toward a corner of the square?

Use Ampres law to obtain the magnetic field produced by the current in an infinitely long, straight wire.

In a TV commercial that advertises a soda pop, a strong electromagnet picks up a delivery truck carrying cans of the soft drink. The picture switches to the interior of the truck, where cans are seen to fly upward and stick to the roof just beneath the electromagnet. Are these cans made entirely of aluminum?

Suppose that you have two bars. Bar 1 is a permanent magnet and bar 2 is not a magnet, but is made from a ferromagnetic material like iron. A third bar (bar 3), which is known to be a permanent magnet, is brought close to one end of bar 1 and then to one end of bar 2. Which one of the following statements is true? (a) Bars 1 and 3 will either be attracted to or repelled from each other, while bars 2 and 3 will always be repelled from each other. (b) Bars 1 and 3 will either be attracted to or repelled from each other, while bars 2 and 3 will always be attracted to each other. (c) Bars 1 and 3 will always be repelled from each other, while bars 2 and 3 will either be attracted to or repelled from each other. (d) Bars 1 and 3 will always be attracted to each other, while bars 2 and 3 will either be attracted to or repelled from each other

Figure 21.43 shows a particle that carries a charge of q0  2.80 10 6 C. It is moving along the y axis at a speed of  4.80 106 m/s. A magnetic field of magnitude 3.35 10 5 T is directed along the z axis, and an electric field of magnitude 123 N/C points along the x axis. Determine the magnitude and direction of the net force that acts on the particle.

What is the net force?

How do you determine the direction of the magnetic force acting on the negative ch

How do you determine the direction of the electric force acting on the negative charge?

Does the fact that the charge is moving affect the values of the magnetic and electric forces

A 125-turn rectangular coil of wire is hung from one arm of a balance, as Figure 21.44 shows. With the magnetic field turned off, an object of mass M is added to the pan on the other arm to balance the weight of the coil. When a constant 0.200-T magnetic field is turned on and there is a current of 8.50 A in the coil, how much additional mass m must be added to regain the balance?

In a balanced, or equilibrium, condition the device has no angular acceleration. What does this imply about the net torque acting on the device?

What is a torque?

In calculating the torques acting on an object in equilibrium, where do you locate the axis of rotation?

At a location near the equator, the earths magnetic field is horizontal and points north. An electron is moving vertically upward from the ground. What is the direction of the magnetic force that acts on the electron? (a) North (b) East (c) South (d) West (e) The magnetic force is zero.

The drawing shows four situations in which a positively charged particle is moving with a velocity through a magnetic field . In each case, the magnetic field is directed out of the page toward you, and the velocity is directed to the right. In only one of these drawings is the magnetic force physically reasonable. Which drawing is it? (a) 1 (b) 2 (c) 3 (d)

Three particles are moving perpendicular to a uniform magnetic field and travel on circular paths (see the drawing). The particles have the same mass and speed. List the particles in order of their charge magnitude, largest to smallest. (a) 3, 2, 1 (b) 3, 1, 2 (c) 2, 3, 1 (d) 1, 3, 2 (e) 1,

The drawing shows the circular paths of an electron and a proton. These particles have the same charge magnitudes, but the proton is more massive. They travel at the same speed in a uniform magnetic field , which is directed into the page everywhere. Which particle follows the larger circle, and does it travel clockwise or counterclockwise?

Four views of a horseshoe magnet and a current-carrying wire are shown in the drawing. The wire is perpendicular to the page, and the current is directed out of the page toward you. In which one or more of these situations does the magnetic force on the current point due north? (a) 1 and 2 (b) 3 and 4 (c) 2 (d) 3 (e)

A square, current-carrying loop is placed in a uniform magnetic field with the plane of the loop parallel to the magnetic field (see the drawing). The dashed line is the axis of rotation. The magnetic field exerts _______. (a) a net force and a net torque on the loop (b) a net force, but not a net torque, on the loop (c) a net torque, but not a net force, on the loop (d) neither a net force nor a net torque on the loop

The drawing shows four situations in which two very long wires are carrying the same current, although the directions of the currents may be different. The point P in the drawings is equidistant from each wire. Which one (or more) of these situations gives rise to a zero net magnetic field at P? (a) 2 and 4 (b) Only 1 (c) Only 2 (d) 2 and 3 (e) 3 and 4

Three long, straight wires are carrying currents that have the same magnitude. In C the current is opposite to the current in A and B. The wires are equally spaced. Each wire experiences a net force due to the other two wires. Which wire experiences a net force with the greatest magnitude? (a) A (b) B (c) C (d) All three wires experience a net force that has the same magnitude.

In New England, the horizontal component of the earths magnetic field has a magnitude of 1.6 10 5 T. An electron is shot vertically straight up from the ground with a speed of 2.1 106 m/s. What is the magnitude of the acceleration caused by the magnetic force? Ignore the gravitational force acting on the electron.

(a) A proton, traveling with a velocity of 4.5 106 m/s due east, experiences a magnetic force that has a maximum magnitude of 8.0 10 14 N and a direction of due south. What are the magnitude and direction of the magnetic field causing the force? (b) Repeat part (a) assuming the proton is replaced by an electron

At a certain location, the horizontal component of the earths magnetic field is 2.5 10 5 T, due north. A proton moves eastward with just the right speed for the magnetic force on it to balance its weight. Find the speed of the proton.

A charge of 8.3 C is traveling at a speed of 7.4 106 m/s in a region of space where there is a magnetic field. The angle between the velocity of the charge and the field is 52. A force of magnitude 5.4 10 3 N acts on the charge. What is the magnitude of the magnetic field?

When a charged particle moves at an angle of 25 with respect to a magnetic field, it experiences a magnetic force of magnitude F. At what angle (less than 90) with respect to this field will this particle, moving at the same speed, experience a magnetic force of magnitude 2F? P

A particle that has an 8.2 C charge moves with a velocity of magnitude 5.0 105 m/s along the x axis. It experiences no magnetic force, although there is a magnetic field present. The maximum possible magnetic force that the charge could experience has a magnitude of 0.48 N. Find the magnitude and direction of the magnetic field. Note that there are two possible answers for the direction of the field.

A magnetic field has a magnitude of 1.2 10 3 T, and an electric field has a magnitude of 4.6 103 N/C. Both fields point in the same direction. A positive 1.8 C charge moves at a speed of 3.1 106 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net force that acts on the charge.

Two charged particles move in the same direction with respect to the same magnetic field. Particle 1 travels three times faster than particle 2. However, each particle experiences a magnetic force of the same magnitude. Find the ratio q1/q2 of the magnitudes of the charges. *

The drawing shows a parallel plate capacitor that is moving with a speed of 32 m/s through a 3.6-T magnetic field. The velocity is perpendicular to the magnetic field. The electric field within the capacitor has a value of 170 N/C, and each plate has an area of 7.5 10 4 m2 . What is the magnetic force (magnitude and direction) exerted on the positive plate of the capacitor?

One component of a magnetic field has a magnitude of 0.048 T and points along the x axis, while the other component has a magnitude of 0.065 T and points along the y axis. A particle carrying a charge of 2.0 10 5 C is moving along the z axis at a speed of 4.2 103 m/s. (a) Find the magnitude of the net magnetic force that acts on the particle. (b) Determine the angle that the net force makes with respect to the x axis.

The electrons in the beam of a television tube have a kinetic energy of 2.40 10 15 J. Initially, the electrons move horizontally from west to east. The vertical component of the earths magnetic field points down, toward the surface of the earth, and has a magnitude of 2.00 10 5 T. (a) In what direction are the electrons deflected by this field component? (b) What is the acceleration of an electron in part (a)?

An ionized helium atom has a mass of 6.6 10 27 kg and a speed of 4.4 105 m/s. It moves perpendicular to a 0.75-T magnetic field on a circular path that has a 0.012-m radius. Determine whether the charge of the ionized atom is e or 2e.

In the operating room, anesthesiologists use mass spectrometers to monitor the respiratory gases of patients undergoing surgery. One gas that is often monitored is the anesthetic isoflurane (molecular mass  3.06 10 25 kg). In a spectrometer, a singly ionized molecule of isoflurane (charge  e) moves at a speed of 7.2 103 m/s on a circular path that has a radius of 0.10 m. What is the magnitude of the magnetic field that the spectrometer uses?

A charged particle with a charge-to-mass ratio of q/m  5.7 108 C/kg travels on a circular path that is perpendicular to a magnetic field whose magnitude is 0.72 T. How much time does it take for the particle to complete one revolution? v

A charged particle enters a uniform magnetic field and follows the circular path shown in the drawing. (a) Is the particle positively or negatively charged? Why? (b) The particles speed is 140 m/s, the magnitude of the magnetic field is 0.48 T, and the radius of the path is 960 m. Determine the mass of the particle, given that its charge has a magnitude of 8.2 10 4 C

A proton is projected perpendicularly into a magnetic field that has a magnitude of 0.50 T. The field is then adjusted so that an electron will follow a circular path of the same radius when it is projected perpendicularly into the field with the same velocity that the proton had. What is the magnitude of the field used for the electron?

When beryllium-7 ions (m  11.65 10 27 kg) pass through a mass spectrometer, a uniform magnetic field of 0.283 T curves their path directly to the center of the detector (see Figure 21.14). For the same accelerating potential difference, what magnetic field should be used to send beryllium-10 ions (m  16.63 10 27 kg) to the same location in the detector? Both types of ions are singly ionized (q  e).

Suppose that an ion source in a mass spectrometer produces doubly ionized gold ions (Au2), each with a mass of 3.27 10 25 kg. The ions are accelerated from rest through a potential difference of 1.00 kV. Then, a 0.500-T magnetic field causes the ions to follow a circular path. Determine the radius of the path.

An -particle has a charge of 2e and a mass of 6.64 10 27 kg. It is accelerated from rest through a potential difference that has a value of 1.20 106 V and then enters a uniform magnetic field whose magnitude is 2.20 T. The -particle moves perpendicular to the magnetic field at all times. What is (a) the speed of the -particle, (b) the magnitude of the magnetic force on it, and (c) the radius of its circular path?

Particle 1 and particle 2 have masses of m1  2.3 10 8 kg and m2  5.9 10 8 kg, but they carry the same charge q. The two particles accelerate from rest through the same electric potential difference V and enter the same magnetic field, which has a magnitude B. The particles travel perpendicular to the magnetic field on circular paths. The radius of the circular path for particle 1 is r1  12 cm. What is the radius (in cm) of the circular path for particle 2?

Two of the isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 10 27 kg and 21.59 10 27 kg, respectively. These two isotopes are singly ionized (e), each given a speed of 6.667 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.8500 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle

The ion source in a mass spectrometer produces both singly and doubly ionized species, X and X2. The difference in mass between these species is too small to be detected. Both species are accelerated through the same electric potential difference, and both experience the same magnetic field, which causes them to move on circular paths. The radius of the path for the species X is r1, while the radius for species X2 is r2. Find the ratio r1/r2 of the radii.

A proton with a speed of 3.5 106 m/s is shot into a region between two plates that are separated by a distance of 0.23 m. As the drawing shows, a magnetic field exists between the plates, and it is perpendicular to the velocity of the proton. What must be the magnitude of the magnetic field so the proton just misses colliding with the opposite plate?

Review Conceptual Example 2 as an aid in understanding this problem. A velocity selector has an electric field of magnitude 2470 N/C, directed vertically upward, and a horizontal magnetic field that is directed south. Charged particles, traveling east at a speed of 6.50 103 m/s, enter the velocity selector and are able to pass completely through without being deflected. When a different particle with an electric charge of 4.00 10 12 C enters the velocity selector traveling east, the net force (due to the electric and magnetic fields) acting on it is 1.90 10 9 N, pointing directly upward. What is the speed of this particle?

A particle of mass 6.0 10 8 kg and charge 7.2 C is traveling due east. It enters perpendicularly a magnetic field whose magnitude is 3.0 T. After entering the field, the particle completes one-half of a circle and exits the field traveling due west. How much time does the particle spend traveling in the magnetic field?

Conceptual Example 4 provides background pertinent to this problem. An electron has a kinetic energy of 2.0 10 17 J. It moves on a circular path that is perpendicular to a uniform magnetic field of magnitude 5.3 10 5 T. Determine the radius of the path.

A positively charged particle of mass 7.2 10 8 kg is traveling due east with a speed of 85 m/s and enters a 0.31-T uniform magnetic field. The particle moves through one-quarter of a circle in a time of 2.2 10 3 s, at which time it leaves the field heading due south. All during the motion the particle moves perpendicular to the magnetic field. (a) What is the magnitude of the magnetic force acting on the particle? (b) Determine the magnitude of its charge.

Review Conceptual Example 2 as background for this problem. A charged particle moves through a velocity selector at a constant speed in a straight line. The electric field of the velocity selector is 3.80 103 N/C, while the magnetic field is 0.360 T. When the electric field is turned off, the charged particle travels on a circular path whose radius is 4.30 cm. Find the charge-to-mass ratio of the particle

Refer to Check Your Understanding Question 10 before starting this problem. Suppose that the target discussed there is located at the coordinates x  0.10 m and y  0.10 m. In addition, suppose that the particle is a proton and the magnetic field has a magnitude of 0.010 T. The speed at which the particle is projected is the same for either of the two paths leading to the target. Find the speed.

At New York City, the earths magnetic field has a vertical component of 5.2 10 5 T that points downward (perpendicular to the ground) and a horizontal component of 1.8 10 5 T that points toward geographic north (parallel to the ground). What are the magnitude and direction of the magnetic force on a 6.0-m long, straight wire that carries a current of 28 A perpendicularly into the ground?

A 45-m length of wire is stretched horizontally between two vertical posts. The wire carries a current of 75 A and experiences a magnetic force of 0.15 N. Find the magnitude of the earths magnetic field at the location of the wire, assuming the field makes an angle of 60.0 with respect to the wire.

A straight wire in a magnetic field experiences a force of 0.030 N when the current in the wire is 2.7 A. The current in the wire is changed, and the wire experiences a force of 0.047 N as a result. What is the new current?

A horizontal wire of length 0.53 m, carrying a current of 7.5 A, is placed in a uniform external magnetic field. When the wire is horizontal, it experiences no magnetic force. When the wire is tilted upward at an angle of 19, it experiences a magnetic force of 4.4 10 3 N. Determine the magnitude of the external magnetic field.

The drawing shows a wire composed of three segments, AB, BC, and CD. There is a current of in the wire. There is also a magnetic field that is the same everywhere and points in the direction of the axis. The lengths of the wire segments are and Find the magnitude of the force that acts on each segment.

A wire carries a current of 0.66 A. This wire makes an angle of 58 with respect to a magnetic field of magnitude 4.7 10 5 T. The wire experiences a magnetic force of magnitude 7.1 10 5 N. What is the length of the wire?

Two insulated wires, each 2.40 m long, are taped together to form a two-wire unit that is 2.40 m long. One wire carries a current of 7.00 A; the other carries a smaller current I in the opposite direction. The two-wire unit is placed at an angle of 65.0 relative to a magnetic field whose magnitude is 0.360 T. The magnitude of the net magnetic force experienced by the two-wire unit is 3.13 N. What is the current I? 3

A loop of wire has the shape of a right triangle (see the drawing) and carries a current of I  4.70 A. A uniform magnetic field is directed parallel to side AB and has a magnitude of 1.80 T. (a) Find the magnitude and direction of the magnetic force exerted on each side of the triangle. (b) Determine the magnitude of the net force exerted on the triangle.

A copper rod of length 0.85 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k  75 N/m. A magnetic field with a strength of 0.16 T is oriented perpendicular to the surface of the table. (a) What must be the direction of the current in the copper rod that causes the springs to stretch? (b) If the current is 12 A, by how much does each spring stretch?

The drawing shows a thin, uniform rod that has a length of 0.45 m and a mass of 0.094 kg. This rod lies in the plane of the paper and is attached to the floor by a hinge at point P. A uniform magnetic field of 0.36 T is directed perpendicularly into the plane of the paper. There is a current I  4.1 A in the rod, which does not rotate clockwise or counterclockwise. Find the angle . (Hint: The magnetic force may be taken to act at the center of gravity.)

A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.20 m and a mass of 0.080 kg. A uniform magnetic field of magnitude 0.070 T is directed from the ceiling to the floor. When a current of I  42 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle  with respect to the vertical, as the drawing shows. Find (a) the angle  and (b) the tension in each of the two strings

The two conducting rails in the drawing are tilted upward so they each make an angle of 30.0 with respect to the ground. The vertical magnetic field has a magnitude of 0.050 T. The 0.20-kg aluminum rod (length  1.6 m) slides without friction down the rails at a constant velocity. How much current flows through the rod?

Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic field as in Figure 21.19. Coil 1 has a radius of 5.0 cm and rotates in a 0.18-T field. Coil 2 rotates in a 0.42-T field. Each coil experiences the same maximum torque. What is the radius (in cm) of coil 2?

The 1200-turn coil in a dc motor has an area per turn of 1.1 10 2 m2 . The design for the motor specifies that the magnitude of the maximum torque is 5.8 N m when the coil is placed in a 0.20-T magnetic field. What is the current in the coil?

Two circular coils of current-carrying wire have the same magnetic moment. The first coil has a radius of 0.088 m, has 140 turns, and carries a current of 4.2 A. The second coil has 170 turns and carries a current of 9.5 A. What is the radius of the second coil?

The coil of wire in the drawing is a right triangle and is free to rotate about an axis that is attached along side AC. The current in the loop is I  4.70 A, and the magnetic field (parallel to the plane of the loop and side AB) is B  1.80 T. (a) What is the magnetic moment of the loop, and (b) what is the magnitude of the net torque exerted on the loop by the magnetic field?

Two pieces of the same wire have the same length. From one piece, a square coil containing a single loop is made. From the other, a circular coil containing a single loop is made. The coils carry different currents. When placed in the same magnetic field with the same orientation, they experience the same torque. What is the ratio Isquare/Icircle of the current in the square coil to the current in the circular coil?

You have a wire of length from which to make the square coil of a dc motor. The current in the coil is and the magnetic field of the motor has a magnitude of Find the maximum torque exerted on the coil when the wire is used to make a single-turn square coil and a two-turn square coil.

The rectangular loop in the drawing consists of 75 turns and carries a current of I  4.4 A. A 1.8-T magnetic field is directed along the y axis. The loop is free to rotate about the z axis. (a) Determine the magnitude of the net torque exerted on the loop and (b) state whether the 35 angle will increase or decrease.

A square coil and a rectangular coil are each made from the same length of wire. Each contains a single turn. The long sides of the rectangle are twice as long as the short sides. Find the ratio square/rectangle of the maximum torques that these coils experience in the same magnetic field when they contain the same current.

The coil in Figure 21.19a contains 410 turns and has an area per turn of 3.1 10 3 m2 . The magnetic field is 0.23 T, and the current in the coil is 0.26 A. A brake shoe is pressed perpendicularly against the shaft to keep the coil from turning. The coefficient of static friction between the shaft and the brake shoe is 0.76. The radius of the shaft is 0.012 m. What is the magnitude of the minimum normal force that the brake shoe exerts on the shaft?

In the model of the hydrogen atom created by Niels Bohr, the electron moves around the proton at a speed of 2.2 106 m/s in a circle of radius 5.3 10 11 m. Considering the orbiting electron to be a small current loop, determine the magnetic moment associated with this motion. (Hint: The electron travels around the circle in a time equal to the period of the motion.)

Suppose in Figure 21.27a that I1  I2  25 A and that the separation between the wires is 0.016 m. By applying an external magnetic field (created by a source other than the wires) it is possible to cancel the mutual repulsion of the wires. This external field must point along the vertical direction. (a) Does the external field point up or down? Explain. (b) What is the magnitude of the external field?

A long solenoid has a length of 0.65 m and contains 1400 turns of wire. There is a current of 4.7 A in the wire. What is the magnitude of the magnetic field within the solenoid?

The magnetic field produced by the solenoid in a magnetic resonance imaging (MRI) system designed for measurements on whole human bodies has a field strength of 7.0 T, and the current in the solenoid is 2.0 102 A. What is the number of turns per meter of length of the solenoid? Note that the solenoid used to produce the magnetic field in this type of system has a length that is not very long compared to its diameter. Because of this and other design considerations, your answer will be only an approximation.

A long solenoid has 1400 turns per meter of length, and it carries a current of 3.5 A. A small circular coil of wire is placed inside the solenoid with the normal to the coil oriented at an angle of 90.0 with respect to the axis of the solenoid. The coil consists of 50 turns, has an area of 1.2 10 3 m2 , and carries a current of 0.50 A. Find the torque exerted on the coil.

Two circular loops of wire, each containing a single turn, have the same radius of 4.0 cm and a common center. The planes of the loops are perpendicular. Each carries a current of 1.7 A. What is the magnitude of the net magnetic field at the common center?

Multiple-Concept Example 8 reviews the concepts from this chapter that are pertinent here. Two rigid rods are oriented parallel to each other and to the ground. The rods carry the same current in the same direction. The length of each rod is 0.85 m, and the mass of each is 0.073 kg. One rod is held in place above the ground, while the other floats beneath it at a distance of 8.2 10 3 m. Determine the current in the rods.

Two long, straight wires are separated by 0.120 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the points labeled (a) A and (b)

A long, straight wire carrying a current of 305 A is placed in a uniform magnetic field that has a magnitude of 7.00 10 3 T. The wire is perpendicular to the field. Find a point in space where the net magnetic field is zero. Locate this point by specifying its perpendicular distance from the wire.

Two circular coils are concentric and lie in the same plane. The inner coil contains 140 turns of wire, has a radius of 0.015 m, and carries a current of 7.2 A. The outer coil contains 180 turns and has a radius of 0.023 m. What must be the magnitude and direction (relative to the current in the inner coil) of the current in the outer coil, so that the net magnetic field at the common center of the two coils is zero?

A small compass is held horizontally, the center of its needle a distance of 0.280 m directly north of a long wire that is perpendicular to the earths surface. When there is no current in the wire, the compass needle points due north, which is the direction of the horizontal component of the earths magnetic field at that location. This component is parallel to the earths surface. When the current in the wire is 25.0 A, the needle points 23.0 east of north. (a) Does the current in the wire flow toward or away from the earths surface? (b) What is the magnitude of the horizontal component of the earths magnetic field at the location of the compass?

Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1 carries four times the current that wire 2 carries. On a line drawn perpendicular to both wires, locate the spot (relative to wire 1) where the net magnetic field is zero. Assume that wire 1 lies to the left of wire 2 and note that there are three regions to consider on this line: to the left of wire 1, between wire 1 and wire 2, and to the right of wire 2.

The drawing shows two perpendicular, long, straight wires, both of which lie in the plane of the paper. The current in each of the wires is I  5.6 A. Find the magnitudes of the net magnetic fields at points A and B.

A piece of copper wire has a resistance per unit length of 5.90 10 3 /m. The wire is wound into a thin, flat coil of many turns that has a radius of 0.140 m. The ends of the wire are connected to a 12.0-V battery. Find the magnetic field strength at the center of the coil.

The drawing shows two wires that both carry the same current of I  85.0 A and are oriented perpendicular to the plane of the paper. The current in one wire is directed out of the paper, while the current in the other is directed into the paper. Find the magnitude and direction of the net magnetic field at point P.

The drawing shows two long, straight wires that are suspended from a ceiling. The mass per unit length of each wire is 0.050 kg/m. Each of the four strings suspending the wires has a length of 1.2 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 15. What is the current in each wire?

Suppose that a uniform magnetic field is everywhere perpendicular to this page. The field points directly upward toward you. A circular path is drawn on the page. Use Ampres law to show that there can be no net current passing through the circular surface.

The wire in Figure 21.38 carries a current of 12 A. Suppose that a second long, straight wire is placed right next to this wire. The current in the second wire is 28 A. Use Ampres law to find the magnitude of the magnetic field at a distance of r  0.72 m from the wires when the currents are (a) in the same direction and (b) in opposite directions.

A very long, hollow cylinder is formed by rolling up a thin sheet of copper. Electric charges flow along the copper sheet parallel to the axis of the cylinder. The arrangement is, in effect, a hollow tube of current I. Use Ampres law to show that the magnetic field (a) is outside the cylinder at a distance r from the axis and (b) is zero at any point within the hollow interior of the cylinder. (Hint: For closed paths, use circles perpendicular to and centered on the axis of the cylinder.)

A long, cylindrical conductor is solid throughout and has a radius R. Electric charges flow parallel to the axis of the cylinder and pass uniformly through the entire cross section. The arrangement is, in effect, a solid tube of current I0. The current per unit crosssectional area (i.e., the current density) is Use Ampres law I0/(R2). to show that the magnetic field inside the conductor at a distance r from the axis is (Hint: For a closed path, use a circle of radius r perpendicular to and centered on the axis. Note that the current through any surface is the area of the surface times the current density.)

In a certain region, the earths magnetic field has a magnitude of 5.4 10 5 T and is directed north at an angle of 58 below the horizontal. An electrically charged bullet is fired north and 11 above the horizontal, with a speed of 670 m/s. The magnetic force on the bullet is 2.8 10 10 N, directed due east. Determine the bullets electric charge, including its algebraic sign ( or ). 7

An electron is moving through a magnetic field whose magnitude is 8.70 10 4 T. The electron experiences only a magnetic force and has an acceleration of magnitude 3.50 1014 m/s2 . At a certain instant, it has a speed of 6.80 106 m/s. Determine the angle (less than 90) between the electrons velocity and the magnetic field. 7

A very long, straight wire carries a current of 0.12 A. This wire is tangent to a single-turn, circular wire loop that also carries a current. The directions of the currents are such that the net magnetic field at the center of the loop is zero. Both wires are insulated and have diameters that can be neglected. How much current is there in the loop?

The maximum torque experienced by a coil in a 0.75-T magnetic field is 8.4 10 4 N m. The coil is circular and consists of only one turn. The current in the coil is 3.7 A. What is the length of the wire from which the coil is made?

Multiple-Concept Example 7 discusses how problems like this one can be solved. A 6.00 C charge is moving with a speed of 7.50 104 m/s parallel to a very long, straight wire. The wire is 5.00 cm from the charge and carries a current of 67.0 A in a direction opposite to that of the moving charge. Find the magnitude and direction of the force on the charge.

The x, y, and z components of a magnetic field are Bx  0.10 T, By  0.15 T, and Bz  0.17 T. A 25-cm wire is oriented along the z axis and carries a current of 4.3 A. What is the magnitude of the magnetic force that acts on this wire?

In a lightning bolt, a large amount of charge flows during a time of 1.8 10 3 s. Assume that the bolt can be treated as a long, straight line of current. At a perpendicular distance of 27 m from the bolt, a magnetic field of 8.0 10 5 T is measured. How much charge has flowed during the lightning bolt? Ignore the earths magnetic field.

A charge is moving perpendicular to a magnetic field and experiences a force whose magnitude is 2.7 10 3 N. If this same charge were to move at the same speed and the angle between its velocity and the same magnetic field were 38, what would be the magnitude of the magnetic force that the charge would experience?

The drawing shows four insulated wires overlapping one another, forming a square with 0.050-m sides. All four wires are much longer than the sides of the square. The net magnetic field at the center of the square is Calculate the current I.

A particle of charge 7.3 C and mass 3.8 10 8 kg is traveling perpendicular to a 1.6-T magnetic field, as the drawing shows. The speed of the particle is 44 m/s. (a) What is the value of the angle , such that the particles subsequent path will intersect the y axis at the greatest possible value of y? (b) Determine this value of y.

A particle has a charge of and is located at the coordinate origin. As the drawing shows, an electric field of exists along the axis. A magnetic field also exists, and its x and y components are and Calculate the force (magnitude and direction) exerted on the particle by each of the three fields when it is (a) stationary, (b) moving along the axis at a speed of 375 m/s, and (c) moving along the axis at a speed of 375 m/s.

Two parallel rods are each 0.50 m in length. They are attached at their centers to either end of a spring (spring constant  150 N/m) that is initially neither stretched nor compressed. When 950 A of current is in each rod in the same direction, the spring is observed to be compressed by 2.0 cm. Treat the rods as long, straight wires and find the separation between them when the current is present.

A solenoid is formed by winding 25.0 m of insulated silver wire around a hollow cylinder. The turns are wound as closely as possible without overlapping, and the insulating coat on the wire is negligibly thin. When the solenoid is connected to an ideal (no internal resistance) 3.00-V battery, the magnitude of the magnetic field inside the solenoid is found to be 6.48 10 3 T. Determine the radius of the wire. (Hint: Because the solenoid is closely coiled, the number of turns per unit length depends on the radius of the wire.)

A charge of 4.0 10 6 C is placed on a small conducting sphere that is located at the end of a thin insulating rod whose length is 0.20 m. The rod rotates with an angular speed of  150 rad/s about an axis that passes perpendicularly through its other end. Find the magnetic moment of the rotating charge. (Hint: The charge travels around a circle in a time equal to the period of the motion.)

A wire has a length of 7.00 10 2 m and is used to make a circular coil of one turn. There is a current of 4.30 A in the wire. In the presence of a 2.50-T magnetic field, what is the maximum torque that this coil can experience?