m A long, cylindrical conductor is solid throughout and

In New England, the horizontal component of the earths magnetic fi eld has a magnitude of 1.6 3 1025 T. An electron is shot vertically straight up from the ground with a speed of 2.1 3 106 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 3 106 m/s due east, experiences a magnetic force that has a maximum magnitude of 8.0 3 10214 N and a direction of due south. What are the magnitude and direction of the magnetic fi eld 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 fi eld is 2.5 3 1025 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 28.3 mC is traveling at a speed of 7.4 3 106 m/s in a region of space where there is a magnetic fi eld. The angle between the velocity of the charge and the fi eld is 528. A force of magnitude 5.4 3 1023 N acts on the charge. What is the magnitude of the magnetic fi eld?

When a charged particle moves at an angle of 258 with respect to a magnetic fi eld, it experiences a magnetic force of magnitude F. At what angle (less than 908) with respect to this fi eld will this particle, moving at the same speed, experience a magnetic force of magnitude 2F?

A particle that has an 8.2 mC charge moves with a velocity of magnitude 5.0 3 105 m/s along the 1x axis. It experiences no magnetic force, although there is a magnetic fi eld 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 fi eld. Note that there are two possible answers for the direction of the fi eld.

A magnetic fi eld has a magnitude of 1.2 3 1023 T, and an electric fi eld has a magnitude of 4.6 3 103 N/C. Both fi elds point in the same direction. A positive 1.8 mC charge moves at a speed of 3.1 3 106 m/s in a direction that is perpendicular to both fi elds. 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 fi eld. Particle 1 travels three times faster than particle 2. However, each particle experiences a magnetic force of the same magnitude. Find the ratio uq1u/uq2u 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 fi eld. The velocity v B is perpendicular to the magnetic fi eld. The electric fi eld within the capacitor has a value of 170 N/C, and each plate has an area of 7.5 3 1024 m2 . What is the magnetic force (magnitude and direction) exerted on the positive plate of the capacitor?

One component of a magnetic fi eld has a magnitude of 0.048 T and points along the 1x axis, while the other component has a magnitude of 0.065 T and points along the 2y axis. A particle carrying * * a charge of 12.0 3 1025 C is moving along the 1z axis at a speed of 4.2 3 103 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 1x axis.

The electrons in the beam of a television tube have a kinetic energy of 2.40 3 10215 J. Initially, the electrons move horizontally from west to east. The vertical component of the earths magnetic fi eld points down, toward the surface of the earth, and has a magnitude of 2.00 3 1025 T. (a) In what direction are the electrons defl ected by this fi eld component? (b) What is the acceleration of an electron in part (a)?

An ionized helium atom has a mass of 6.6 3 10227 kg and a speed of 4.4 3 105 m/s. It moves perpendicular to a 0.75-T magnetic fi eld on a circular path that has a 0.012-m radius. Determine whether the charge of the ionized atom is 1e or 12e.

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 isofl urane (molecular mass 5 3.06 3 10225 kg). In a spectrometer, a singly ionized molecule of isofl urane (charge 5 1e) moves at a speed of 7.2 3 103 m/s on a circular path that has a radius of 0.10 m. What is the magnitude of the magnetic fi eld that the spectrometer uses?

A charged particle with a charge-to-mass ratio of uqu/m 5 5.7 3 108 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?

A charged particle enters a uniform magnetic fi eld 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 fi eld 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 3 1024 C.

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

When beryllium-7 ions (m 5 11.65 3 10227 kg) pass through a mass spectrometer, a uniform magnetic fi eld of 0.283 T curves their path directly to the center of the detector (see Figure 21.14). For the same accelerating potential diff erence, what magnetic fi eld should be used to send beryllium-10 ions (m 5 16.63 3 10227 kg) to the same location in the detector? Both types of ions are singly ionized (q 5 1e).

Suppose that an ion source in a mass spectrometer produces doubly ionized gold ions (Au21), each with a mass of 3.27 3 10225 kg. The ions are accelerated from rest through a potential diff erence of 1.00 kV. Then, a 0.500-T magnetic fi eld causes the ions to follow a circular path. Determine the radius of the path.

An a-particle has a charge of 12e and a mass of 6.64 3 10227 kg. It is accelerated from rest through a potential diff erence that has a value of 1.20 3 106 V and then enters a uniform magnetic fi eld whose magnitude is 2.20 T. The a-particle moves perpendicular to the magnetic fi eld at all times. What is (a) the speed of the a-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 5 2.3 3 1028 kg and m2 5 5.9 3 1028 kg, but they carry the same charge q. The two particles accelerate from rest through the same electric potential diff erence V and enter the same magnetic fi eld, which has a magnitude B. The particles travel perpendicular to the magnetic fi eld on circular paths. The radius of the circular path for particle 1 is r1 5 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 3 10227 kg and 21.59 3 10227 kg, respectively. These two isotopes are singly ionized (1e), each given a speed of 6.667 3 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic fi eld 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, X1 and X21. The diff erence in mass between these species is too small to be detected. Both species are accelerated through the same electric potential diff erence, and both experience the same magnetic fi eld, which causes them to move on circular paths. The radius of the path for the species X1 is r1, while the radius for species X21 is r2. Find the ratio r1/r2 of the radii.

A proton with a speed of 3.5 3 106 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 fi eld exists between the plates, and it is perpendicular to the velocity of the proton. What must be the magnitude of the magnetic fi eld 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 fi eld of magnitude 2470 N/C, directed vertically upward, and a horizontal magnetic fi eld that is directed south. Charged particles, traveling east at a speed of 6.50 3 103 m/s, enter the velocity selector and are able to pass completely through without being defl ected. When a diff erent particle with an electric charge of 14.00 3 10212 C enters the velocity selector traveling east, the net force (due to the electric and magnetic fi elds) acting on it is 1.90 3 1029 N, pointing directly upward. What is the speed of this particle?

A particle of mass 6.0 3 1028 kg and charge 17.2 mC is traveling due east. It enters perpendicularly a magnetic fi eld whose magnitude is 3.0 T. After entering the fi eld, the particle completes one-half of a circle and exits the fi eld traveling due west. How much time does the particle spend traveling in the magnetic fi eld?

Conceptual Example 4 provides background pertinent to this problem. An electron has a kinetic energy of 2.0 3 10217 J. It moves on a circular path that is perpendicular to a uniform magnetic fi eld of magnitude 5.3 3 1025 T. Determine the radius of the path.

A positively charged particle of mass 7.2 3 1028 kg is traveling due east with a speed of 85 m/s and enters a 0.31-T uniform magnetic fi eld. The particle moves through one-quarter of a circle in a time of * * * * * * 2.2 3 1023 s, at which time it leaves the fi eld heading due south. All during the motion the particle moves perpendicular to the magnetic fi eld. (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 fi eld of the velocity selector is 3.80 3 103 N/C, while the magnetic fi eld is 0.360 T. When the electric fi eld 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 5 20.10 m and y 5 20.10 m. In addition, suppose that the particle is a proton and the magnetic fi eld 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 fi eld has a vertical component of 5.2 3 1025 T that points downward (perpendicular to the ground) and a horizontal component of 1.8 3 1025 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 fi eld at the location of the wire, assuming the fi eld makes an angle of 60.08 with respect to the wire.

A straight wire in a magnetic fi eld 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 fi eld. When the wire is horizontal, it experiences no magnetic force. When the wire is tilted upward at an angle of 198, it experiences a magnetic force of 4.4 3 1023 N. Determine the magnitude of the external magnetic fi eld.

The drawing shows a wire composed of three segments, AB, BC, and CD. There is a current of I 5 2.8 A in the wire. There is also a magnetic fi eld B B (magnitude 5 0.26 T) that is the same everywhere and points in the direction of the 1z axis. The lengths of the wire segments are LAB 5 1.1 m, LBC 5 0.55 m, and L CD 5 0.55 m. 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 588 with respect to a magnetic fi eld of magnitude 4.7 3 1025 T. The wire experiences a magnetic force of magnitude 7.1 3 1025 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 twowire unit is placed at an angle of 65.08 relative to a magnetic fi eld 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?

A loop of wire has the shape of a right triangle (see the drawing) and carries a current of I 5 4.70 A. A uniform magnetic fi eld 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 fi xed wire by an unstretched spring that has a spring constant of k 5 75 N/m. A magnetic fi eld 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 fl oor by a hinge at point P. A uniform magnetic fi eld of 0.36 T is directed perpendicularly into the plane of the paper. There is a current I 5 4.1 A in the rod, which does not rotate clockwise or counterclockwise. Find the angle u. (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 fi eld of magnitude 0.070 T is directed from the ceiling to the fl oor. When a current of I 5 42 A exists in the wire, the wire swings upward and, at equilibrium, makes an angle f with respect to the vertical, as the drawing shows. Find (a) the angle f 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 30.08 with respect to the ground. The vertical magnetic fi eld has a magnitude of 0.050 T. The 0.20-kg aluminum rod (length 5 1.6 m) slides without friction down the rails at a constant velocity. How much current fl ows through the rod?

Two coils have the same number of circular turns and carry the same current. Each rotates in a magnetic fi eld as in Figure 21.19. Coil 1 has a radius of 5.0 cm and rotates in a 0.18-T fi eld. Coil 2 rotates in a 0.42-T fi eld. 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 3 1022 m2 . The design for the motor specifi es that the magnitude of the maximum torque is 5.8 N ? m when the coil is placed in a 0.20-T magnetic fi eld. What is the current in the coil?

Two circular coils of current-carrying wire have the same magnetic moment. The fi rst 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?

A wire has a length of 7.00 3 1022 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 fi eld, what is the maximum torque that this coil can experience?

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 5 4.70 A, and the magnetic fi eld (parallel to the plane of the loop and side AB) is B 5 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 fi eld?

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 L 5 1.00 m from which to make the square coil of a dc motor. The current in the coil is I 5 1.7 A, and the magnetic fi eld of the motor has a magnitude of B 5 0.34 T. 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 5 4.4 A. A 1.8-T magnetic fi eld is directed along the 1y 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 358 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 tsquare/trectangle of the maximum torques that these coils experience in the same magnetic fi eld when they contain the same current.

The coil in Figure 21.19a contains 410 turns and has an area per turn of 3.1 3 1023 m2 . The magnetic fi eld 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 coeffi cient 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 3 106 m/s in a circle of radius 5.3 3 10211 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 the fi gure that I1 5 I2 5 25 A and that the separation between the wires is 0.016 m. By applying an external magnetic fi eld (created by a source other than the wires) it is possible to cancel the mutual repulsion of the wires. This external fi eld must point along the vertical direction. (a) Does the external fi eld point up or down? Explain. (b) What is the magnitude of the external fi eld?

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 fi eld within the solenoid?

The magnetic fi eld produced by the solenoid in a magnetic resonance imaging (MRI) system designed for measurements on whole human bodies has a fi eld strength of 7.0 T, and the current in the solenoid is 2.0 3 102 A. What is the number of turns per meter of length of the solenoid? Note that the solenoid used to produce the magnetic fi eld 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 90.08 with respect to the axis of the solenoid. The coil consists of 50 turns, has an area of 1.2 3 1023 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 fi eld at the common center?

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 fl oats beneath it at a distance of 8.2 3 1023 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 fi eld at the points labeled (a) A and (b) B.

A long, straight wire carrying a current of 305 A is placed in a uniform magnetic fi eld that has a magnitude of 7.00 3 1023 T. The wire is perpendicular to the fi eld. Find a point in space where the net magnetic fi eld 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 fi eld 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 fi eld at that location. This component is parallel to the earths surface. When the current in the wire is 25.0 A, the needle points 23.08 east of north. (a) Does the current in the wire fl ow toward or away from the earths surface? (b) What is the magnitude of the horizontal component of the earths magnetic fi eld at the location of the compass?

Two infi nitely 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 fi eld 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 5.6 A. Find the magnitudes of the net magnetic fi elds at points A and B.

A piece of copper wire has a resistance per unit length of 5.90 3 1023 V/m. The wire is wound into a thin, fl at 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 fi eld strength at the center of the coil.

The drawing shows two wires that both carry the same current of I 5 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 158. What is the current in each wire?

Suppose that a uniform magnetic fi eld is everywhere perpendicular to this page. The fi eld 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 21.37 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 fi nd the magnitude of the magnetic fi eld at a distance of r 5 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 fl ow along the copper sheet parallel to the axis of the cylinder. The arrangement is, in eff ect, a hollow tube of current I. Use Ampres law to show that the magnetic fi eld (a) is m0 I/(2pr) 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.)

m A long, cylindrical conductor is solid throughout and has a radius R. Electric charges fl ow parallel to the axis of the cylinder and pass uniformly through the entire cross section. The arrangement is, in eff ect, a solid tube of current I0. The current per unit cross-sectional area (i.e., the current density) is I0/(pR2 ). Use Ampres law to show that the magnetic fi eld inside the conductor at a distance r from the axis is m0I0r/(2pR2 ). (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 fi eld has a magnitude of 5.4 3 1025 T and is directed north at an angle of 588 below the horizontal. An electrically charged bullet is fi red north and 118 above the horizontal, with a speed of 670 m/s. The magnetic force on the bullet is 2.8 3 10210 N, directed due east. Determine the bullets electric charge, including its algebraic sign (1 or 2).

An electron is moving through a magnetic fi eld whose magnitude is 8.70 3 1024 T. The electron experiences only a magnetic force and has an acceleration of magnitude 3.50 3 1014 m/s2 . At a certain instant, it has a speed of 6.80 3 106 m/s. Determine the angle u (less than 908) between the electrons velocity and the magnetic fi eld.

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 fi eld 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 fi eld is 8.4 3 1024 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 16.00 mC charge is moving with a speed of 7.50 3 104 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 fi eld are Bx 5 0.10 T, By 5 0.15 T, and Bz 5 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 fl ows during a time of 1.8 3 1023 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 fi eld of 8.0 3 1025 T is measured. How much charge has fl owed during the lightning bolt? Ignore the earths magnetic fi eld.

A charge is moving perpendicular to a magnetic fi eld and experiences a force whose magnitude is 2.7 3 1023 N. If this same charge were to move at the same speed and the angle between its velocity and the same magnetic fi eld were 388, 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 fi eld at the center of the square is 61 mT. Calculate the current I.

A particle of charge 17.3 mC and mass 3.8 3 1028 kg is traveling perpendicular to a 1.6-T magnetic fi eld, as the drawing shows. The speed of the particle is 44 m/s. (a) What is the value of the angle u, 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 q 5 15.60 mC and is located at the coordinate origin. As the drawing shows, an electric fi eld of Ex 5 1245 N/C exists along the 1x axis. A magnetic fi eld also exists, and its x and y components are Bx 5 11.80 T and By 5 11.40 T. Calculate the force (magnitude and direction) exerted on the particle by each of the three fi elds when it is (a) stationary, (b) moving along the 1x axis at a speed of 375 m/s, and (c) moving along the 1z 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 5 150 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 fi nd 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 fi eld inside the solenoid is found to be 6.48 3 1023 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 3 1026 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 v 5 150 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.)

The fi gure 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 5 15 A and I2 5 7.0 A. Find the magnitude and direction of the force that the magnetic fi eld of wire 1 applies to a 1.5-m section of wire 2 when the currents have (a) opposite and (b) the same directions.

The fi gure shows a particle that carries a charge of q0 5 22.80 3 1026 C. It is moving along the 1y axis at a speed of v 5 4.8 3 106 m/s. A magnetic fi eld B B of magnitude 3.35 3 1025 T is directed along the 1z axis, and an electric fi eld E B of magnitude 123 N/C points along the 2x axis. Concepts: (i) What forces make up the net force acting on the particle? (ii) How do you determine the direction of the magnetic force acting on the negative charge? (iii) How do you determine the direction of the electric force acting on the * negative charge? (iv) Does the fact that the charge is moving aff ect the values of the magnetic and electric forces? Calculations: Determine the magnitude and direction of the net force that acts on the particle.

A 125-turn rectangular coil of wire is hung from one arm of a balance, as the fi gure shows. With the magnetic fi eld B B turned off , an object of mass M is added to the pan on the other arm to balance the weight of the coil. Concepts: (i) In a balanced, or equilibrium, condition the device has no angular acceleration. What does this imply about the net torque acting on the device? (ii) What is torque? (iii) In calculating the torques acting on an object in equilibrium, where do you locate the axis of rotation? Calculations: When a constant 0.200-T magnetic fi eld 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?