Transcranial Magnetic Stimulation A recently developed

Predict/Explain Proton 1 moves with a speed v from the east coast to the west coast in the continental United States; proton 2 moves with the same speed from the southern United States toward Canada. (a) Is the magnitude of the magnetic force experienced by proton 2 greater than, less than, or equal to the force experienced by proton 1? (b) Choose the best explanation from among the following: I. The protons experience the same force because the magnetic eld is the same and their speeds are the same. II. Proton 1 experiences the greater force because it moves at right angles to the magnetic eld. III. Proton 2 experiences the greater force because it moves in the same direction as the magnetic eld.

An electron moves west to east in the continental United States. Does the magnetic force experienced by the electron point in a direction that is generally north, south, east, west, upward, or downward? Explain.

An electron moving in the positive xdirection, at right angles to a magnetic eld, experiences a magnetic force in the positive y direction. What is the direction of the magnetic eld?

Suppose particles A, B, and C in Figure 2231have identical masses and charges of the same magnitude. Rank the particles in order of increasing speed. Indicate ties where appropriate.

Referring to Figure 2231, what is the sign of the charge for each of the three particles? Explain.

Suppose the three particles in Figure 2231 have the same mass and speed. Rank the particles in order of increasing magnitude of their charge. Indicate ties where appropriate.

What is the acceleration of a proton moving with a speed of 6.5 m/s at right angles to a magnetic eld of 1.6 T?

An electron moves at right angles to a magnetic eld of 0.18 T. What is its speed if the force exerted on it is

A negatively charged ion moves due north with a speed of at the Earths equator. What is the magnetic force exerted on this ion?

Aproton high above the equator approaches the Earth moving straight downward with a speed of 355 m/s. Find the acceleration of the proton, given that the magnetic eld at its altitude is

A particle moves with a speed of 16 m/s through a region where the magnetic eld has a strength of 0.95 T. At what angle to the eld is the particle moving if the force exerted on it is (a) , (b) , or (c) ?

A particle with a charge of experiences a force of when it moves at right angles to a magnetic eld with a speed of 27 m/s. What force does this particle experience when it moves with a speed of 6.3 m/s at an angle of 25 relative to the magnetic eld?

An ion experiences a magnetic force of when moving in the positive x direction but no magnetic force when moving in the positive ydirection. What is the magnitude of the magnetic force exerted on the ion when it moves in the x-y plane along the line ? Assume that the ions speed is the same in all cases.

An electron moving with a speed of in the positive x direction experiences zero magnetic force. When it moves in the positive y direction, it experiences a force of that points in the negative z direction. What are the direction and magnitude of the magnetic eld?

Two charged particles with different speeds move one at a time through a region of uniform magnetic eld. The particles move in the same direction and experience equal magnetic forces. (a) If particle 1 has four times the charge of particle 2, which particle has the greater speed? Explain. (b)Find the ratio of the speeds, .

A particle moves through a region of space where an electric eld of magnitude 1250 N/C points in the positive x direction, and a magnetic eld of magnitude 1.02 T points in the positive z direction. If the net force acting on the particle is in the positive x direction, nd the magnitude and direction of the particles velocity. Assume the particles velocity is in the x-y plane.

When at rest, a proton experiences a net electromagnetic force of magnitude pointing in the positive x direction. When the proton moves with a speed of in the positive y direction, the net electromagnetic force on it decreases in magnitude to , still pointing in the positivexdirection. Find the magnitude and direction of (a)the electric eld and (b) the magnetic eld.

A velocity selector is to be constructed using a magnetic eld in the positive y direction. If positively charged particles move through the selector in the positive z direction, (a) what must be the direction of the electric eld? (b)Repeat part (a) for the case of negatively charged particles.

Find the radius of an electrons orbit when it moves perpendicular to a magnetic eld of 0.66 T with a speed of

Find the radius of a protons orbit when it moves perpendicular to a magnetic eld of 0.66 T with a speed of

Charged particles pass through a velocity selector with electric and magnetic elds at right angles to each other, as shown in Figure 2232. If the electric eld has a magnitude of 450 N/C and the magnetic eld has a magnitude of 0.18 T, what speed must the particles have to pass through the selector undeected?

The velocity selector in Figure 2233 is designed to allow charged particles with a speed of to pass through undeected. Find the direction and magnitude of the required electric eld, given that the magnetic eld has a magnitude of

The artery in Figure 2211has an inside diameter of 2.75 mm and passes through a region where the magnetic eld is 0.065 T. (a) If the voltage difference between the electrodes is , what is the speed of the blood? (b) Which electrode is at the higher potential? Does your answer depend on the sign of the ions in the blood? Explain.

An electron accelerated from rest through a voltage of 550 V enters a region of constant magnetic eld. If the electron follows a circular path with a radius of 17 cm, what is the magnitude of the magnetic eld?

A particle with a mass of moves perpendicular to a 1.01-T magnetic eld in a circular path of radius 21.8 m. (a)How fast is the particle moving? (b)How long will it take the particle to complete one orbit?

When a charged particle enters a region of uniform magnetic eld, it follows a circular path, as indicated in Figure 2234. (a) Is this particle positively or negatively charged? Explain. (b) Suppose that the magnetic eld has a magnitude of 0.180 T, the particles speed is , and the radius of its path is 52.0 cm. Find the mass of the particle, given that its charge has a magnitude of . Give your result in atomic mass units, u, where .

A proton with a kinetic energy of moves perpendicular to a magnetic eld of 0.26 T. What is the radius of its circular path?

An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mass of (a)How long does it take for an alpha particle to move halfway through a complete circle? (b)If the speed of the alpha particle is doubled, does the time found in part (a) increase, decrease, or stay the same? Explain. (c) Repeat part (a) for alpha particles with a speed of

An electron and a proton move in circular orbits in a plane perpendicular to a uniform magnetic eld . Find the ratio of the radii of their circular orbits when the electron and the proton have (a) the same momentum and (b) the same kinetic energy.

What is the magnetic force exerted on a 2.15-m length of wire carrying a current of 0.899 Aperpendicular to a magnetic eld of 0.720 T?

Awire with a current of 2.8 Ais at an angle of 36.0relative to a magnetic eld of 0.88 T. Find the force exerted on a 2.25-m length of the wire.

The magnetic force exerted on a 1.2-m segment of straight wire is 1.6 N. The wire carries a current of 3.0 Ain a region with a constant magnetic eld of 0.50 T. What is the angle between the wire and the magnetic eld?

A0.45-m copper rod with a mass of 0.17 kg carries a current of 11 Ain the positive x direction. What are the magnitude and direction of the minimum magnetic eld needed to levitate the rod?

The long, thin wire shown in Figure 2235 is in a region of constant magnetic eld . The wire carries a current of 6.2 A and is oriented at an angle of 7.5 to the direction of the magnetic eld. (a) If the magnetic force exerted on this wire per meter is 0.033 N, what is the magnitude of the magnetic eld? (b)At what angle will the force exerted on the wire per meter be equal to 0.015 N?

A wire with a length of 3.6 m and a mass of 0.75 kg is in a region of space with a magnetic eld of 0.84 T. What is the minimum current needed to levitate the wire?

Ahigh-voltage power line carries a current of 110 Aat a location where the Earths magnetic eld has a magnitude of 0.59 G and points to the north, 72 below the horizontal. Find the direction and magnitude of the magnetic force exerted on a 250-m length of wire if the current in the wire ows (a) horizontally toward the east or (b) horizontally toward the south.

Ametal bar of mass mand length Lis suspended from two conducting wires, as shown in Figure 2236. Auniform magnetic eld of magnitude B points vertically downward. Find the angle the suspending wires make with the vertical when the bar carries a current I.

For each of the three situations shown in Figure 2237, indicate whether there will be a tendency for the square current loop to rotate clockwise, counterclockwise, or not at all, when viewed from above the loop along the indicated axis.

Arectangular loop of 260 turns is 33 cm wide and 16 cm high. What is the current in this loop if the maximum torque in a eld of 0.48 T is

A single circular loop of radius 0.23 m carries a current of 2.6 Ain a magnetic eld of 0.95 T. What is the maximum torque exerted on this loop?

In the previous problem, nd the angle the plane of the loop must make with the eld if the torque is to be half its maximum value.

Consider a current loop in a region of uniform magnetic eld, as shown in Figure 2237 (a) (Problem 38). Find the magnitude of the torque exerted on the loop about the vertical axis of rotation, using the data given in Problem 68.

Two current loops, one square the other circular, have one turn made from wires of the same length. (a) If these loops carry the same current and are placed in magnetic elds of equal magnitude, is the maximum torque of the square loop greater than, less than, or the same as the maximum torque of the circular loop? Explain. (b) Calculate the ratio of the maximum torques, .

Each of the 10 turns of wire in a vertical, rectangular loop carries a current of 0.22 A. The loop has a height of 8.0 cm and a width of 15 cm. Ahorizontal magnetic eld of magnitude 0.050 T is oriented at an angle of relative to the normal to the plane of the loop, as indicated in Figure 2238. Find (a)the magnetic force on each side of the loop, (b) the net magnetic force on the loop, and (c)the magnetic torque on the loop. (d)If the loop can rotate about a vertical axis with only a small amount of friction, will it end up with an orientation given by , or ? Explain.

Find the magnetic eld 6.25 cm from a long, straight wire that carries a current of 7.81 A.

Along, straight wire carries a current of 7.2 A. How far from this wire is the magnetic eld it produces equal to the Earths magnetic eld, which is approximately

You travel to the north magnetic pole of the Earth, where the magnetic eld points vertically downward. There, you draw a circle on the ground. Applying Ampres law to this circle, show that zero current passes through its area.

Two power lines, each 270 m in length, run parallel to each other with a separation of 25 cm. If the lines carry parallel currents of 110 A, what are the magnitude and direction of the magnetic force each exerts on the other?

Pacemaker Switches Some pacemakers employ magnetic reed switches to enable doctors to change their mode of operation without surgery. A typical reed switch can be switched from one position to another with a magnetic eld of . What current must a wire carry if it is to produce a eld at a distance of 0.50 m?

Consider the long, straight, current-carrying wires shown in Figure 2239. One wire carries a current of 6.2 Ain the positive y direction; the other wire carries a current of 4.5 Ain the positive x direction. (a) At which of the two points, Aor B, do you expect the magnitude of the net magnetic eld to be greater? Explain. (b) Calculate the magnitude of the net magnetic eld at points Aand B.

Repeat Problem 50 for the case where the 6.2-Acurrent is reversed in direction.

In Oersteds experiment, suppose that the compass was 0.25 m from the current-carrying wire. If a magnetic eld of half the Earths magnetic eld of was required to give a noticeable deection of the compass needle, what current must the wire have carried?

Two long, straight wires are separated by a distance of 9.25 cm. One wire carries a current of 2.75 A, the other carries a current of 4.33 A. (a) Find the force per meter exerted on the 2.75-Awire. (b)Is the force per meter exerted on the 4.33-Awire greater than, less than, or the same as the force per meter exerted on the 2.75-Awire? Explain.

Two long, straight wires are oriented perpendicular to the page, as shown in Figure 2240. The current in one wire is , pointing into the page, and the current in the other wire is , pointing out of the page. Find the magnitude and direction of the net magnetic eld at point P.

Aloop of wire is connected to the terminals of a battery, as indicated in Figure 2241. If the loop is to attract the bar magnet, which of the terminals, Aor B, should be the positive terminal of the battery? Explain.

Predict/Explain The number of turns in a solenoid is doubled, and at the same time its length is doubled. Does the magnetic eld within the solenoid increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. Doubling the number of turns in a solenoid doubles its magnetic eld, and hence the eld increases. II. Making a solenoid longer decreases its magnetic eld, and therefore the eld decreases. III. The magnetic eld remains the same because the number of turns per length is unchanged.

It is desired that a solenoid 38 cm long and with 430 turns produce a magnetic eld within it equal to the Earths magnetic eld . What current is required?

A solenoid that is 62 cm long produces a magnetic eld of 1.3 T within its core when it carries a current of 8.4 A. How many turns of wire are contained in this solenoid?

The maximum current in a superconducting solenoid can be as large as 3.75 kA. If the number of turns per meter in such a solenoid is 3650, what is the magnitude of the magnetic eld it produces?

To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 12 cm in diameter and 55 cm in length. You would like a 2.0-A current to produce a 2.5-kG magnetic eld inside your solenoid. What is the total length of wire you will need to meet these specications?

At a point near the equator, the Earths magnetic eld is horizontal and points to the north. If an electron is moving vertically upward at this point, does the magnetic force acting on it point north, south, east, west, upward, or downward? Explain.

A proton is to orbit the Earth at the equator using the Earths magnetic eld to supply part of the necessary centripetal force. Should the proton move eastward or westward? Explain.

The accompanying photograph shows an electron beam whose initial direction of motion is horizontal, from right to left. Amagnetic eld deects the beam downward. What is the direction of the magnetic eld?

The three wires shown in Figure 2242 are long and straight, and they each carry a current of the same magnitude, I. The currents in wires 1 and 3 are out of the page; the current in wire 2 is into the page. What is the direction of the magnetic force experienced by wire 3?

Each of the current-carrying wires in Figure 2242 is long and straight, and carries the current I either into or out of the page, as shown. What is the direction of the net magnetic eld produced by these three wires at the center of the triangle?

The four wires shown in Figure 2243are long and straight, and they each carry a current of the same magnitude, I. The currents in wires 1, 2, and 3 are out of the page; the current in wire 4 is into the page. What is the direction of the magnetic force experienced by wire 2?

Each of the current-carrying wires in Figure 2243 is long and straight, and carries the current I either into or out of the page, as shown. What is the direction of the net magnetic eld produced by these four wires at the center of the square?

Consider a current loop immersed in a magnetic eld, as in Figure 2237 (a) (Problem 38). It is given that and . In addition, the loop is a square 0.46 m on a side. Find the magnitude of the magnetic force exerted on each side of the loop.

A stationary proton is located between the poles of a horseshoe magnet, where the magnetic eld is 0.35 T. What is the magnitude of the magnetic force acting on the proton?

Brain Function and Magnetic Fields Experiments have shown that thought processes in the brain can be affected if the parietal lobe is exposed to a magnetic eld with a strength of 1.0 T. How much current must a long, straight wire carry if it is to produce a 1.0-T magnetic eld at a distance of 0.50 m? (For comparison, a typical lightning bolt carries a current of about 20,000 A, which would melt most wires.)

Amixture of two isotopes is injected into a mass spectrometer. One isotope follows a curved path of radius ; the other follows a curved path of radius . Find the mass ratio, , assuming that the two isotopes have the same charge and speed.

High above the surface of the Earth, charged particles (such as electrons and protons) can become trapped in the Earths magnetic eld in regions known as Van Allen belts. A typical electron in a Van Allen belt has an energy of 45 keV and travels in a roughly circular orbit with an average radius of 220 m. What is the magnitude of the Earths magnetic eld where such an electron orbits?

Credit-Card Magnetic Strips Experiments carried out on the television show Mythbusters determined that a magnetic eld of 1000 gauss is needed to corrupt the information on a credit cards magnetic strip. (They also busted the myth that a credit card can be demagnetized by an electric eel or an eelskin wallet.) Suppose a long, straight wire carries a current of 3.5 A. How close can a credit card be held to this wire without damaging its magnetic strip?

Superconducting Solenoid Cryomagnetics, Inc., advertises a high-eld, superconducting solenoid that produces a magnetic eld of 17 T with a current of 105 A. What is the number of turns per meter in this solenoid?

A positively charged particle moves through a region with a uniform electric eld pointing toward the top of the page and a uniform magnetic eld pointing into the page. The particle can have one of the four velocities shown in Figure 2244. (a) Rank the four possibilities in order of increasing magnitude of the net force the particle experiences. Indicate ties where appropriate. (b) Which of the four velocities could potentially result in zero net force?

Suppose the elds in Figure 2244are interchanged, with the magnetic eld pointing toward the top of the page and the electric eld pointing into the page. (a) Rank the four possibilities in order of increasing magnitude of the net force the particle experiences. Indicate ties where appropriate. (b) Which of the four velocities could potentially result in zero net force?

A proton follows the path shown in Figure 2245 as it moves through three regions with different uniform magnetic elds, , and . In each region the proton completes a halfcircle, and the magnetic eld is perpendicular to the page. (a)Rank the three elds in order of increasing magnitude. Indicate ties where appropriate. (b)Give the direction (into or out of the page) for each of the elds.

Predict/Explain Suppose the initial speed of the proton in Figure 2245 is increased. (a) Does the radius of each halfcircular path segment increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The radius of a circular orbit in a magnetic eld is proportional to the speed of the proton; therefore, the radius of the half-circular path will increase. II. A greater speed means the proton will experience more force from the magnetic eld, resulting in a decrease of the radius. III. The increase in speed offsets the increase in magnetic force, resulting in no change of the radius.

Predict/Explain Suppose the initial speed of the proton in Figure 2245 is decreased. (a) Does the time spent in each of the eld regions increase, decrease, or stay the same? (b)Choose the best explanation from among the following: I. The proton moves more slowly, and therefore the time spent moving through each of magnetic regions will increase. II. With a smaller speed the proton is forced out of each magnetic region more quickly, which results in a decrease in the time. III. The time for an orbit in a magnetic eld is independent of speed. Therefore, the time the proton spends in each of magnetic regions is the same no matter what its speed.

Magnetic Resonance Imaging An MRI (magnetic resonance imaging) solenoid produces a magnetic eld of 1.5 T. The solenoid is 2.5 m long, 1.0 m in diameter, and wound with insulated wires 2.2 mm in diameter. Find the current that ows in the solenoid. (Your answer should be rather large. Atypical MRI solenoid uses niobiumtitanium wire kept at liquid helium temperatures, where it is superconducting.)

Along, straight wire carries a current of 14 A. Next to the wire is a square loop with sides 1.0 m in length, as shown in Figure 2246. The loop carries a current of 2.5 Ain the direction indicated. (a) What is the direction of the net force exerted on the loop? Explain. (b) Calculate the magnitude of the net force acting on the loop.

Suppose the 14-Acurrent in the straight wire in Figure 2246 is reversed in direction, but the current in the loop is unchanged. (a) Calculate the magnitude and direction of the net force acting on the loop. (b) If the loop is extended in the horizontal direction, so that it is 1.0 m high and 2.0 m wide, does the net force exerted on the loop increase or decrease? By what factor? Explain. (c) If, instead, the loop is extended in the vertical direction, so it is 2.0 m high and 1.0 m wide, does the net force exerted on the loop increase or decrease? Explain.

Acharged particle moves through a region of space containing both electric and magnetic elds. The velocity of the particle is and the magnetic eld is . Find the electric eld vector necessary to yield zero net force on the particle. (Note: You may wish to use cross products in this problem. They are discussed in Appendix A.)

Medical X-raysAn electron in a medical X-ray machine is accelerated from rest through a voltage of 10.0 kV. (a)Find the maximum force a magnetic eld of 0.957 T can exert on this electron. (b) If the voltage of the X-ray machine is increased, does the maximum force found in part (a) increase, decrease, or stay the same? Explain. (c) Repeat part (a) for an electron accelerated through a potential of 25.0 kV.

A particle with a charge of moves with a speed of 73 m/s in the positive x direction. The magnetic eld in this region of space has a component of 0.40 T in the positive y direction, and a component of 0.85 T in the positive zdirection. What are the magnitude and direction of the magnetic force on the particle?

Abeam of protons with various speeds is directed in the positive x direction. The beam enters a region with a uniform magnetic eld of magnitude 0.52 T pointing in the negative zdirection, as indicated in Figure 2247. It is desired to use a uniform electric eld (in addition to the magnetic eld) to select from this beam only those protons with a speed of that is, only these protons should be undeected by the two elds. (a) Determine the magnitude and direction of the electric eld that yields the desired result. (b) Suppose the electric eld is to be produced by a parallel-plate capacitor with a plate separation of 2.5 cm. What potential difference is required between the plates?(c)Which plate in Figure 2247(top or bottom) should be positively charged? Explain.

A charged particle moves in a horizontal plane with a speed of . When this particle encounters a uniform magnetic eld in the vertical direction it begins to move on a circular path of radius 15.9 cm. (a) If the magnitude of the magnetic eld is 1.21 T, what is the charge-to-mass ratio (q/m) of this particle? (b) If the radius of the circular path were greater than 15.9 cm, would the corresponding charge-to-mass ratio be greater than, less than, or the same as that found in part (a)? Explain. (Assume that the magnetic eld remains the same.)

Two parallel wires, each carrying a current of 2.2 A in the same direction, are shown in Figure 2248. Find the direction and magnitude of the net magnetic eld at points A, B, and C.

Repeat Problem 88 for the case where the current in wire 1 is reversed in direction.

Lightning Bolts A powerful bolt of lightning can carry a current of 225 kA. (a) Treating a lightning bolt as a long, thin wire, calculate the magnitude of the magnetic eld produced by such a bolt of lightning at a distance of 35 m. (b) If two such bolts strike simultaneously at a distance of 35 m from each other, what is the magnetic force per meter exerted by one bolt on the other?

Consider the two current-carrying wires shown in Figure 2249. The current in wire 1 is 3.7 A; the current in wire 2 is adjusted to make the net magnetic eld at point A equal to zero. (a) Is the magnitude of the current in wire 2 greater than, less than, or the same as that in wire 1? Explain. (b)Find the magnitude and direction of the current in wire 2.

Consider the physical system shown in Figure 2249, which consists of two current-carrying wires each with a length of 71 cm. (a) If the net magnetic eld at the point Ais out of the page, is the force between the wires attractive or repulsive? Explain. (b) Calculate the magnitude of the force exerted by each wire on the other wire, given that the magnetic eld at point A is out of the page with a magnitude of .

Magnetars The astronomical object has the distinction of creating the most powerful magnetic eld ever observed. This object is referred to as a magnetar (a subclass of pulsars), and its magnetic eld is times greater than the Earths magnetic eld. (a)Suppose a 2.5-m straight wire carrying a current of 1.1 A is placed in this magnetic eld at an angle of 65 to the eld lines. What force does this wire experience? (b)Aeld this strong can signicantly change the behavior of an atom. To see this, consider an electron moving with a speed of . Compare the maximum magnetic force exerted on the electron to the electric force a proton exerts on an electron in a hydrogen atom. The radius of the hydrogen atom is .

Consider a system consisting of two concentric solenoids, as illustrated in Figure 2250. The current in the outer solenoid is , and the current in the inner solenoid is . Given that the number of turns per centimeter is 105 for the outer solenoid and 125 for the inner solenoid, nd the magnitude and direction of magnetic eld (a) between the solenoids and (b) inside the inner solenoid.

A long, straight wire on the x axis carries a current of 3.12 Ain the positive xdirection. The magnetic eld produced by the wire combines with a uniform magnetic eld of that points in the positive z direction. (a) Is the net magnetic eld of this system equal to zero at a point on the positive y axis or at a point on the negative y axis? Explain. (b) Find the distance from the wire to the point where the eld vanishes.

Find the angle between the plane of a loop and the magnetic eld for which the magnetic torque acting on the loop is equal to x times its maximum value, where

Solenoids produce magnetic elds that are relatively intense for the amount of current they carry. To make a direct comparison, consider a solenoid with 55 turns per centimeter, a radius of 1.05 cm, and a current of 0.622 A. (a) Find the magnetic eld at the center of the solenoid. (b) What current must a long, straight wire carry to have the same magnetic eld as that found in part (a)? Let the distance from the wire be the same as the radius of the solenoid, 1.05 cm.

The current in a solenoid with 22 turns per centimeter is 0.50 A. The solenoid has a radius of 1.5 cm. A long, straight wire runs along the axis of the solenoid, carrying a current of 13 A. Find the magnitude of the net magnetic eld a radial distance of 0.75 cm from the straight wire.

Transcranial Magnetic Stimulation A recently developed method to study brain function is to produce a rapidly changing magnetic eld within the brain. When this technique, known as transcranial magnetic stimulation (TMS), is applied to the prefrontal cortex, for example, it can reduce a persons ability to conjugate verbs, though other thought processes are unaffected. The rapidly varying magnetic eld is produced with a circular coil of 21 turns and a radius of 6.0 cm placed directly on the head. The current in this loop increases at the rate of (by discharging a capacitor). (a)At what rate does the magnetic eld at the center of the coil increase? (b) Suppose a second coil with half the area of the rst coil is used instead. Would your answer to part (a) increase, decrease, or stay the same? By what factor?

An electron with a velocity given by moves through a region of space with a magnetic eld and an electric eld . Using cross products, nd the magnitude of the net force acting on the electron. (Cross products are discussed in Appendix A.)

A thin ring of radius R and charge per length rotates with an angular speed about an axis perpendicular to its plane and passing through its center. Find the magnitude of the magnetic eld at the center of the ring.

Asolenoid is made from a 25-m length of wire of resistivity . The wire, whose radius is 2.1 mm, is wrapped uniformly onto a plastic tube 4.5 cm in diameter and 1.65 m long. Find the emf to which the ends of the wire must be connected to produce a magnetic eld of 0.015 T within the solenoid.

A single current-carrying circular loop of radius R is placed next to a long, straight wire, as shown in Figure 2251. The current in the wire points to the right and is of magnitude I. (a) In which direction must current ow in the loop to produce zero magnetic eld at its center? Explain. (b) Calculate the magnitude of the current in part (a).

Magnetic Fields in the Bohr Model In the Bohr model of the hydrogen atom, the electron moves in a circular orbit of radius about the nucleus. Given that the charge on the electron is , and that its speed is , nd the magnitude of the magnetic eld the electron produces at the nucleus of the atom.

A single-turn square loop carries a current of 18 A. The loop is 15 cm on a side and has a mass of 0.035 kg. Initially the loop lies at on a horizontal tabletop. When a horizontal magnetic eld is turned on, it is found that only one side of the loop experiences an upward force. Find the minimum magnetic eld, , necessary to start tipping the loop up from the table.

Consider the physical system shown in Figure 2240. (a)Find the net magnetic eld (direction and magnitude) at an arbitrary point on the bottom side of the square, a distance to the right of wire 1. (b) Find the magnitude of the net magnetic eld at an arbitrary point on the left side of the square, a distance above wire 1.

Approximating a neuron by a straight wire, what electric current is needed to produce a magnetic eld of T at a distance of 5.0 cm? A. A B. A C. A D

Suppose a neuron in the brain carries a current of A. Treating the neuron as a straight wire, what is the magnetic eld it produces at a distance of 7.5 cm? A. T B. T C. T D.

Agiven neuron in the brain carries a current of A. If the SQUID detects a magnetic eld of T, how far away is the neuron? Treat the neuron as a straight wire. A. 22 cm B. 70 cm C. 140 cm D.

ASQUID detects a magnetic eld of T at a distance of 13 cm. How many electrons ow through the neuron per second? Treat the neuron as a straight wire. A. B. C. D

Referring to Example 223 Suppose the speed of the isotopes is doubled. (a) Does the separation distance, d, increase, decrease, or stay the same? Explain. (b) Find the separation distance for this case.

Referring to Example 223 Suppose we change the initial speed of , leaving everything else the same. (a)If we want the separation distance to be zero, should the initial speed of be increased or decreased? Explain. (b) Find the required initial speed.

Referring to Active Example 222 The current is adjusted until the magnetic eld halfway between the wires has a magnitude of and points into the page. Everything else in the system remains the same as in Active Example 222. Find the magnitude and direction of

Referring to Active Example 222 The current is adjusted until the magnetic eld 5.5 cm below wire 2 has a magnitude of and points out of page. Everything else in the system remains the same as in Active Example 222. Find the magnitude and direction of .