(III) (a) Use ampere’s law to show that the magnetic field

Problem 62 PE Integrated Concepts How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from 37.0ºC to 100ºC and then boil away 0.500 g of water, if it puts out 2.00 mA at 15.0 kV? Ignore heat transfer to the surroundings.

Problem 63 PE Integrated Concepts Hydroelectric generators (see Figure 20.43) at Hoover Dam produce a maximum current of 8.00×103 A at 250 kV. (a) What is the power output? (b) The water that powers the generators enters and leaves the system at low speed (thus its kinetic energy does not change) but loses 160 m in altitude. How many cubic meters per second are needed, assuming 85.0% efficiency?

Problem 67 PE Integrated Concepts 2 (a) An immersion heater utilizing 120 V can raise the temperature of a 1.00 × 10? -g aluminum cup containing 350 g of water from 20.0ºC to 95.0ºC in 2.00 min. Find its resistance, assuming it is constant during the process. (b) A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

Problem 71 PE Construct Your Own Problem Consider an electric immersion heater used to heat a cup of water to make tea. Construct a problem in which you calculate the needed resistance of the heater so that it increases the temperature of the water and cup in a reasonable amount of time. Also calculate the cost of the electrical energy used in your process. Among the things to be considered are the voltage used, the masses and heat capacities involved, heat losses, and the time over which the heating takes place. Your instructor may wish for you to consider a thermal safety switch (perhaps bimetallic) that will halt the process before damaging temperatures are reached in the immersion unit.

Problem 73 PE Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the Rms voltage?

Problem 75 PE Military aircraft use 400-Hz AC power, because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?

Problem 66 PE Integrated Concepts (a) An aluminum power transmission line has a resistance of 0.0580 ? / km . What is its mass per kilometer? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.

Problem 68 PE Integrated Concepts (a) What is the cost of heating a hot tub containing 1500 kg of water from 10.0ºC to 40.0ºC , assuming 75.0% efficiency to account for heat transfer to the surroundings? The cost of electricity is 9 cents/kWh . (b) What current was used by the 220-V AC electric heater, if this took 4.00 h?

Problem 69 PE Unreasonable Results (a) What current is needed to transmit 1.00×10? MW of 2? power at 480 V? (b) What power is dissipated by the transmission lines if they have a 1.00 - ? resistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?

Problem 65PE Integrated Concepts A light-rail commuter train draws 630 A of 650-V DC electricity when accelerating. (a) What is its power consumption rate in kilowatts? (b) How long 4? does it take to reach 20.0 m/s starting from rest if it's loaded mass is 5.30×10? kg , assuming 95.0% efficiency and constant power? (c) Find its average acceleration. (d) Discuss how the acceleration you found for the light-rail train compares to what might be typical for an automobile. Given: Current: 630 A Voltage = 650-V DC Mass = 5.30×10? kg , Distance-= 20.0 m/s Efficiency= 95.0% Calculate: 1) Power consumption rate in kilowatts=? 2) Time or duration to reach 20.0 m/s starting from rest if it's loaded mass is 5.30×10? kg , assuming 95.0% efficiency= ? 3) Find its average acceleration. 4) Comparing the calculated acceleration with typical automobile acceleration.

Problem 61 PE Integrated Concepts What current must be produced by a 12.0-V battery-operated bottle warmer in order to heat 75.0 g of glass, 250 g of baby formula, and 2? 3.00×10? g of aluminum from 20.0ºC to 90.0ºC in 5.00 min?

Problem 64 PE Integrated Concepts (a) Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0-V batteries of a 750-kg electric car be able to supply: (a) To accelerate from rest to 25.0 m/s in 1.00 min? (b) To climb a 2.00 × 10? -m - high hill in 2.00 min at a constant 25.0-m/s speed while exerting 5.00 × 2? 10? N of force to overcome air resistance and friction? (c) To travel at a constant 25.0-m/s speed, exerting a 5.00×10? N force to overcome air resistance and friction? See Figure 20.44.

Problem 60PE Integrated Concepts (a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of 1.00×10? MV , and a length of 1.00 ms? (b) What mass of tree sap could be raised from 18.0ºC to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

Problem 58 PE 00-gauge copper wire has a diameter of 9.266 mm.Calculate the power loss in 2 ? a kilometer of such wire when it carries 1.00 × 10? A .

Problem 59 PE Integrated Concepts Cold vaporizers pass a current through water, evaporating it with only a small increase in temperature. One such home device is rated at 3.50 A and utilizes 120 V AC with 95.0% efficiency. (a) What is the vaporization rate in grams per minute? (b) How much water must you put into the vaporizer for 8.00 h of overnight operation? (See Figure 20.42.)

Problem 57 PE An old light bulb draws only 50.0 W, rather than its original 60.0 W, due to evaporative thinning of its filament. By what factor is its diameter reduced, assuming uniform thinning along its length? Neglect any effects caused by temperature differences.

Problem 1Q A compass needle is not always balanced parallel to the Earth's surface, but one end may dip downward. Explain.

In what direction are the magnetic field lines surrounding a straight wire carrying a current that is moving directly away from you?

Problem 4Q A horseshoe magnet is held vertically with the north pole on the left and south pole on the right. A wire passing between the poles, equidistant from them, carries a current directly away from you. In what direction is the force on the wire? Explain.

Problem 5Q Will a magnet attract any metallic object, such as those made of aluminum or copper? (Try it and see.) Why is this so?

Problem 6Q Two iron bars attract each other no matter which ends are placed close together. Are both magnets? Explain.

Problem 7Q The magnetic field due to current in wires in your home can affect a compass. Discuss the effect in terms of currents, including if they are ac or dc.

Problem 8P (II) Suppose a straight 1.00-mm-diameter copper wire could just "float" horizontally in air because of the force due to the Earth's magnetic field B which is horizontal, perpendicular to the wire, and of magnitude 5.0 X 10-5 T. What current would the wire carry? Does the answer seem feasible? Explain briefly.

Problem 8Q If a negatively charged particle enters a region of uniform magnetic field which is perpendicular to the particle's velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field.)

In Fig. charged particles move in the vicinity of a current-carrying wire. For each charged particle, the arrow indicates the direction of motion of the particle, and the \(+\text { or }-\) indicates the sign of the charge. For each of the particles, indicate the direction of the magnetic force due to the magnetic field produced by the wire. FIGURE 20-45 Question Equation Transcription: Text Transcription: + or -

Three particles, a, b, and c, enter a magnetic field as shown in Fig. 20-46. What can you say about the charge on each particle? FIGURE 20-46 Question 10

A positively charged particle in a nonuniform magnetic field follows the trajectory shown in Fig. . Indicate the direction of the magnetic field everywhere in space, assuming the path is always in the plane of the page, and indicate the relative magnitudes of the field in each region. FIGURE 20-47 Question 11

Problem 12Q Can an iron rod attract a magnet? Can a magnet attract an iron rod?What must you consider to answer these questions?

(I) An electron is projected vertically upward with a speed of \(1.70 \times 10^{6} \mathrm{~m} / \mathrm{s}\) into a uniform magnetic field of 0.350 T that is directed horizontally away from the observer. Describe the electron’s path in this field.

Problem 13Q Explain why a strong magnet held near a CRT television screen (Section 17-11) causes the picture to become distorted. Also, explain why the picture sometimes goes completely black where the field is the strongest. [But don't risk damage to your TV by trying this ]

Problem 14P (II) A 1 ,5-MeV (kinetic energy) proton enters a 0.30-T field, in a plane perpendicular to the field. What is the radius of its path? See Section 17-4. (II) A 1 ,5-MeV (kinetic energy) proton enters a 0.30-T field, in a plane perpendicular to the field. What is the radius of its path? See Section 17-4. 17—4 The Electron Volt, a Unit of Energy The joule is a very large unit for dealing with energies of electrons, atoms, or molecules. For this purpose, the unit electron volt (eV) is used. One electron volt is defined as the energy acquired by a particle carrying a charge whose magnitude equals that on the electron (q = e) as a result of moving through a potential difference of 1 V. Hie charge on an electron has magnitude 1.6022 x 10I9C, and the change in potential energy equals qV. So 1 eV is equal to (1.6022 x 10~,9C)(1.00 V) = 1.6022 X 10_,9J: 1 eV = 1.6022 x 10 19 « 1.60 x 10 ,9J. An electron that accelerates through a potential difference of 1000 V will lose l(XX) eV of potential energy and thus gain 1000 eV or 1 keV (kiloelectron volt) of kinetic energy. On the other hand, if a particle with a charge equal to twice the magnitude of the charge on the electron (= 2e = 3.2 x 10_,9C) moves through a potential difference of 1000 V. its kinetic energy will increase by 2000 eV = 2 keV. Although the electron volt is handy for stating the energies of molecules and elementary particles, it is not a proper SI unit. For calculations, electron volts should be converted to joules using the conversion factor just given. In Example 17-2, for example, the electron acquired a kinetic energy of 8.0 x 10~16 J. We can quote this energy as 5000 eV (= 8.0 x 10~16 J/1.6 x 10_19J/eV), but when determining the speed of a particle in SI units, we must use the ke in joules (J). EXERCISE B What is the kinetic energy of a He2 ion released from rest and accelerated through a potential difference of 2.5 kV? (a) 2500 eV, (b) 500 eV. (c) 5000 eV. (d) 10.000 eV. (e) 250 eV.

Problem 14Q Suppose you have three iron rods, two of which are magnetized but the third is not. How would you determine which two are the magnets without using any additional objects?

(II) An electron experiences the greatest force as it travels \(2.9 \times 10^6 \mathrm{~m} / \mathrm{s}\) in a magnetic field when it is moving northward. The force is upward and of magnitude \(7.2 \times 10^{-13} \mathrm{~N}\). What are the magnitude and direction of the magnetic field?

Problem 15Q Can you set a resting electron into motion with a magnetic field? With an electric field? Explain.

A charged particle is moving in a circle under the influence of a uniform magnetic field. If an electric field that points in the same direction as the magnetic field is turned on. describe the path the charged particle will take.

(II) A proton (mass \(\left.m_p\right)\), a deuteron \(\left(m=2 m_{\mathrm{p}}, Q=e\right)\), and an alpha particle \(\left(m=4 m_{\mathrm{p}}, Q=2 e\right)\) are accelerated by the same potential difference V and then enter a uniform magnetic field \(\overrightarrow{\mathbf{B}}\), where they move in circular paths perpendicular to \(\overrightarrow{\mathbf{B}}\). Determine the radius of the paths for the deuteron and alpha particle in terms of that for the proton.

Problem 20Q A charged particle moves in a straight line through a particular region of space. Could there be a nonzero magnetic field in this region? If so. give two possible situations.

Problem 26Q A horizontal current-carrying wire, free to move in Earth's gravitational field, is suspended directly above a parallel, current-carrying wire, (a) In what direction is the current in the lower wire? (b) Can the lower wire be held in stable equilibrium due to the magnetic force of the upper wire? Explain.

If a moving charged particle is deflected sideways in some region of space, can we conclude, for certain, that \(\overrightarrow{\mathbf{B}} \neq 0\) in that region? Explain.

Problem 27Q Why will either pole of a magnet attract an unmagnetized piece of iron?

An unmagnetized nail will not attract an unmagnetized paper clip. However, if one end of the nail is in contact with a magnet, the other end will attract a paperclip. Explain.

Two ions have the same mass, but one is singly ionized and the other is doubly ionized. How will their positions on the film of a mass spectrometer (Fig. differ?

Problem 30Q What would be the effect on B inside a long solenoid if (a) the diameter of all the loops was doubled, (b) the spacing between loops was doubled, or (c) the solenoid’s length was doubled along with a doubling in the total number of loops?

A type of magnetic switch similar to a solenoid is a relay (Fig. A relay is an electromagnet (the iron rod inside the coil does not move) which, when activated, attracts a piece of iron on a pivot. Design a relay to close an electrical switch. A relay is used when you need to switch on a circuit carrying a very large current but you do not want that large current flowing through the main switch. For example, the starter switch of a car is connected to a relay so that the large current needed for the starter doesn't pass to the dashboard switch. FIGURE 20-50 Question 31

(II) Two long straight parallel wires are \(15 \mathrm{~cm}\) apart. Wire \(\mathrm{A}\) carries \(2.0 \mathrm{~A}\) current. Wire B's current is \(4.0 \mathrm{~A}\) in the same direction. (a) Determine the magnetic field magnitude due to wire \(\mathrm{A}\) at the position of wire B. (b) Determine the magnetic field due to wire B at the position of wire A. (c) Are these two magnetic fields equal and opposite? Why or why not? (d) Determine the force on wire A due to wire B, and the force on wire B due to wire A. Are these two forces equal and opposite? Why or why not?

(II) A toroid is a solenoid in the shape of a circle (Fig. 20-62). Use Ampère's law along the circular path, shown dashed in Fig. , to determine that the magnetic field inside the toroid is \(B=\mu_{0} N I / 2 \pi R\), where is the total number of turns, and outside the toroid is \(B=0\) Is the field inside a toroid uniform like a solenoid's? If not, how does it vary? FIGURE 20-62 Problem 52. (a) A toroid. (b) A section of the toroid showing direction of the current for three loops: \(\odot\) means current toward you, and \(\odot\) means current away from you. Equation Transcription: Text Transcription: B=\mu_{0} N I / 2 \pi R B=0 \odot \otimes

(III) Use Ampère's law to show that the magnetic field between the conductors of a coaxial cable (Fig. ) is \(B=\mu_{0} I / 2 \pi r\) if is greater than the radius of the inner wire and less than the radius of the outer cylindrical braid. (b) Show that \(B=0\) outside the coaxial cable. FIGURE 20-63 Coaxial cable Problem 53 Equation Transcription: Text Transcription: B=\mu_{0} I / 2 \pi r B=0

(I) If the current to a motor drops by 12%, by what factor does the output torque change?

Problem 61P (I) In a mass spectrometer, germanium atoms have radii of curvature equal to 21.0, 21.6, 21.9, 22.2, and 22.8 cm. The largest radius corresponds to an atomic mass of 76 u. What are the atomic masses of the other isotopes?

Problem 1P (a) What is the magnitude of the force per meter of length on a straight wire carrying an 8.40-A current when perpendicular to a 0.90-T uniform magnetic field? (b) What if the angle between the wire and field is 45.0°?

Problem 2P Calculate the magnitude of the magnetic force on a 160-m length of straight wire stretched between two towers carrying a 150-A current. The Earth’s magnetic field of 5.0 × 10?5 T makes an angle of 65° with the wire.

Problem 64P (II) One form of mass spectrometer accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an ion m =qB2R2/2V, is where R is the radius of the ions' path in the magnetic field and q is their charge.

Problem 2Q Draw the magnetic field lines around a straight section of wire carrying a current horizontally to the left.

(I) How much current is flowing in a wire 4.80 m long if the maximum force on it is 0.750 N when placed in a uniform 0.0800-T field?

(II) A 1.5-m length of wire carrying 4.5 A of current is oriented horizontally. At that point on the Earth’s surface, the dip angle of the Earth’s magnetic field makes an angle of \(38^\circ\) to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth’s magnetic field of \(5.5 \times 10^{?5} \ \mathrm {T}\) at this point.

A proton and an electron have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular paths?

Problem 5P The force on a wire carrying 8.75 A is a maximum of 1.28 N when placed between the pole faces of a magnet. If the pole faces are 55.5 cm in diameter, what is the approximate strength of the magnetic field?

Problem 71GP Near the equator, the Earth's magnetic field points almost horizontally to the north and has magnitude B=0.50*10-4 T. What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?

The magnetic force per meter on a wire is measured to be only 35% of its maximum possible value. Sketch the relationship of the wire and the field if the force had been a maximum, and sketch the relationship as it actually is, calculating the angle between the wire and the magnetic field.

(II) The force on a wire is a maximum of \(6.50 \times 10^{-2} \mathrm{~N}\) when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is observed to "jump" toward the observer when the current is turned on. (a) What type of magnetic pole is the top pole face? (b) If the pole faces have a diameter of \(10.0 \mathrm{~cm}\), estimate the current in the wire if the field is \(0.16 \mathrm{~T}\). (c) If the wire is tipped so that it makes an angle of \(10.0^{\circ}\) with the horizontal, what force will it now feel?

Problem 9P Alpha particles of charge q = +2e and mass m = 6.6 × 10?27 kg are emitted from a radioactive source at a speed of 1.6 × 107m/s. What magnetic field strength would be required to bend them into a circular path of radius r = 0.25 m?

Four very long straight parallel wires, located at the corners of a square of side I, carry equal currents \(I_0\) perpendicular to the page as shown in Fig. 20-68. Determine the magnitude and direction of \(\vec {\mathbf{B}}\) at the center C of the square.

Magnetic fields are very useful in particle accelerators for "beam steering"; that is, the magnetic fields can be used to change the beam's direction without altering its speed (Fig. 20-69). Show how this works with a beam of protons. What happens to protons that are not moving with the speed that the magnetic field is designed for? If the field extends over a region wide and has a magnitude of , by approximately what angle will a beam of protons traveling at \(1.0 \times 10^{7} \mathrm{~m} / \mathrm{s}\) be bent? FIGURE 20-69 Problem 79 . Equation Transcription: Text Transcription: 1.0 x 107 m/s

Problem 10P Determine the magnitude and direction of the force on an electron traveling 8.75 × 105 m/s horizontally to the east in a vertically upward magnetic field of strength 0.75 T.

The magnetic field at the center of a circular coil of wire carrying a current (as in Fig. ) is \(B=\frac{\mu_{0} N I}{2 r}\) where is the number of loops in the coil and is its radius. Suppose that an electromagnet uses a coil in diameter made from square copper wire on a side. The power supply produces at a maximum power output of . How many turns are needed to run the power supply at maximum power? (b) What is the magnetic field strength at the center of the coil? (c) If you use a greater number of turns and this same power supply (so the voltage remains at ), will a greater magnetic field strength result? Explain. Equation Transcription: Text Transcription: B=\frac{\mu_0 N I 2 r

(I) Find the direction of the force on a negative charge for each diagram shown in Fig. , where \(\vec{v}\) (green) is the velocity of the charge and \(\vec{B}\) (blue) is the direction of the magnetic field. (\(\otimes\) means the vector points inward. \(\odot\) means it points outward, toward you.) FIGURE 20-51 Problem 11. Equation Transcription: Text Transcription: \vec{v} \vec{B} \otimes \odot

Problem 83GP (a) What value of magnetic field would make a beam of electrons, traveling to the west at a speed of 4.8*106 m/s. go undeflected through a region where there is a uniform electric field of12000 V/m pointing south? (b) What is the direction of the magnetic field if it is perpendicular to the electric field? (c) What is the frequency of the circular orbit of the electrons if the electric field is turned off?

(I) Determine the direction of \(\vec{B}\) for each case in Fig. 20-52, where \(\vec{F}\) represents the maximum magnetic force on a positively charged particle moving with velocity \(\vec{v}\). FIGURE 20-52 Problem 12. Equation Transcription: Text Transcription: \vec{B} \vec{F} \vec{v}

A proton follows a spiral path through a gas in a magnetic field of , perpendicular to the plane of the spiral, as shown in Fig. . In two successive loops, at points and , the radii are \(10.0 \mathrm{~mm} \text { and } 8.5 \mathrm{~mm}\) respectively. Calculate the change in the kinetic energy of the proton as it travels from to . FIGURE 20-70 Problem 84. Equation Transcription: Text Transcription: 10.0 mm and 8.5 mm

An electron enters a uniform magnetic field \(B=0.23 \mathrm{~T}\) at a \(45^{u}\) angle to \(\vec{B}\). Determine the radius and pitch (distance between loops) of the electron's helical path assuming its speed is \(3.0 \times 10^{6} \mathrm{~m} / \mathrm{s}\). See Fig. . FIGURE 20-72 Problem 87. Equation Transcription: Text Transcription: B=0.23 T 45u \vec B 3.0 x 106 m/s

Problem 16P What is the velocity of a beam of electrons that go undeflected when passing through perpendicular electric and magnetic fields of magnitude 8.8 ×103 V/m and 3.5 × 10?3 T, respectively? What is the radius of the electron orbit if the electric field is turned off?

Problem 17P A doubly charged helium atom whose mass is 6.6 × 10?27 kg is accelerated by a voltage of 2100 V. (a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340-T field? (b) What is its period of revolution?

The force on a particle in a magnetic field is the idea behind electromagnetic pumping. It is used to pump metallic fluids (such as sodium) and to pump blood in artificial heart machines. The basic design is shown in Fig. 20-48. An electric field is applied perpendicular to a blood vessel and to a magnetic field. Explain how ions are caused to move. Do positive and negative ions feel a force in the same direction?

A beam of electrons is directed toward a horizontal wire carrying a current from left to right (Fig. 20-49). In what direction is the beam deflected? FIGURE 20-48 Question 18

Problem 19Q Describe electric and/or magnetic fields that surround a moving electric charge.

(II) Show that the time required for a particle of charge moving with constant speed to make one circular revolution in a uniform magnetic field \(\vec{B}(\perp \vec{v})\) is \(T=\frac{2 \pi m}{q B}\) [Hint: see Example and Chapter ] Equation Transcription: Text Transcription: \vec{B}(\perp \vec{v}) T=\frac{2 \pi m}{q B}

Problem 20P A particle of charge q moves in a circular path of radius r in a uniform magnetic field B. Show that its momentum is p = qBr.

(II) A particle of mass m and charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is proportional to \(r^2\), the square of the radius of curvature of its path.

Problem 22P Show that the angular momentum of the particle in Problem 21 is L = qBr2 about the center of the circle. Problem 21 A particle of mass m and charge q moves in a circular path in a magnetic field B. Show that its kinetic energy is proportional to r2, the square of the radius of curvature of its path.

In a particular region of space there is a uniform magnetic field \(\vec{B}\). Outside this region, \(B=0\).Can you inject an electron from outside into the field perpendicularly so that it will move in a closed circular path in the field? What if the electron is injected near the center? Equation Transcription: Text Transcription: \vec{B} B=0

(III) A \(3.40-\mathrm{g}\) bullet moves with a speed of \(160 \mathrm{~m} / \mathrm{s}\) perpendicular to the Earth's magnetic field of \(5.00 \times 10^{-5} \mathrm{~T}\). If the bullet possesses a net charge of \(13.5 \times 10^{-9} \mathrm{C}\). by what distance will it be deflected from its path due to the Earth's magnetic field after it has traveled \(1.00 \mathrm{~km}\)?

How could you tell whether moving electrons in a certain region of space are being deflected by an electric field or by a magnetic field (or by both)?

(III) Suppose the Earth's magnetic field at the equator has magnitude \(0.40 \times 10^{-4} \mathrm{~T}\) and a northerly direction at all points. Estimate the speed a singly ionized uranium ion \((m=238 \mathrm{u}, q=e\) ) would need to circle the Earth \(5.0 \mathrm{~km}\) above the equator. Can you ignore gravity?

How can you make a compass without using iron or other ferromagnetic material?

(III) A proton moving with speed \(v=2.0 \times 10^{5} \mathrm{~m} / \mathrm{s}\) in a field-free region abruptly enters essentially uniform magnetic \(B=0.850 T(\vec{B} \perp \vec{v})\). If the enters the magnetic field region \(45^{\circ}\) angle as shown in Fig. (a) at what angle does it leave, (b) at what distance does it field? FIGURE 20-53 Problem 25 Equation Transcription: Text Transcription: v=2.0 \times 10^5m /s B=0.850 T(\vec B \perp \vec v) 45^\circ

Two long wires carrying equal currents I are at right angles to each other, but don’t quite touch. Describe the magnetic force one exerts on the other.

(I) A jumper cable used to start a stalled vehicle carries a 65-A current. How strong is the magnetic field 6.0 cm away from it? Compare to the Earth’s magnetic field.

(I) If an electric wire is allowed to produce a magnetic field no larger than that of the Earth \(\left(0.55 \times 10^{-4} \mathrm{~T}\right)\) at a distance of \(25 \mathrm{~cm}\), what is the maximum current the wire can carry?

(I) In Fig. , a long straight wire carries current out of the page toward you. Indicate, with appropriate arrows, the direction of \(\vec{B}\) at each of the points C, D, and E in the plane of the page. FIGURE 20-54 Problem 28 Equation Transcription: Text Transcription: \vec{B}

(I) A vertical straight wire carrying an upward 24-A current exerts an attractive force per unit length of \(8.8 \times 10^{-4} \mathrm{~N} / \mathrm{m}\) on a second parallel wire 7.0 cm away. What current (magnitude and direction) flows in the second wire?

Problem 30P Determine the magnitude and direction of the force between two parallel wires 35 m long and 6.0 cm apart, each carrying 25 A in the same direction.

(II) An experiment on the Earth's magnetic field is being carried out \(1.00 \mathrm{~m}\) from an electric cable. What is the maximum allowable current in the cable if the experiment is to be accurate to \(\pm 1.0 \%\) ?

(II) A power line carries a current of along the tops of \(8.5-m \) -high poles. What is the magnitude of the magnetic field produced by this wire at the ground? How does this compare with the Earth's field of about \(\frac{1}{2} G\) ? Equation Transcription: Text Transcription: 8.5-m \frac{1}{2} G

(II) Two long thin parallel wires \(13.0 \mathrm{~cm}\) apart carry \(25-A\) currents in the same direction. Determine the magnetic field at point \(P, 12.0 \mathrm{~cm}\) from one wire and \(5.0 \mathrm{~cm}\) from the other (Fig. 20-55). FIGURE 20-55 Problem 33. Equation Transcription: Text Transcription: 13.0 cm 25-A P, 12.0 cm 5.0 cm

Problem 34P A horizontal compass is placed 18 cm due south from a straight vertical wire carrying a 35-A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth’s field at this point is 0.45 × 10?4 T and the magnetic declination is 0°.

(II) A straight stream of protons passes a given point in space at a rate of \(1.5 \times 10^9 protons / \mathrm{s}\). What magnetic field do they produce \(2.0 \mathrm{~m}\) from the beam?

Problem 35P A long horizontal wire carries 22.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points north but downward, 37° below the horizontal, and has magnitude 5.0 × 10?4 T?

(II) Determine the magnetic field midway between two long straight wires 2.0 cm apart in terms of the current I in one when the other carries 15 A. Assume these currents are (a) in the same direction, and (b) in opposite directions.

(II) A long pair of wires conducts \(25.0 \mathrm{~A}\) of de current to, and from, an instrument. If the insulated wires are of negligible diameter but are \(2.8 \mathrm{~mm}\) apart, what is the magnetic field \(10.00 \mathrm{~cm}\) from their midpoint, in their plane (Fig. ? Compare to the magnetic field of the Earth. FIGURE 20-56 Problem 38 and 39. Equation Transcription: Text Transcription: 25.0 A 2.8 mm 10.00 cm

(II) A third wire is placed in the plane or the two wires shown in Fig. , parallel and just to the right. If it carries \(25.0 \mathrm{~A}\) upward, what force per meter of length does it exert on each of the other two wires? Assume it is \(2.8 \mathrm{~mm}\) from the nearest wire, center to center. FIGURE 20-56 Problem 38 and 39. Equation Transcription: Text Transcription: 25.0 A 2.8 mm

Problem 40P A compass needle points 23° E of N outdoors. However, when it is placed 12.0 cm to the cast of a vertical wire inside a building, it points 55° E of N. What are the magnitude and direction of the current in the wire? The Earth’s field there is 0.50 × 10?4 T and is horizontal.

A rectangular loop of wire lies in the same plane as a straight wire, as shown in Fig, 20-57. There is a current of 2.5 A in both wires. Determine the magnitude and direction of the net force on the loop.

(II) A long horizontal wire carries a current of 48 A. A second wire, made of 2.5 - mm -diameter copper wire and parallel to the first, is kept in suspension magnetically 15 cm below (Fig. 20-58). (a) Determine the magnitude and direction of the current in the lower wire. (b) Is the lower wire in stable equilibrium? (c) Repeat parts (a) and (b) if the second wire is suspended 15 cm above the first due to the latter's field.

(II) Two long wires are oriented so that they are perpendicular to each other. At their closest, they are \(20.0 . \mathrm{cm}\) apart (Fig. . What is the magnitude of the magnetic field at a point midway between them if the top one carries a current of \(20.0 \mathrm{~A}) and the bottom one carries \(5.0 \mathrm{~A}\) ? FIGURE 20-59 Problem 43. Equation Transcription: Text Transcription: 20.0. cm 20.0 A 5.0 A

Three long parallel wires are \(3.8 \mathrm{~cm}\) from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is \(8.00 \mathrm{~A}\), but its direction in wire M is opposite to that in wires N and P (Fig. 20-60). Determine the magnetic force per unit length on each wire due to the other two.

(II) In Fig. , determine the magnitude and direction of the magnetic field at the midpoint of the side of the triangle between wire and wire . FIGURE 20-60 Problems 45,46 , and 74 .

(II) Let two long parallel wires, a distance d apart, carry equal currents I in the same direction. One wire is at x = 0, the other is at x = d Fig. 20-61. Determine \(\vec{B}\) along the x axis between the wires as a function of x.

(I) A thin 12-cm-long solenoid has a total of 420 turns of wire and carries a current of \(2.0 \mathrm{~A}\). Calculate the field inside near the center.

(I) A 30.0 -cm long solenoid 1.25 cm in diameter is to produce a field of 0.385 T at its center. How much current should the solenoid carry if it has 975 turns of the wire?

(II) A 550-turn solenoid is 15 cm long. The current in it is 33 A. A 3.0-cm-long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22-A current downward (and is connected by other wires that don’t concern us). What is the force on this wire assuming the solenoid’s field points due east?

(III) You have \(1.0 \mathrm{~kg}\) of copper and want to make a practical solenoid that produces the greatest possible magnetic field for a given voltage. Should you make your copper wire long and thin, short and fat, or something else? Consider other variables, such as solenoid diameter, length, and so on.

Problem 54P A single square loop of wire 22.0 cm on a side is placed with its face parallel to the magnetic field between the pole pieces of a large magnet. When 6.30 A flows in the coil, the torque on it is 0.325 m·N. What is the magnetic field strength?

Problem 55P A galvanometer needle deflects full scale for a 53.0-µA current.What current will give full-scale deflection if the magnetic field weakens to 0.860 of its original value?

Problem 56P If the restoring spring of a galvanometer weakens by 25% over the year, what current will give full-scale deflection if it originally required 36 µA?

(II) Show that the magnetic dipole moment M of an electron orbiting the proton nucleus of a hydrogen atom is related to the orbital angular momentum L of the electron by \(M=\frac{e}{2 m} L\).

(II) A circular coil 16.0 cm in diameter and containing nine loops lies flat on the ground. The Earth’s magnetic field at this location has magnitude \(5.50 \times 10^{?5} T\) and points into the Earth at an angle of \(56.0^\circ\) below a line pointing due north. If a 7.20-A clockwise current passes through the coil, (a) determine the torque on the coil, and (b) which edge of the coil rises up: north, east, south, or west?

Problem 60P Protons move in a circle of radius 5.10 cm in a 0.566-T magnetic field. What value of electric field could make their paths straight? In what direction must it point?

(II) Suppose the electric field between the electric plates in the mass spectrometer of Fig. 20-39 is \(2.48 \times 10^{4} \mathrm{~V} / \mathrm{m}\) and the magnetic fields \(B=B^{\prime}=0.68 \mathrm{~T}\). The source contains carbon isotopes of mass numbers 12,13, and 14 from a long-dead piece of a tree. (To estimate atomic masses, multiply by \(1.67 \times 10^{-27} \mathrm{~kg}\).) How far apart are the lines formed by the singly charged ions of each type on the photographic film? What if the ions were doubly charged?

(II) A mass spectrometer is being used to monitor air pollutants. It is difficult, however, to separate molecules with nearly equal mass such as CO (28.0106 u) and \(\mathrm {N}_2\) (28.0134 u). How large a radius of curvature must a spectrometer have if these two molecules are to be separated on the film by 0.50 mm?

Problem 65P A long thin solenoid has 430 loops of wire per meter, and a 25-A current flows through the wire. If the permeability of the iron is 3000µ0, what is the total field B inside the solenoid?

(II) An iron-core solenoid is \(38 \mathrm{~cm}\) long and \(1.8 \mathrm{~cm}\) in diameter, and has 640 turns of wire. The magnetic field inside the solenoid is \(2.2 \mathrm{~T}\) when \(48 \mathrm{~A}\) flows in the wire. What is the permeability \(\mu\) at this high field strength?

Protons with momentum \(4.8 \times 10^{-16} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}\) are magnetically steered clockwise in a circular path \(2.0 \mathrm{~km}\) in diameter at Fermi National Accelerator Laboratory in Illinois. Determine the magnitude and direction of the field in the magnets surrounding the beam pipe.

The power cable for an electric trolley (Fig. ) carries a horizontal current of toward the east. The Earth's magnetic field has a strength \(5.0 \times 10^{-5} T\) and makes an angle of dip of at this location. Calculate the magnitude and direction of the magnetic force on a \(15-m\) length of this cable. FIGURE 20-64 Problem 69. Equation Transcription: Text Transcription: 5.0 x 10^-5T 15-m

Problem 70GP Calculate the force on an airplane which has acquired a net charge of 1550 µC and moves with a speed of 120 m/s perpendicular to the Earth’s magnetic field of 5.0 × 10?5 T.

A doubly charged helium atom, whose mass is \(6.6 \times 10^{-27}~\mathrm {kg}\), is accelerated by a voltage of 2400 V. (a) What will be its radius of curvature in a uniform 0.240-T field? (b) What is its period of revolution?

A sort of "projectile launcher" is shown in Fig. 20-65. A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. If the bar has a length \(L=22 \mathrm{~cm}\), a mass of \(1.5 \mathrm{~g}\), and is placed in a field of \(1.7 \mathrm{~T}\), what constant current flow is needed to accelerate the bar from rest to \(28 \mathrm{~m} / \mathrm{s}\) in a distance of \(1.0 \mathrm{~m}\)? In what direction must the magnetic field point?

In Fig. the top wire is \(1.00-\mathrm{mm}\) -diameter copper wire and is suspended in air due to the two magnetic forces from the bottom two wires. The current flow through the two bottom wires is in each. Calculate the required current flow in the suspended wire. Equation Transcription: Text Transcription: 1.00-mm

Two stiff parallel wires a distance apart in a horizontal plane act as rails to support a light metal rod of mass (perpendicular to each rail). Fig. A magnetic field \(\vec{B}\). directed vertically upward (outward in the diagram), acts throughout. At \(t=0\), wires connected to the rails are connected to a constant current source and a current begins to flow through the system. Determine the speed of the rod, which starts from rest at \(t=0\), as a function of time (a) assuming no friction between the rod and the rails, and if the coefficient of friction is \(\mu_{k}\). (c) Does the rod move east or west if the current through it heads north? FIGURE 20-66 Looking down on a rod sliding on rails. Problem 75 . Equation Transcription: Text Transcription: \vec{B} t=0 t=0 \mu_{k}

Problem 76GP Estimate the approximate maximum deflection of the electron beam near the center of a TV screen due to the Earth’s 5.0 × 10?5 T field. Assume the CRT screen (Section 17-10) is 22 cm from the electron gun, where the electrons are accelerated (a) by 2.0 kV, or (b) by 30 kV. Note that in color TV sets, the CRT beam must be directed accurately to within less than 1 mm in order to strike the correct phosphor. Because the Earth’s field is significant here, mu-metal shields are used to reduce the Earth’s field in the CRT.

The cyclotron (Fig. 20-67) is a device used to accelerate elementary particles such as protons to high speeds. Particles starting at point A with some initial velocity travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass through the gap between the metal "dees," where there is an electric field E. (There is no electric field inside the hollow metal dees.) The electric field changes direction each half-cycle, owing to an ac voltage \(V=V_{0} \sin 2 \pi f t\), so that the particles are increased in speed at each passage through the gap. (a) Show that the frequency \(f\) of the voltage must be \(f=B q / 2 \pi m\), where q is the charge on the particles and m their mass. (b) Show that the kinetic energy of the particles increases by \(2 q V_{0}\) each revolution, assuming that the gap is small. (c) If the radius of the cyclotron is 2.0 m and the magnetic field strength is 0.50 T, what will be the maximum kinetic energy of accelerated protons in MeV? FIGURE 20-67 A cyclotron. Problem 77 . Equation Transcription: V=V0 sin? 2?ft f=Bq/2?m 2qV0 Text Transcription: V=V_0 sin? 2pi ft f=Bq/2pi m 2qV_0

You want to get an idea of the magnitude of magnetic fields produced by overhead power lines. You estimate that the two wires are each about 30 m above the ground and are about 3 m apart. The local power company tells you that the lines operate at 10 kV and provide a maximum of 40 MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth’s field. [For an ac current, values are rms, and the magnetic field will be changing.]

Near the Earth's poles the magnetic field is about \(I G\left(1 \times 10^{-4} T\right)\). Imagine a simple model in which the Earth's field is produced by a single current loop around the equator. Roughly estimate the current this loop would carry. [Hint: use the formula given in Problem Equation Transcription: Text Transcription: IG (1 x 10-4T)

Problem 85GP A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum cunent is 5.7 A, how many turns must the solenoid have?

Two long straight aluminum wires, each of diameter \(0.50 \mathrm{~mm}\), carry the same current but in opposite directions. They are suspended by \(0.50-m\) -long strings as shown in Fig. . If the suspension strings make an angle of \(3.0^{\circ}\) with the vertical, what is the current in the wires? FIGURE 20-71 Problem 86 . Equation Transcription: Text Transcription: 0.50 mm 0.50-m 3.0°