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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

A current balance is a device to measure magnetic forces. It is constructed from two parallel coils, each with an average radius of 12.5 cm. The lower coil rests on a balance; it has 20 turns and carries a constant current of 4.0 A. The upper coil, suspended 0.314 cm above the lower coil, has 50
In a certain region of space, there is a uniform electric field E = 3.0 × 104 V/m directed due east and a uniform magnetic field B = 0.080 T also directed due east. What is the electromagnetic force on an electron moving due south at 5.0 × 106 m/s?
A uniform magnetic field points vertically upward; its magnitude is 0.800 T. An electron with kinetic energy 7.2 × 10−18 J is moving horizontally eastward in this field. What is the magnetic force acting on it?
An early cyclotron at Cornell University was used from the 1930s to the 1950s to accelerate protons, which would then bombard various nuclei. The cyclotron used a large electromagnet with an iron yoke to produce a uniform magnetic field of 1.3 T over a region in the shape of a flat cylinder. Two
In a certain region of space, there is a uniform electric field E = 2.0 × 104 V/m to the east and a uniform magnetic field B = 0.0050 T to the west. (a) What is the electromagnetic force on an electron moving north at 1.0 × 107 m/s? (b) With the electric and magnetic fields as specified, is there
An electron moves in a circle of radius R in a uniform magnetic field B. The field is into the page.(a) Does the electron move clockwise or counterclockwise? (b) How much time does the electron take to make one complete revolution? Derive an expression for the time, starting with the magnetic force
A proton moves in a helical path at speed v = 4.0 × 107 m/s high above the atmosphere, where Earth's magnetic field has magnitude B = 1.0 × 10−6 T. The proton's velocity makes an angle of 25° with the magnetic field. (a) Find the radius of the helix. (b) Find the pitch of the helix-the
Find the magnetic force on the electron at point a.Several electrons move at speed 8.0 Ã— 105 m/s in a uniform magnetic field with magnitude B = 0.40 T directed downward.
Find the magnetic force on the electron at point b.Several electrons move at speed 8.0 Ã— 105 m/s in a uniform magnetic field with magnitude B = 0.40 T directed downward.
Find the magnetic force on the electron at point c.Several electrons move at speed 8.0 Ã— 105 m/s in a uniform magnetic field with magnitude B = 0.40 T directed downward.
Electrons in a television's CRT are accelerated from rest by an electric field through a potential difference of 2.5 kV. In contrast to an oscilloscope, where the electron beam is deflected by an electric field, the beam is deflected by a magnetic field. (a) What is the speed of the electrons? (b)
A magnet produces a 0.30-T field between its poles, directed to the east. A dust particle with charge q = − 8.0 × 10−18 C is moving straight down at 0.30 cm/s in this field. What is the magnitude and direction of the magnetic force on the dust particle?
At a certain point on Earth's surface in the southern hemisphere, the magnetic field has a magnitude of 5.0 × 10−5 T and points upward and toward the north at an angle of 55° above the horizontal. A cosmic ray muon with the same charge as an electron and a mass of 1.9 × 10−28 kg is moving
An electron beam in vacuum moving at 1.8 Ã— 107 m/s passes between the poles of an electromagnet. The diameter of the magnet pole faces is 2.4 cm and the field between them is 0.20 Ã— 10ˆ’2 T. How far and in what direction is the beam deflected when it hits the
A positron (q = +e) moves at 5.0 × 107 m/s in a magnetic field of magnitude 0.47 T. The magnetic force on the positron has magnitude 2.3 × 10−12 N. (a) What is the component of the positron's velocity perpendicular to the magnetic field? (b) What is the component of the positron's velocity
Draw vector arrows to indicate the direction and relative magnitude of the magnetic field at each of the points A - F.
An electron moves with speed 2.0 × 105 m/s in a 1.2-T uniform magnetic field. At one instant, the electron is moving due west and experiences an upward magnetic force of 3.2 × 10−14 N. What is the direction of the magnetic field? Be specific: give the angle(s) with respect to N, S, E, W, up,
An electron moves with speed 2.0 × 105 m/s in a uniform magnetic field of 1.4 T, pointing south. At one instant, the electron experiences an upward magnetic force of 1.6 × 10−14 N. In what direction is the electron moving at that instant? Be specific: give the angle(s) with respect to N, S, E,
The magnetic field in a cyclotron is 0.50 T. Find the magnitude of the magnetic force on a proton with speed 1.0 × 107 m/s moving in a plane perpendicular to the field.
An electron moves at speed 8.0 × 105 m/s in a plane perpendicular to a cyclotron's magnetic field. The magnitude of the magnetic force on the electron is 1.0 × 10−13 N. What is the magnitude of the magnetic field?
When two particles travel through a region of uniform magnetic field pointing out of the plane of the paper, they follow the trajectories shown. What are the signs of the charges of each particle?
The magnetic field in a cyclotron is 0.360 T. The dees have radius 82.0 cm. What maximum speed can a proton achieve in this cyclotron?
The magnetic field in a cyclotron is 0.50 T. What must be the minimum radius of the dees if the maximum proton speed desired is 1.0 × 107 m/s?
A singly charged ion of unknown mass moves in a circle of radius 12.5 cm in a magnetic field of 1.2 T. The ion was accelerated through a potential difference of 7.0 kV before it entered the magnetic field. What is the mass of the ion?
Natural carbon consists of two different isotopes (excluding14 C, which is present in only trace amounts). The isotopes have different masses, Which is due to different numbers of neutrons in the nucleus; however, the number of protons is the same, and subsequently the chemical properties are the
After being accelerated through a potential difference of 5.0 kV, a singly charged carbon ion (12C+) moves in a circle of radius 21 cm in the magnetic field of a mass spectrometer. What is the magnitude of the field? The conversion between atomic mass units and kilograms is 1 u = 1.66 × 10−27 kg
Two identical bar magnets lie next to one another on a table. Sketch the magnetic field lines if the north poles are at the same end.
A sample containing carbon (atomic mass 12 u), oxygen (16 u), and an unknown element is placed in a mass spectrometer. The ions all have the same charge and are accelerated through the same potential difference before entering the magnetic field. The carbon and oxygen lines are separated by 2.250
A sample containing sulfur (atomic mass 32 u), manganese (55 u), and an unknown element is placed in a mass spectrometer. The ions have the same charge and are accelerated through the same potential difference before entering the magnetic field. The sulfur and manganese lines are separated by 3.20
In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12C+ and 14C+ ions that have the same charge. The 12C+ ions move in a circle of diameter 25 cm. (a) What is the diameter of the orbit of 14C+
Prove that the time for one revolution of a charged particle moving perpendicular to a uniform magnetic field is independent of its speed. (This is the principle on which the cyclotron operates.) In doing so, write an expression that gives the period T (the time for one revolution) in terms of the
Crossed electric and magnetic fields are established over a certain region. The magnetic field is 0.635 T vertically downward. The electric field is 2.68 × 106 V/m horizontally east. An electron, traveling horizontally northward, experiences zero net force from these fields and so continues moving
A current I = 40.0 A flows through a strip of metal. An electromagnet is switched on so that there is a uniform magnetic field of magnitude 0.30 T directed into the page.(a) How would you hook up a voltmeter to measure the Hall voltage? Show how the voltmeter is connected on a sketch of the
In Problem 35, if the width of the strip is 3.5 cm, the magnetic field is 0.43 T, and the Hall voltage is measured to be 7.2 Î¼ V, what is the drift velocity of the carriers in the strip?
In Problem 35, the width of the strip is 3.5 cm, the magnetic field is 0.43 T, the Hall voltage is measured to be 7.2 Î¼V, the thickness of the strip is 0.24 mm, and the current in the wire is 54 A. What is the density of carriers (number of carriers per unit volume) in the strip?
The strip in the diagram is used as a Hall probe to measure magnetic fields.(a) What happens if the strip is not perpendicular to the field? Does the Hall probe still read the correct field strength? Explain. (b) What happens if the field is in the plane of the strip?
A strip of copper 2.0 cm wide carries a current I = 30.0 A to the right. The strip is in a magnetic field B = 5.0 T into the page.(a) What is the direction of the average magnetic force on the conduction electrons?(b) The Hall voltage is 20.0 Î¼ V. What is the drift velocity?
Two identical bar magnets lie next to one another on a table. Sketch the magnetic field lines if the north poles are at opposite ends.
A proton is initially at rest and moves through three different regions as shown in the figure. In region 1, the proton accelerates across a potential difference of 3330 V. In region 2, there is a magnetic field of 1.20 T pointing out of the page and an electric field pointing perpendicular to the
An electromagnetic flow meter is used to measure blood flow rates during surgery. Blood containing Na+ ions flows due south through an artery with a diameter of 0.40 cm. The artery is in a downward magnetic field of 0.25 T and develops a Hall voltage of 0.35 mV across its diameter. (a) What is the
An electromagnetic flow meter is used to measure blood flow rates during surgery. Blood containing ions (primarily Na+) flows through an artery with a diameter of 0.50 cm, The artery is in a magnetic field of 0.35 T and develops a Hall voltage of 0.60 mV across its diameter. (a) What is the blood
A charged particle is accelerated from rest through a potential difference ΔV. The particle then passes straight through a velocity selector (field magnitudes E and B). Derive an expression for the charge-to-mass ratio (q/m) of the particle in terms of ΔV, E, and B.
A straight wire segment of length 0.60 m carries a current of 18.0 A and is immersed in a uniform external magnetic field of magnitude 0.20 T. (a) What is the magnitude of the maximum possible magnetic force on the wire segment? (b) Explain why the given information enables you to calculate only
A straight wire segment of length 25 cm carries a current of 33.0 A and is immersed in a uniform external magnetic field. The magnetic force on the wire segment has magnitude 4.12 N. (a) What is the minimum possible magnitude of the magnetic field? (b) Explain why the given information enables you
Parallel conducting tracks, separated by 2.0 cm, run north and south. There is a uniform magnetic field of 1.2 T pointing upward (out of the page). A 0.040-kg cylindrical metal rod is placed across the tracks and a battery is connected between the tracks, with its positive terminal connected to the
An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two conducting rails that are 0.500 m apart with a 50.0-g conducting rod connecting the two rails as in the figure with Problem 46. A magnetic field of magnitude 0.750 T is directed
A straight, stiff wire of length 1.00 m and mass 25 g is suspended in a magnetic field B = 0.75 T. The wire is connected to an emf. How much current must flow in the wire and in what direction so that the wire is suspended and the tension in the supporting wires is zero?
A 20.0 cm Ã— 30.0 cm rectangular loop of wire carries 1.0 A of current clockwise around the loop.(a) Find the magnetic force on each side of the loop if the magnetic field is 2.5 T out of the page. (b) What is the net magnetic force on the loop?
Two identical bar magnets lie on a table along a straight line with their north poles facing each other. Sketch the magnetic field lines.
Repeat Problem 49 if the magnetic field is 2.5 T to the left (in the ˆ’ x -direction).A 20.0 cm Ã— 30.0 cm rectangular loop of wire carries 1.0 A of current clockwise around the loop.(a) Find the magnetic force on each side of the loop if the magnetic field is 2.5 T out of the
A straight wire is aligned east-west in a region where Earth's magnetic field has magnitude 0.48 mT and direction 72° below the horizontal, with the horizontal component directed due north. The wire carries a current I toward the west. The magnetic force on the wire per unit length of wire has
Earth's magnetic field is directed 58.0° above the horizontal, with the horizontal component directed due north. The wire carries a current of 8.00 A toward the south. The magnetic force on the wire per unit length of wire has magnitude 2.80 × 10−3 N/m.(a) What is the direction of the magnetic
In an electric motor, a circular coil with 100 turns of radius 2.0 cm can rotate between the poles of a magnet. When the current through the coil is 75 mA, the maximum torque that the motor can deliver is 0.0020 N ˆ™ m.(a) What is the strength of the magnetic field?(b) Is the torque on
In an electric motor, a coil with 100 turns of radius 2.0 cm can rotate between the poles of a magnet. The magnetic field strength is 0.20 T. When the current through the coil is 50.0 mA, what is the maximum torque that the motor can deliver?
A square loop of wire of side 3.0 cm carries 3.0 A of current. A uniform magnetic field of magnitude 0.67 T makes an angle of 37° with the plane of the loop. (a) What is the magnitude of the torque on the loop? (b) What is the net magnetic force on the loop?
The torque on a loop of wire (a magnetic dipole) in a uniform magnetic field is τ = NIAB sin θ, where θ is the angle between B and a line perpendicular to the loop of wire. Suppose an electric dipole, consisting of two charges ±q a fixed distance d apart is in a uniform electric field E. (a)
A certain fixed length L of wire carries a current I. (a) Show that if the wire is formed into a square coil, then the maximum torque in a given magnetic field B is developed when the coil has just one turn. (b) Show that the magnitude of this torque is τ = 1/16 L2IB.
Use the following method to show that the torque on an irregularly shaped planar loop is given by Eq. (19- 13a). The irregular loop of current in part(a) Of the figure carries current I. There is a perpendicular magnetic field B. To find the torque on the irregular loop, sum up the torques on each
A square loop of wire with side 0.60 m carries a current of 9.0 A as shown in the figure. When there is no applied magnetic field, the plane of the loop is horizontal and the non conducting, non magnetic spring (k = 550 N/m) is unstretched. A horizontal magnetic field of magnitude 1.3 T is now
Two identical bar magnets lie on a table along a straight line with opposite poles facing each other. Sketch the magnetic field lines.
Two wires each carry 10.0 A of current (in opposite directions) and are 3.0 mm apart. Calculate the magnetic field 25 cm away at point P, in the plane of the wires.
What is the magnetic field at point P if the currents instead both run to the left in Problem 61?
Point P is midway between two long, straight, parallel wires that run north-south in a horizontal plane. The distance between the wires is 1.0 cm. Each wire carries a current of 1.0 A toward the north. Find the magnitude and direction of the magnetic field at point P.
Repeat Problem 63 if the current in the wire on the east side runs toward the south instead. Point P is midway between two long, straight, parallel wires that run north-south in a horizontal plane. The distance between the wires is 1.0 cm. Each wire carries a current of 1.0 A toward the north. Find
A long straight wire carries a current of 3.2 A in the positive x -direction. An electron, traveling at 6.8 Ã— 106 m/s in the positive x - direction, is 4.6 cm from the wire. What force acts on the electron?
A long straight wire carries a current of 3.2 A in the positive x -direction. An electron, traveling at 6.8 Ã— 106 m/s in the positive x - direction, is 4.6 cm from the wire. What force acts on the electron?
Two long straight wires carry the same amount of current in the directions indicated. The wires cross each other in the plane of the paper. Rank points A, B, C, and D in order of decreasing field strength.
In Problem 67, find the magnetic field at points C and D when d = 3.3 cm and I = 6.50 A.
In Problem 67, find the magnetic field at points A and B when d = 6.75 cm and I = 57.0 mA.
The magnetic forces on a magnetic dipole result in a torque that tends to make the dipole line up with the magnetic field. In this problem we show that the electric forces on an electric dipole result in a torque that tends to make the electric dipole line up with the electric field.(a) For each
A solenoid of length 0.256 m and radius 2.0 cm has 244 turns of wire. What is the magnitude of the magnetic field well inside the solenoid when there is a current of 4.5 A in the wire?
Two long straight parallel wires separated by 8.0 cm carry currents of equal magnitude but heading in opposite directions. The wires are shown perpendicular to the plane of this page. Point P is 2.0 cm from wire 1, and the magnetic field at point P is 1.0 Ã— 10ˆ’2 T directed
Two parallel wires in a horizontal plane carry currents I1 and I2 to the right. The wires each have length L and are separated by a distance d.(a) What are the magnitude and direction of the field due to wire 1 at the location of wire 2?(b) What are the magnitude and direction of the magnetic force
Two concentric circular wire loops in the same plane each carry a current. The larger loop has a current of 8.46 A circulating clockwise and has a radius of 6.20 cm. The smaller loop has a radius of 4.42 cm. What is the current in the smaller loop if the total magnetic field at the center of the
A solenoid has 4850 turns per meter and radius 3.3 cm. The magnetic field inside has magnitude 0.24 T. What is the current in the solenoid?
Find the magnetic field at the center of the square.Four long parallel wires pass through the corners of a square with side 0.10 m. All four wires carry the same magnitude of current I = 10.0 A in the directions indicated.
Find the magnetic field at point P, the midpoint of the top side of the square.Four long parallel wires pass through the corners of a square with side 0.10 m. All four wires carry the same magnitude of current I = 10.0 A in the directions indicated.
Find the magnetic field at point R, the midpoint of the left side of the square.Four long parallel wires pass through the corners of a square with side 0.10 m. All four wires carry the same magnitude of current I = 10.0 A in the directions indicated.
Four long straight wires, each with current I overlap to form a square with side 2r.(a) Find the magnetic field at the center of the square.(b) Compare your answer with the magnetic field at the center of a circular loop of radius r carrying current.
Two parallel long straight wires are suspended by strings of length L = 1.2 m. Each wire has mass per unit length 0.050 kg/m. When the wires each carry 50.0 A of current, the wires swing apart.(a) How far apart are the wires in equilibrium? (Assume that this distance is small compared with L.) (b)
Find the magnetic force exerted on an electron moving vertically upward at a speed of 2.0 × 107 m/s by a horizontal magnetic field of 0.50 T directed north.
A number of wires carry currents into or out of the page as indicated in the figure.(a) Using loop 1 for AmpÃ¨re's law, what is the net current through the interior of the loop? (b) Repeat for loop 2.
An infinitely long, thick cylindrical shell of inner radius a and outer radius b carries a current I uniformly distributed across a cross section of the shell.(a) On a sketch of a cross section of the shell, draw some magnetic field lines. The current flows out of the page. Consider all regions ( r
In this problem, use AmpÃ¨re's law to show that the magnetic field inside a long solenoid is B = Î¼0nI. Assume that the field inside the solenoid is uniform and parallel to the axis and that the field outside is zero. Choose a rectangular path for AmpÃ¨re's law.(a) Write down B||Î”l for
A toroid is like a solenoid that has been bent around in a circle until its ends meet. The field lines are circular, as shown in the figure. What is the magnitude of the magnetic field inside a toroid of N turns carrying current I? Apply AmpÃ¨re's law, following a field line at a
The intrinsic magnetic dipole moment of the electron has magnitude 9.3 × 10−24 A∙m2. In other words, the electron acts as though it were a tiny current loop with NIA = 9.3 × 10−24 A∙m2. What is the maximum torque on an electron due to its intrinsic dipole moment in a 1.0-T magnetic field?
An electromagnet is made by inserting a soft iron core into a solenoid. The solenoid has 1800 turns, radius 2.0 cm, and length 15 cm. When 2.0 A of current flows through the solenoid, the magnetic field inside the iron core has magnitude 0.42 T. What is the relative permeability kB of the iron core?
The figure shows hysteresis curves for three different materials. A hysteresis curve is a plot of the magnetic field strength inside the material (B) as a function of the externally applied field (B0).(a) Which material would make the best permanent magnet? Explain.(b) Which would make the best
In a simple model, the electron in a hydrogen atom orbits the proton at a radius of 53 pm and at a constant speed of 2.2 × 106 m/s. The orbital motion of the electron gives it an orbital magnetic dipole moment. (a) What is the current I in this current loop? (b) What is the orbital dipole moment
A compass is placed directly on top of a wire (needle not shown). The current in the wire flows to the right. Which way does the north end of the needle point? Explain. (Ignore Earth's magnetic field.)
Find the magnetic force exerted on a proton moving east at a speed of 6.0 × 106 m/s by a horizontal magnetic field of 2.50 T directed north.
You want to build a cyclotron to accelerate protons to a speed of 3.0 × 107 m/s. The largest magnetic field strength you can attain is 1.5 T. What must be the minimum radius of the dees in your cyclotron? Show how your answer comes from Newton's second law.
A long straight wire carries a 4.70-A current in the positive x -direction. At a particular instant, an electron moving at 1.00 Ã— 107 m/s in the positive y -direction is 0.120 m from the wire. Determine the magnetic force on the electron at this instant. See the figure with Problem 65.
A uniform magnetic field of 0.50 T is directed to the north. At some instant, a particle with charge +0.020 μC is moving with velocity 2.0 m/s in a direction 30° north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b) What is the direction of the magnetic force?
Two identical long straight conducting wires with a mass per unit length of 25.0 g/m are resting parallel to each other on a table. The wires are separated by 2.5 mm and are carrying currents in opposite directions. (a) If the coefficient of static friction between the wires and the table is 0.035,
Two long insulated wires lie in the same horizontal plane. A current of 20.0 A flows toward the north in wire A and a current of 10.0 A flows toward the east in wire B. What is the magnitude and direction of the magnetic field at a point that is 5.00 cm above the point where the wires cross?
(a) A proton moves with uniform circular motion in a magnetic field of magnitude 0.80 T. At what frequency f does it circulate? (b) Repeat for an electron.
The concentration of free electrons in silver is 5.85 Ã— 1028 per m3. A strip of silver of thickness 0.050 mm and width 20.0 mm is placed in a magnetic field of 0.80 T. A current of 10.0 A is sent down the strip.(a) What is the drift velocity of the electrons? (b) What is the Hall
An electromagnetic flow meter is to be used to measure blood speed. A magnetic field of 0.115 T is applied across an artery of inner diameter 3.80 mm. The Hall voltage is measured to be 88.0 μV. What is the average speed of the blood flowing in the artery?
Two conducting wires perpendicular to the page are shown in cross section as gray dots in the figure. They each carry 10.0 A out of the page. What is the magnetic field at point P?

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