A uniform horizontal wire with a linear mass densityof

A wire of length 0.50 m carries a current of 0.10 A inthe positive x-direction, parallel to the ground. If thewire has a weight of 1.0 3 1022 N, what is the minimummagnitude magnetic field that exerts a magneticforce on the wire equal to the wires weight? (a) 0.20 T(b) 0.30 T (c) 0.40 T (d) 0.50 T (e) 0.60 T

An electron moves across Earths equator at a speedof 2.5 3 106 m/s and in a direction 35 N of E. Atthis point, Earths magnetic field has a direction duenorth, is parallel to the surface, and has a magnitudeof 0.10 3 1024 T. What is the force acting on the electrondue to its interaction with Earths magnetic field?(a) 5.1 3 10218 N due west (b) 4.0 3 10218 N towardEarths surface (c) 2.4 3 10218 N away from Earths surface(d) 3.3 3 10218 N toward Earths surface (e) 4.0 310218 N away from Earths surface

A rectangular coil of wire consisting of ten loops, eachwith length 0.20 m and width 0.30 m, lies in the xyplane.If the coil carries a current of 2.0 A, what isthe torque exerted by a magnetic field of magnitude0.010 T directed at an angle of 30.0 with respect to thepositive z-axis? (a) 1.2 3 1022 N ? m (b) 2.4 3 1022 N ? m(c) 6.0 3 1023 N ? m (d) 4.0 3 1023 N ? m (e) 3.0 31023 N ? m

A long wire carries a current of 1 A. Find the magnitudeof the magnetic field 2 m away from the wire.(a) 1 3 1023 T (b) 1 3 1024 T (c) 1 3 1026 T (d) 1 31027 T (e) 1 3 10210 T

A proton enters a constant magnetic field of magnitude0.050 T and traverses a semicircle of radius1.0 mm before leaving the field. What is the protonsspeed? (a) 1.6 3 103 m/s (b) 2.3 3 103 m/s (c) 2.8 3104 m/s (d) 1.8 3 102 m/s (e) 4.8 3 103 m/s

Estimate the magnitude of the magnetic force perunit length between a pair of parallel wires separatedby 2 m if they each carry a current of 3 A.(a) 1 3 1021 N/m (b) 1 3 1023 N/m (c) 1 3 1024 N/m(d) 1 3 1026 N/m (e) 1 3 1028 N/m

What is the magnitude of the magnetic field at thecore of a 120-turn solenoid of length 0.50 m carryinga current of 2.0 A? (a) 2.4 3 1024 T (b) 4.8 3 1025 T(c) 1.2 3 1026 T (d) 3.6 3 1025 T (e) 6.0 3 1024 T

A charged particle is traveling through a uniformmagnetic field. Which of the following statementsare true of the magnetic field? (There may be morethan one correct statement.) (a) It exerts a force onthe particle that is parallel to the field. (b) It exerts aforce on the particle along the direction of its motion.(c) It increases the kinetic energy of the particle. (d) Itexerts a force that is perpendicular to the directionof motion. (e) It doesnt change the magnitude of themomentum of the particle.

A spatially uniform magnetic field cannot exert a magneticforce on a particle in which of the following circumstances?(There may be more than one correctstatement.) (a) The particle is charged. (b) The particlemoves perpendicular to the field. (c) The particlemoves parallel to the field. (d) The magnitude of themagnetic field changes with time. (e) The particle is atrest.

A proton moving horizontally enters a region where auniform magnetic field is directed perpendicular tothe protons velocity, as shown in Figure MCQ19.10.After the proton enters the field, does it (a) deflectdownward, with its speed remaining constant; (b) continueto move in the horizontal direction with constantvelocity; (c) move in a circular orbit and becometrapped by the field; (d) deflect upward, moving in asemicircular path with constant speed, and exit thefield moving to the left; or (e) deflect out of the planeof the paper?

Two long, parallel wireseach carry the same currentI in the same direction(Fig. MCQ19.11). Isthe total magnetic fieldat the point P midwaybetween the wires (a) zero,(b) directed into the page,(c) directed out of the page, (d) directed to the left, or(e) directed to the right?

Two long, straight wires cross each other at rightangles, and each carries the same current as in FigureMCQ19.12. Which of the following statements are trueregarding the total magnetic field at the various pointsdue to the two wires? (There may be more than onecorrect statement.) (a) The field is strongest at pointsB and D. (b) The field is strongest at points A and C.(c) The field is out of the page at point B and into thepage at point D. (d) The field is out of the page at pointC and out of the page at point D. (e) The field has thesame magnitude at all four points.

A magnetic field exerts a torque on each of thecurrent-carrying single loops of wire shown in FigureMCQ19.13. The loops lie in the xy-plane, each carryingthe same magnitude current, and the uniform magneticfield points in the positive x-direction. Rank thecoils by the magnitude of the torque exerted on themby the field, from largest to smallest. (a) A, B, C (b) A,C, B (c) B, A, C (d) B, C, A (e) C, A, B

Two long, parallel wires carry currents of 20 A and 10 Ain opposite directions, as in Figure MCQ19.14. Whichof the following statements must be true? (There maybe more than one correct statement.) (a) In region Ithe magnetic field is into the page and is never zero.(b) In region II the field is into the page and can bezero. (c) In region III it is possible for the field to bezero. (d) In region I the magnetic field is out of thepage and is never zero. (e) There are no points wherethe field is zero.

A long, straight wire carriesa current I as in FigureMCQ19.15. Which ofthe following statementsare true regarding themagnetic field due tothe wire? (There may be more than one correct state-ment.) (a) The field is proportional to I/r and is outof the page at P. (b) The field is proportional to I/r 2and is out of the page at P. (c) The field is proportionalto I/r and is into the page at P. (d) The field strengthis proportional to I, but doesnt depend on r. (e) Thefield is proportional to I/r 2 and is into the page at P.

Solenoid A has length L and N turns, solenoid B haslength 2L and N turns, and solenoid C has length L/2and 2N turns. If each solenoid carries the same current,rank by the strength of the magnetic field in thecenter of each solenoid from largest to smallest. (a) A,B, C (b) A, C, B (c) B, C, A (d) C, A, B (e) C, B, A

At a certain instant, a proton is moving in the positivex-direction through a magnetic field in the negativez-direction. What is the direction of the magnetic forceexerted on the proton? (a) positive z-direction (b) negativez-direction (c) positive y-direction (d) negativey-direction (e) The force is zero.

Answer each question yes or no. Assume the motionsand currents mentioned are along the x-axis and fieldsare in the y-direction. (a) Does an electric field exerta force on a stationary charged object? (b) Does amagnetic field do so? (c) Does an electric field exert aforce on a moving charged object? (d) Does a magneticfield do so? (e) Does an electric field exert a force ona straight current-carrying wire? (f) Does a magneticfield do so? (g) Does an electric field exert a force ona beam of moving electrons? (h) Does a magnetic fielddo so?

A wire with a mass of 1.00 g/cm is placed on a horizontalsurface with a coefficient of friction of 0.200. Thewire carries a current of 1.50 A eastward and moveshorizontally to the north. What are the magnitude andthe direction of the smallest vertical magnetic field thatenables the wire to move in this fashion?

A conductor suspended bytwo flexible wires as shown inFigure P19.20 has a mass perunit length of 0.040 0 kg/m.(a) What current must existin the conductor for the tensionin the supporting wiresto be zero when the magneticfield is 3.60 T into the page? (b) What is the requireddirection for the current?

Consider the system pictured in Figure P19.21. A15-cm length of conductor of mass 15 g, free to movevertically, is placed between two thin, vertical conductors,and a uniform magnetic field acts perpendicularto the page. When a 5.0-A current is directed as shownin the figure, the horizontal wire moves upward at constantvelocity in the presence of gravity. (a) What forcesact on the horizontal wire, and under what conditionis the wire able to move upward at constant velocity?(b) Find the magnitude and direction of the minimummagnetic field required to move the wire at constantspeed. (c) What happens if the magnetic field exceedsthis minimum value? (The wire slides without frictionon the two vertical conductors.)

A metal rod of mass m carrying a current I glideson two horizontal rails a distance d apart. If the coefficientof kinetic friction between the rod and rails is mk,what vertical magnetic field is required to keep the rodmoving at a constant speed?

In Figure P19.23 the cube is40.0 cm on each edge. Fourstraight segments of wireab,bc, cd, and daform a closedloop that carries a current I 55.00 A in the direction shown.A uniform magnetic field ofmagnitude B 5 0.020 0 T isin the positive y-direction.Determine the magnitude and direction of the magneticforce on each segment.

A horizontal power line of length 58 m carries a currentof 2.2 kA as shown in Figure P19.24. Earths magneticfield at this location has a magnitude equal to5.0 3 1025 T and makes an angle of 65 with the powerline. Find the magnitude and direction of the magneticforce on the power line.

A wire is formed into a circle having a diameter of10.0 cm and is placed in a uniform magnetic field of3.00 mT. The wire carries a current of 5.00 A. Find themaximum torque on the wire.

A current of 17.0 mA is maintained in a single circularloop with a circumference of 2.00 m. A magnetic fieldof 0.800 T is directed parallel to the plane of the loop.What is the magnitude of the torque exerted by themagnetic field on the loop?

An eight-turn coilencloses an elliptical areahaving a major axis of 40.0cm and a minor axis of 30.0cm (Fig. P19.27). The coillies in the plane of the pageand carries a clockwise currentof 6.00 A. If the coil isin a uniform magnetic fieldof 2.00 3 1024 T directed toward the left of the page,what is the magnitude of the torque on the coil? Hint:The area of an ellipse is A 5 pab, where a and b are,respectively, the semimajor and semiminor axes of theellipse.

A rectangular loop consistsof 100 closely wrapped turnsand has dimensions 0.400 mby 0.300 m. The loop ishinged along the y-axis, andthe plane of the coil makesan angle of 30.0 with thex-axis (Fig. P19.28). What isthe magnitude of the torqueexerted on the loop by auniform magnetic field of0.800 T directed along the x-axis when the currentin the windings has a value of 1.20 A in the directionshown? What is the expected direction of rotation ofthe loop?

A 200-turn rectangular coil having dimensions of3.0 cm by 5.0 cm is placed in a uniform magneticfield of magnitude 0.90 T. (a) Find the current in thecoil if the maximum torque exerted on it by the magneticfield is 0.15 N ? m. (b) Find the magnitude of thetorque on the coil when the magnetic field makes anangle of 25 with the normal to the plane of the coil.

A copper wire is 8.00 m long and has a cross-sectionalarea of 1.00 3 1024 m2. The wire forms a one-turn loopin the shape of square and is then connected to a batterythat applies a potential difference of 0.100 V. If theloop is placed in a uniform magnetic field of magnitude0.400 T, what is the maximum torque that can acton it? The resistivity of copper is 1.70 3 1028 V ? m.

A long piece of wire with a mass of 0.100 kg and a totallength of 4.00 m is used to make a square coil with aside of 0.100 m. The coil is hinged along a horizontalside, carries a 3.40-A current, and is placed in a verticalmagnetic field with a magnitude of 0.010 0 T.(a) Determine the angle that the plane of the coilmakes with the vertical when the coil is in equilibrium.(b) Find the torque acting on the coil due to the magneticforce at equilibrium.

A rectangular loophas dimensions 0.500 mby 0.300 m. The loop ishinged along the x-axisand lies in the xy-plane(Fig. P19.32). A uniformmagnetic field of 1.50 Tis directed at an angle of40.0 with respect to thepositive y-axis and lies parallel everywhere to the yzplane.The loop carries a current of 0.900 A in thedirection shown. (Ignore gravitation.) (a) In whatdirection is magnetic force exerted on wire segmentab? What is the direction of the magnetic torque associatedwith this force, as computed with respect tothe x-axis? (b) What is the direction of the magneticforce exerted on segment cd? What is the direction ofthe magnetic torque associated with this force, againcomputed with respect to the x-axis? (c) Can the forcesexamined in parts (a) and (b) combine to cause theloop to rotate around the x-axis? Can they affect themotion of the loop in any way? Explain. (d) What isthe direction (in the yz-plane) of the magnetic forceexerted on segment bc? Measuring torques with respectto the x-axis, what is the direction of the torque exertedby the force on segment bc? (e) Looking toward the originalong the positive x-axis, will the loop rotate clockwiseor counterclockwise? (f) Compute the magnitudeof the magnetic moment of the loop. (g) What is theangle between the magnetic moment vector and themagnetic field? (h) Compute the torque on the loopusing the values found for the magnetic moment andmagnetic field.

An electron moves in a circular path perpendicular toa magnetic field of magnitude 0.235 T. If the kineticenergy of the electron is 3.30 3 10219 J, find (a) thespeed of the electron and (b) the radius of the circularpath.

A proton travels with a speed of 5.02 3 106 m/s at anangle of 60 with the direction of a magnetic field ofmagnitude 0.180 T in the positive x-direction. Whatare (a) the magnitude of the magnetic force on theproton and (b) the protons acceleration?

Figure P19.35a is a diagram of a device called a velocityselector, in which particles of a specific velocity passthrough undeflected while those with greater or lesservelocities are deflected either upwards or downwards.An electric field is directed perpendicular to a magneticfield, producing an electric force and a magneticforce on the charged particle that can be equal in magnitudeand opposite in direction (Fig. P19.35b) andhence cancel. Show that particles with a speed of v 5E/B will pass through the velocity selector undeflected.

Consider the mass spectrometer shown schematicallyin Figure P19.36. The electric field between the platesof the velocity selector is 950 V/m, and the magneticfields in both the velocity selector and the deflectionchamber have magnitudes of 0.930 T. Calculate theradius of the path in the system for a singly charged ionwith mass m 5 2.18 3 10226 kg. Hint: See Problem 35.

A singly charged positive ion has a mass of 2.50 310226 kg. After being accelerated through a potentialdifference of 250 V, the ion enters a magnetic field of0.500 T, in a direction perpendicular to the field. Calculatethe radius of the path of the ion in the field.

A mass spectrometer is used to examine the isotopesof uranium. Ions in the beam emerge from the velocityselector at a speed of 3.00 3 105 m/s and enter auniform magnetic field of 0.600 T directed perpendicularlyto the velocity of the ions. What is the distancebetween the impact points formed on the photographicplate by singly charged ions of 235U and 238U?

A proton is at rest at the plane vertical boundary of aregion containing a uniform vertical magnetic field B(Fig. P19.39). An alpha particle moving horizontallymakes a head-on elastic collision with the proton.Immediately after the collision, both particles enterthe magnetic field, moving perpendicular to the directionof the field. The radius of the protons trajectory isR. The mass of the alpha particle is four times that ofthe proton, and its charge is twice that of the proton.Find the radius of the alpha particles trajectory.

A particle with charge q and kinetic energy KEtravels in a uniform magnetic field of magnitude B. Ifthe particle moves in a circular path of radius R, findexpressions for (a) its speed and (b) its mass.

A particle passes through a mass spectrometer as illustratedin Figure P19.36. The electric field betweenthe plates of the velocity selector has a magnitude of8 250 V/m, and the magnetic fields in both the velocityselector and the deflection chamber have magnitudesof 0.093 1 T. In the deflection chamber the particlestrikes a photographic plate 39.6 cm removed from itsexit point after traveling in a semicircle. (a) What is themass-to-charge ratio of the particle? (b) What is themass of the particle if it is doubly ionized? (c) What isits identity, assuming its an element?

A proton (charge 1e, mass mp), a deuteron (charge1e, mass 2mp), and an alpha particle (charge 12e, mass4mp) are accelerated from rest through a commonpotential difference DV. Each of the particles enters auniform magnetic field BS, with its velocity in a directionperpendicular to BS. The proton moves in a circularpath of radius rp. In terms of rp, determine (a) theradius rd of the circular orbit for the deuteron and(b) the radius ra for the alpha particle.

A lightning bolt may carry a current of 1.00 3 104 Afor a short time. What is the resulting magnetic field100 m from the bolt? Suppose the bolt extends farabove and below the point of observation.

In each of parts (a), (b), and (c) of Figure P19.44, findthe direction of the current in the wire that would producea magnetic field directed as shown.

Neurons in our bodies carry weak currents thatproduce detectable magnetic fields. A technique calledmagnetoencephalography, or MEG, is used to study electricalactivity in the brain using this concept. Thistechnique is capable of detecting magnetic fields asweak as 1.0 3 10215 T. Model the neuron as a long wirecarrying a current and find the current it must carryto produce a field of this magnitude at a distance of4.0 cm from the neuron.

In 1962 measurements of the magnetic field of a largetornado were made at the Geophysical Observatory inTulsa, Oklahoma. If the magnitude of the tornadosfield was B 5 1.50 3 1028 T pointing north when thetornado was 9.00 km east of the observatory, what currentwas carried up or down the funnel of the tornado?Model the vortex as a long, straight wire carry ing acurrent.

A cardiac pacemaker can be affected by a staticmagnetic field as small as 1.7 mT. How close can apacemaker wearer come to a long, straight wire carrying20 A?

The two wires shown in Figure P19.48 are separatedby d 5 10.0 cm and carry currents of I 5 5.00 A inopposite directions. Find the magnitude and directionof the net magnetic field (a) at a point midway betweenthe wires; (b) at point P1, 10.0 cm to the right of thewire on the right; and (c) at point P2, 2d = 20.0 cm tothe left of the wire on the left.

Four long, parallel conductorscarry equal currents ofI 5 5.00 A. Figure P19.49 isan end view of the conductors.The direction of thecurrent is into the page atpoints A and B (indicatedby the crosses) and out ofthe page at C and D (indicatedby the dots). Calculate the magnitude and directionof the magnetic field at point P, located at the centerof the square with edge of length 0.200 m.

Two long, parallel wires carrycurrents of I1 5 3.00 A and I2 55.00 A in the direction indicatedin Figure P19.50. (a) Find themagnitude and direction of themagnetic field at a point midwaybetween the wires (d 5 20.0 cm).(b) Find the magnitude anddirection of the magnetic fieldat point P, located d 5 20.0 cm above the wire carryingthe 5.00-A current.

A wire carries a 7.00-A current along the x-axis,and another wire carries a 6.00-A current along they-axis, as shown in Figure P19.51. What is the magneticfield at point P, located at x 5 4.00 m, y 5 3.00 m?

A long, straight wire lies on a horizontal table inthe xy-plane and carries a current of 1.20 mA in thepositive x-direction along the x-axis. A proton is travelingin the negative x-direction at speed 2.30 3 104 m/sa distance d above the wire (i.e., z 5 d). (a) What is thedirection of the magnetic field of the wire at the positionof the proton? (b) What is the direction of themagnetic force acting on the proton? (c) Explain whythe direction of the protons motion doesnt change.(d) Using Newtons second law, find a symbolic expressionfor d in terms of the acceleration of gravity g, theproton mass m, its speed v, charge q, and the currentI. (e) Find the numeric answer for the distance d usingthe results of part (d).

The magnetic field 40.0 cm away from a long, straightwire carrying current 2.00 A is 1.00 mT. (a) At what distanceis it 0.100 mT? (b) At one instant, the two conductorsin a long household extension cord carry equal2.00-A currents in opposite directions. The two wiresare 3.00 mm apart. Find the magnetic field 40.0 cmaway from the middle of the straight cord, in the planeof the two wires. (c) At what distance is it one-tenth aslarge? (d) The center wire in a coaxial cable carriescurrent 2.00 A in one direction, and the sheath aroundit carries current 2.00 A in the opposite direction.What magnetic field does the cable create at pointsoutside?

Two long, parallelwires separated by a distance2d carry equal currents in thesame direction. An end view ofthe two wires is shown in FigureP19.54, where the currents areout of the page. (a) What is thedirection of the magnetic fieldat P on the x-axis set up by thetwo wires? (b) Find an expression for the magnitudeof the field at P. (c) From your result to part (b), determinethe field at a point midway between the two wires.Does your result meet with your expectation? Explain.

Two long, parallel wires separated by 2.50 cm carry currentsin opposite directions. The current in one wire is1.25 A, and the current in the other is 3.50 A. (a) Findthe magnitude of the force per unit length that onewire exerts on the other. (b) Is the force attractive orrepulsive?

Two parallel wires separated by 4.0 cm repel eachother with a force per unit length of 2.0 3 1024 N/m.The current in one wire is 5.0 A. (a) Find the currentin the other wire. (b) Are the currents in the samedirection or in opposite directions? (c) What wouldhappen if the direction of one current were reversedand doubled?

A wire with a weight per unit length of 0.080 N/m issuspended directly above a second wire. The top wirecarries a current of 30.0 A, and the bottom wire carriesa current of 60.0 A. Find the distance of separationbetween the wires so that the top wire will be held inplace by magnetic repulsion.

In Figure P19.58 the current in the long, straight wireis I1 5 5.00 A, and the wire lies in the plane of the rectangularloop, which carries 10.0 A. The dimensionsshown are c 5 0.100 m, a 5 0.150 m, and , 5 0.450 m.Find the magnitude and direction of the net forceexerted by the magnetic field due to the straight wireon the loop.

A long solenoid that has 1 000 turns uniformly distributedover a length of 0.400 m produces a magneticfield of magnitude 1.00 3 1024 T at its center. Whatcurrent is required in the windings for that to occur?

A certain superconducting magnet in the form of asolenoid of length 0.50 m can generate a magneticfield of 9.0 T in its core when its coils carry a current of75 A. The windings, made of a niobiumtitanium alloy,must be cooled to 4.2 K. Find the number of turns inthe solenoid.

It is desired to construct a solenoid that will havea resistance of 5.00 V (at 20C) and produce a magneticfield of 4.00 3 1022 T at its center when it carriesa current of 4.00 A. The solenoid is to be constructedfrom copper wire having a diameter of 0.500 mm. Ifthe radius of the solenoid is to be 1.00 cm, determine(a) the number of turns of wire needed and (b) thelength the solenoid should have.

A solenoid 10.0 cm in diameter and 75.0 cm long ismade from copper wire of diameter 0.100 cm, with verythin insulation. The wire is wound onto a cardboardtube in a single layer, with adjacent turns touchingeach other. What power must be delivered to the solenoidif it is to produce a field of 8.00 mT at its center?

An electron is moving at a speed of 1.0 3 104 m/s in acircular path of radius 2.0 cm inside a solenoid. Themagnetic field of the solenoid is perpendicular to theplane of the electrons path. Find (a) the strength ofthe magnetic field inside the solenoid and (b) the currentin the solenoid if it has 25 turns per centimeter.

Figure P19.64 is a setup that can be used to measuremagnetic fields. A rectangular coil of wire containsN turns has a width w. The coil is attached to onearm of a balance and is suspended between the polesof a magnet. The field is uniform and perpendicularto the plane of the coil. The system is first balancedwhen the current in the coil is zero. When the switch isclosed and the coil carries a current I, a mass m must beadded to the right side to balance the system. (a) Findan expression for the magnitude of the magnetic fieldand determine its direction. (b) Why is the result independentof the vertical dimension of the coil? (c) Supposethe coil has 50 turns and width of 5.0 cm. Whenthe switch is closed, the coil carries a current of 0.30 A,and a mass of 20.0 g must be added to the right side tobalance the system. What is the magnitude of the magneticfield?

Two coplanar and concentriccircular loops of wire carrycurrents of I1 5 5.00 A andI2 5 3.00 A in opposite directionsas in Figure P19.65. (a) Ifr1 5 12.0 cm and r2 5 9.00 cm,what are (a) the magnitudeand (b) the direction of thenet magnetic field at the centerof the two loops? (c) Let r1 remain fixed at 12.0 cmand let r2 be a variable. Determine the value of r2 suchthat the net field at the center of the loop is zero.

An electron moves in a circular path perpendicular toa constant magnetic field of magnitude 1.00 mT. Theangular momentum of the electron about the center ofthe circle is 4.00 3 10225 kg ? m2/s. Determine (a) theradius of the circular path and (b) the speed of theelectron.

Two long, straight wires cross each other at rightangles, as shown in Figure P19.67. (a) Find the direcr1tion and magnitude of the magnetic field at point P,which is in the same plane as the two wires. (b) Findthe magnetic field at a point 30.0 cm above the pointof intersection (30.0 cm out of the page, toward you).

A 0.200-kg metal rod carrying a current of 10.0 Aglides on two horizontal rails 0.500 m apart. What verticalmagnetic field is required to keep the rod movingat a constant speed if the coefficient of kinetic frictionbetween the rod and rails is 0.100?

Using an electromagnetic flowmeter (Fig.P19.69), a heart surgeon monitors the flow rate ofblood through an artery. Electrodes A and B make contactwith the outer surface of the blood vessel, whichhas interior diameter 3.00 mm. (a) For a magneticfield magnitude of 0.040 0 T, a potential differenceof 160 mV appears between the electrodes. Calculatethe speed of the blood. (b) Verify that electrode A ispositive, as shown. Does the sign of the emf dependon whether the mobile ions in the blood are predominantlypositively or negatively charged? Explain.

A uniform horizontal wire with a linear mass densityof 0.50 g/m carries a 2.0-A current. It is placed in aconstant magnetic field with a strength of 4.0 3 1023 T.The field is horizontal and perpendicular to the wire.As the wire moves upward starting from rest, (a) whatis its acceleration and (b) how long does it take to rise50 cm? Neglect the magnetic field of Earth.

Three long, parallel conductors carry currents of I 52.0 A. Figure P19.71 is an end view of the conductors,with each current coming out of the page. Given thata 5 1.0 cm, determine the magnitude and direction ofthe magnetic field at points A, B, and C.

Two long, parallel wires, each with a mass per unitlength of 40 g/m, are supported in a horizontal planeby 6.0-cm-long strings, as shown in Figure P19.72. Eachwire carries the same current I, causing the wires torepel each other so that the angle u between the supportingstrings is 16. (a) Are the currents in the sameor opposite directions? (b) Determine the magnitudeof each current.

Protons having a kinetic energy of 5.00 MeV are movingin the positive x-direction and enter a magneticfield of 0.050 0 T in the z-direction, out of the plane ofthe page, and extending from x 5 0 to x 5 1.00 m asin Figure P19.73. (a) Calculate the y-component of theprotons momentum as they leave the magnetic field.(b) Find the angle a between the initial velocity vectorof the proton beam and the velocity vector after thebeam emerges from the field. Hint: Neglect relativisticeffects and note that 1 eV 5 1.60 3 10219 J.

A straight wire of mass 10.0 g and length 5.0 cm is suspendedfrom two identical springs that, in turn, forma closed circuit (Fig. P19.74). The springs stretch a distanceof 0.50 cm under the weight of the wire. The circuithas a total resistance of 12 V. When a magneticfield directed out of the page (indicated by the dots inthe figure) is turned on, the springs are observed tostretch an additional 0.30 cm. What is the strength ofthe magnetic field? (The upper portion of the circuit isfixed.)

A 1.00-kg ball having net charge Q 5 5.00 mC is thrownout of a window horizontally at a speed v 5 20.0 m/s.The window is at a height h 5 20.0 m above the ground.A uniform horizontal magnetic field of magnitudeB 5 0.010 0 T is perpendicular to the plane of theballs trajectory. Find the magnitude of the magneticforce acting on the ball just before it hits the ground.Hint: Ignore magnetic forces in finding the balls finalvelocity.

Two long, parallel conductors separated by 10.0 cmcarry currents in the same direction. The first wire carriesa current I1 5 5.00 A, and the second carries I2 58.00 A. (a) What is the magnitude of the magnetic fieldcreated by I1 at the location of I2? (b) What is the forceper unit length exerted by I1 on I2? (c) What is the magnitudeof the magnetic field created by I2 at the locationof I1? (d) What is the force per length exerted by I2on I1?