Essential University Physics, 3e (Wolfson) Chapter 26 Magnetism: Force and Field 26.1 Conceptual Questions 1) A vertical wire carries a current straight down To the east of this wire, the magnetic field points A) toward the north B) toward the east C) toward the west D) toward the south E) downward Answer: D Var: 2) A current carrying loop of wire lies flat on a table top When viewed from above, the current moves around the loop in a counterclockwise sense (a) For points OUTSIDE the loop, the magnetic field caused by this current A) circles the loop in a clockwise direction B) circles the loop in a counterclockwise direction C) points straight up D) points straight down E) is zero (b) For points INSIDE the loop, the magnetic field caused by this current\ A) circles the loop in a clockwise direction B) circles the loop in a counterclockwise direction C) points straight up D) points straight down E) is zero Answer: (a) D (b) C Var: 3) A horizontal wire carries a current straight toward you From your point of view, the magnetic field at a point directly below the wire points A) directly away from you B) to the left C) to the right D) directly toward you E) vertically upward Answer: C Var: 1 Copyright © 2016 Pearson Education, Inc 4) An electron moving in the direction of the +x-axis enters a magnetic field If the electron experiences a magnetic deflection in the -y direction, the direction of the magnetic field in this region points in the direction of the A) +z-axis B) -z-axis C) -x-axis D) +y-axis E) -y-axis Answer: B Var: 5) An electron, moving toward the west, enters a uniform magnetic field Because of this field the electron curves upward The direction of the magnetic field is A) towards the north B) towards the south C) towards the west D) upward E) downward Answer: A Var: 6) Three particles travel through a region of space where the magnetic field is out of the page, as shown in the figure The electric charge of each of the three particles is, respectively, A) is neutral, is negative, and is positive B) is neutral, is positive, and is negative C) is positive, is neutral, and is negative D) is positive, is negative, and is neutral E) is negative, is neutral, and is positive Answer: E Var: Copyright © 2016 Pearson Education, Inc 7) A charge is accelerated from rest through a potential difference V and then enters a uniform magnetic field oriented perpendicular to its path The field deflects the particle into a circular arc of radius R If the accelerating potential is tripled to 3V, what will be the radius of the circular arc? A) 9R B) 3R C) R D) R/ E) R/9 Answer: C Var: 8) Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter? A) 4R B) 3R C) R D) R/ E) R/2 Answer: D Var: 9) A charged particle is moving with speed v perpendicular to a uniform magnetic field A second identical charged particle is moving with speed 2v perpendicular to the same magnetic field If the frequency of revolution of the first particle is f, the frequency of revolution of the second particle is A) f B) 2f C) 4f D) f/2 E) f/4 Answer: A Var: 10) A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north What is the direction of the magnetic force on this current due to the field? A) downward B) toward the north C) toward the south D) toward the east E) toward the west Answer: E Var: Copyright © 2016 Pearson Education, Inc 11) Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions The wire on your right carries current toward you, and the wire on your left carries current away from you From your point of view, the magnetic field at the point exactly midway between the two wires A) points upward B) points downward C) points toward you D) points away from you E) is zero Answer: B Var: 12) The figure shows two long wires carrying equal currents I1 and I2 flowing in opposite directions Which of the arrows labeled A through D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire? A) A B) B C) C D) D E) The magnetic field is zero at that point Answer: B Var: Copyright © 2016 Pearson Education, Inc 13) The figure shows four different sets of insulated wires that cross each other at right angles without actually making electrical contact The magnitude of the current is the same in all the wires, and the directions of current flow are as indicated For which (if any) configuration will the magnetic field at the center of the square formed by the wires be equal to zero? A) A B) B C) C D) D E) The field is not equal to zero in any of these cases Answer: C Var: 14) A negatively charged particle is moving to the right, directly above a wire having a current flowing to the right, as shown in the figure In which direction is the magnetic force exerted on the particle? A) into the page B) out of the page C) downward D) upward E) The magnetic force is zero since the velocity is parallel to the current Answer: D Var: Copyright © 2016 Pearson Education, Inc 15) Two very long parallel wires are a distance d apart and carry equal currents in opposite directions The locations where the net magnetic field due to these currents is equal to zero are A) midway between the wires B) a distance d/2 to the left of the left wire and also a distance d/2 to the right of the right wire C) a distance d to the left of the left wire and also a distance d to the right of the right wire D) a distance d/ to the left of the left wire and also a distance d/ to the right of the right wire E) The net field is not zero anywhere Answer: E Var: 16) Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure The +z direction points perpendicular to the xyplane in a right-handed coordinate system If both currents flow in the +y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.) Copyright © 2016 Pearson Education, Inc A) B) C) D) E) Answer: C Var: Copyright © 2016 Pearson Education, Inc 17) Two very long parallel wires in the xy-plane, a distance 2a apart, are parallel to the y-axis and carry equal currents I as shown in the figure The +z direction points perpendicular to the xyplane in a right-handed coordinate system If the left current flows in the +y direction and the right current flows in the -y direction, which one of the graphs shown in the figure below best represents the z component of the net magnetic field, in the xy-plane, as a function of x? (Caution: These graphs are not magnetic field lines.) Copyright © 2016 Pearson Education, Inc A) B) C) D) E) Answer: D Var: Copyright © 2016 Pearson Education, Inc 18) The figure shows three long, parallel current-carrying wires The magnitudes of the currents are equal and their directions are indicated in the figure Which of the arrows drawn near the wire carrying current correctly indicates the direction of the magnetic force acting on that wire? A) A B) B C) C D) D E) The magnetic force on current is equal to zero Answer: A Var: 10 Copyright © 2016 Pearson Education, Inc 33) A rigid circular loop has a radius of 0.20 m and is in the xy-plane A clockwise current I is carried by the loop, as shown The magnitude of the magnetic moment of the loop is 0.75 A ∙ m2 A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present (a) What is the current in the loop? (b) Find the magnitude of the magnetic torque exerted on the loop (c) If the loop is released from rest, in what direction will points a and c initially move? Answer: (a) 6.0 A (b) 0.15 N ∙ m (c) a moves out of the plane and c moves into the plane Var: 34) A circular coil of wire of 200 turns and diameter 2.0 cm carries a current of 4.0 A It is placed in a magnetic field of with the plane of the coil making an angle of 30° with the magnetic field What is the magnetic torque on the coil? A) 0.15 N ∙ m B) 0.088 N ∙ m C) 0.29 N ∙ m D) 0.40 N ∙ m E) 0.076 N ∙ m Answer: A Var: 50+ 35) A round loop of diameter 12 cm, carrying a current of 0.40 A, is placed inside a magnetic field = 0.20 T + 0.40 T The normal to the loop is parallel to the unit vector = -0.60 0.80 What is the potential energy of the loop? A) -4.5 × 10-3 J B) +2.0 × 10-3 J C) -2.0 × 10-3 J D) -2.3 × 10-3 J E) +4.5 × 10-3 J Answer: B Var: 29 Copyright © 2016 Pearson Education, Inc 36) A rigid circular loop has a radius of 0.20 m and is in the xy-plane A clockwise current I is carried by the loop, as shown The magnitude of the magnetic moment of the loop is 0.75 A ∙ m2 A uniform external magnetic field, B = 0.20 T in the positive x-direction, is present An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy The work done by this external torque is closest to A) 0.20 J B) 0.30 J C) 0.40 J D) 0.50 J E) 0.60 J Answer: B Var: 37) At what distance from the central axis of a long straight thin wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of the Earth's magnetic field of about 5.0 × 10-5 T? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.0 cm B) 2.0 cm C) 3.0 cm D) 4.0 cm E) 5.0 cm Answer: B Var: 38) A very long thin wire produces a magnetic field of at a distance of from the central axis of the wire What is the magnitude of the current in the wire? (μ0 = 4π × 107 T ∙ m/A) A) 7.5 mA B) 1.7 mA C) 3300 mA D) 24,000 mA Answer: A Var: 27 30 Copyright © 2016 Pearson Education, Inc 39) The magnetic field at a distance of cm from a current carrying wire is μT What is the magnetic field at a distance of cm from the wire? A) 1/2 µT B) µT C) µT D) µT E) µT Answer: C Var: 40) Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions The wires are separated by 0.20 m What is the magnitude of the magnetic field midway between the two wires? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.0 × 10-5 T B) 2.0 × 10-5 T C) 3.0 × 10-5 T D) 4.0 × 10-5 T E) 5.0 × 10-5 T Answer: E Var: 41) Two long parallel wires carry currents of 10 A in opposite directions They are separated by 40 cm What is the magnitude of the magnetic field in the plane of the wires at a point that is 20 cm from one wire and 60 cm from the other? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.5 µT B) 3.3 µT C) 6.7 µT D) 33 µT E) 67 µT Answer: C Var: 31 Copyright © 2016 Pearson Education, Inc 42) The figure shows two long, parallel current-carrying wires The wires carry equal currents I1 = I2 = 20 A in the directions indicated and are located a distance d = 0.5 m apart Calculate the magnitude and direction of the magnetic field at the point P that is located an equal distance d from each wire (μ0 = 4π × 10-7 T ∙ m/A) A) µT downward B) µT upward C) µT downward D) µT upward E) µT to the right Answer: B Var: 32 Copyright © 2016 Pearson Education, Inc 43) Three very long, straight, parallel wires each carry currents of 4.00 A, directed out of the page as shown in the figure The wires pass through the vertices of a right isosceles triangle of side 2.00 cm What is the magnitude of the magnetic field at point P at the midpoint of the hypotenuse of the triangle? A) 4.42 × 10-6 T B) 1.77 × 10-5 T C) 5.66 × 10-5 T D) 1.26 × 10-4 T E) 1.77 × 10-6 T Answer: C Var: 44) As shown in the figure, two long straight wires are separated by a distance of The currents are to the right in the upper wire and to the left in the lower wire What are the magnitude and direction of the magnetic field at point P, which is a distance below the lower wire? Answer: B = 3.2 × 10-6 T, directed out of the plane of the paper Var: 50+ 33 Copyright © 2016 Pearson Education, Inc 45) As shown in the figure, a rectangular current loop is carrying current = 3.0 A, in the direction shown, and is located near a long wire carrying a current The long wire is parallel to the sides of the rectangle The rectangle loop has length 0.80 m and its sides are 0.10 m and 0.70 m from the wire, as shown We measure that the net force on the rectangular loop is and is directed towards the wire (a) What is the magnitude of the current Iw? (b) In which direction does Iw flow: from top to bottom or from bottom to top in the sketch? Answer: (a) 1.2 A (b) from bottom to top Var: 50+ 46) A very long straight wire carries a 12-A current eastward and a second very long straight wire carries a 14-A current westward The wires are parallel to each other and are 42 cm apart Calculate the force on a 6.4 m length of one of the wires (μ0 = 4π × 10-7 T ∙ m/A) A) 8.0 × 10-7 N B) 5.1 × 10-4 N C) 8.0 × 10-5 N D) 5.1 × 10-6 N E) 2.2 × 10-4 N Answer: B Var: 47) A rectangular loop of wire measures 1.0 m by 1.0 cm If a 7.0-A current flows through the wire, what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0m side of the loop? (μ0 = 4π × 10-7 T ∙ m/A) A) 9.8 × 10-6 N B) 7.8 × 10-7 N C) 9.8 × 10-8 N D) 4.9 × 10-6 N Answer: A Var: 34 Copyright © 2016 Pearson Education, Inc 48) A circular loop of wire of radius 10 cm carries a current of 6.0 A What is the magnitude of the magnetic field at the center of the loop? (μ0 = 4π × 10-7 T ∙ m/A) A) 3.8 × 10-5 T B) 3.8 × 10-7 T C) 1.2 × 10-5 T D) 1.2 × 10-7 T E) 3.8 × 10-8 T Answer: A Var: 49) A wire carrying a current is shaped in the form of a circular loop of radius magnetic field strength that this current produces at the center of the loop is magnitude of the current that flows through the wire? (μ0 = 4π × 10-7 T ∙ m/A) A) 5.3 A B) 16 A C) 9.1 A D) 23 A Answer: A If the what is the Var: 30 50) Two coaxial circular coils of radius R = 15 cm, each carrying 4.0 A in the same direction, are positioned a distance d = 20 cm apart, as shown in the figure Calculate the magnitude of the magnetic field halfway between the coils along the line connecting their centers (μ0 = 4π × 10-7 T ∙ m/A) A) 0.90 × T B) 3.9 × T C) 1.9 × T D) 6.3 × T E) 9.2 × T Answer: C Var: 35 Copyright © 2016 Pearson Education, Inc 51) A long straight very thin wire on the y-axis carries a 10-A current in the positive y-direction A circular loop 0.50 m in radius, also of very thin wire and lying in the yz-plane, carries a 9.0-A current, as shown Point P is on the positive x-axis, at a distance of 0.50 m from the center of the loop What is the magnetic field vector at point P due to these two currents? (μ0 = 4π × 10-7 T ∙ m/A) A) zero B) -8.0 × 10-6 T C) (+4.0 × 10-6 T) - (4.0 × 10-6 T) D) (-4.0 × 10-6 T) - (4.0 × 10-6 T) E) (-4.0 × 10-6 T) - (8.0 × 10-6 T) Answer: D Var: 36 Copyright © 2016 Pearson Education, Inc 52) A long straight wire on the z-axis carries a current of 6.0 A in the positive direction A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure Point P, at the center of the loop, is 25 cm from the z-axis An electron is projected from P with a velocity of 1.0 × 106 m/s in the negative x-direction What is the y component of the force on the electron? (e = 1.60 × 10-19 C, μ0 = 4π × 10-7 T ∙ m/A) A) -1.0 × 10-18 N B) +1.0 × 10-18 N C) -2.0 × 10-18 N D) +2.0 × 10-18 N E) zero Answer: A Var: 53) Two circular coils of diameter 30.0 cm are parallel to each other and have their centers along the same line L but separated by 22.0 cm When an experimenter views the coils along L, the coil closer to her carries a clockwise current of 2.50 A Find the magnitude and sense (clockwise or counterclockwise) of the current needed in the other coil so that the net magnetic field on L midway between the two coils will have a magnitude of 4.10 µT and point away from the experimenter who is viewing the coils along L (μ0 = 4π × 10-7 T ∙ m/A) Answer: 0.633 A, counterclockwise Var: 37 Copyright © 2016 Pearson Education, Inc 54) As shown in the figure, an insulated wire is bent into a circular loop of radius 6.0 cm and has two long straight sections The loop is in the xy-plane, with the center at the origin The straight sections are parallel to the z-axis The wire carries a current of 8.0 A What is the magnitude of the magnetic field at the origin? (μ0 = 4π × 10-7 T ∙ m/A) A) 75 µT B) 81 µT C) 88 µT D) 110 µT E) 120 µT Answer: C Var: 55) As shown in the figure, a wire is bent into the shape of a tightly closed omega (Ω), with a circular loop of radius 4.0 cm and two long straight sections The loop is in the xy-plane, with the center at the origin The straight sections are parallel to the x-axis The wire carries a 5.0-A current, as shown What is the magnitude of the magnetic field at the center of the loop? (μ0 = 4π × 10-7 T ∙ m/A) A) 25 µT B) 40 µT C) 54 µT D) 80 µT E) 104 µT Answer: C Var: 38 Copyright © 2016 Pearson Education, Inc 56) A type of transmission line for electromagnetic waves consists of two parallel conducting plates (assumed infinite in width) separated by a distance a Each plate carries the same uniform surface current density of 16.0 A/m, but the currents run in opposite directions What is the magnitude of the magnetic field between the plates at a point 1.00 mm from one of the plates if a = 0.800 cm? (μ0 = 4π × 10-7 T ∙ m/A) A) 3.20 × 10-3 T B) 1.00 × 10-5 T C) 4.63 × 10-5 T D) 2.01 × 10-5 T E) 7.07 × 10-4 T Answer: D Var: 57) A coaxial cable consists of an inner cylindrical conductor of radius R1 = 0.040 m on the axis of an outer hollow cylindrical conductor of inner radius R2 = 0.080 m and outer radius The inner conductor carries current in one direction, and the outer conductor carries current in the opposite direction What is the magnitude of the magnetic field at the following distances from the central axis of the cable? (μ0 = 4π × 10-7 T ∙ m/A) (a) At r = 0.060 m (in the gap midway between the two conductors) (b) At r = 0.150 m (outside the cable) Answer: (a) B = 1.47 × 10-5 T (b) B = 4.40 × 10-6 T Var: 50+ 39 Copyright © 2016 Pearson Education, Inc 58) The figure shows the cross-section of a hollow cylinder of inner radius a = 5.0 cm and outer radius b = 7.0 cm A uniform current density of 1.0 A/ cm2 flows through the cylinder parallel to its axis Calculate the magnitude of the magnetic field at a distance of d = 10 cm from the axis of the cylinder (μ0 = 4π × 10-7 T ∙ m/A) A) 0.00 T B) 1.5 × 10-4 T C) 2.5 × 10-4 T D) 4.5 × 10-4 T E) 0.50 × 10-4 T Answer: B Var: 59) A tube with a 3.0-mm radius has ions flowing through it along its length To determine the rate at which the charge is being moved through the tube, the magnetic field just outside the tube is measured and found to be If the only contributor to the magnetic field is the moving ions, and if the walls of the container are very thin and not screen magnetism, what is the magnitude of the current flowing through the tube? (μ0 = 4π × 10-7 T ∙ m/A) A) 66 A B) 132 A C) 829 A D) 415 A Answer: A Var: 50+ 40 Copyright © 2016 Pearson Education, Inc 60) A long, straight wire with current flowing through it produces magnetic field strength at its surface If the wire has a radius R, where within the wire is the field strength equal to of the field strength at the surface of the wire? Assume that the current density is uniform throughout the wire (μ0 = 4π × 10-7 T ∙ m/A) A) 0.36 R B) 0.060 R C) 0.64 R D) 0.030 R Answer: A Var: 50+ 61) A hollow cylinder with an inner radius of and an outer radius of conducts a 3.0-A current flowing parallel to the axis of the cylinder If the current density is uniform throughout the wire, what is the magnitude of the magnetic field at a point from its center? (μ0 = 4π × 10-7 T ∙ m/A) A) 7.2 × 10-6 T B) 8.0 × 10-6 T C) 8.9 × 10-7 T D) 7.1 × 10-8 T Answer: A Var: 50+ 62) A solenoid with 400 turns has a radius of 0.040 m and is 40 cm long If this solenoid carries a current of what is the magnitude of the magnetic field near the center of the solenoid? (μ0 = 4π × 10-7 T ∙ m/A) A) 16 mT B) 4.9 mT C) 15 mT D) 6.0 mT E) 9.0 mT Answer: C Var: 63) A solenoid having N turns and carrying a current of 2.000 A has a length of 34.00 cm If the magnitude of the magnetic field generated at the center of the solenoid is 9.000 mT, what is the value of N? (μ0 = 4π × 10-7 T ∙ m/A) A) 860.0 B) 1591 C) 2318 D) 3183 E) 1218 Answer: E Var: 41 Copyright © 2016 Pearson Education, Inc 64) A cylindrical insulated wire of diameter 5.0 mm is tightly wound 200 times around a cylindrical core to form a solenoid with adjacent coils touching each other When a 0.10 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ0 = 4π × 10-7 T ∙ m/A) A) 6.6 × T B) 2.5 × T C) 1.3 × T D) 3.6 × T E) 9.8 × T Answer: B Var: 65) A solenoid is wound with 970 turns on a form 4.0 cm in diameter and 50 cm long The windings carry a current I in the sense that is shown in the figure The current produces a magnetic field, of magnitude near the center of the solenoid Find the current in the solenoid windings (μ0 = 4π × 10-7 T ∙ m/A) A) 1.8 A B) 1.5 A C) 1.3 A D) 2.2 A E) 2.0 A Answer: A Var: 50+ 66) A solenoid of length 18 cm consists of closely spaced coils of wire wrapped tightly around a wooden core The magnetic field strength is inside the solenoid near its center when a certain current flows through the coils If the coils of the solenoid are now pulled apart slightly, stretching it to without appreciably changing the size of the coils, what does the magnetic field become near the center of the solenoid when the same current flows through the coils? (μ0 = 4π × 10-7 T ∙ m/A) A) 1.7 mT B) 3.4 mT C) 0.85 mT D) 2.0 mT Answer: A Var: 42 Copyright © 2016 Pearson Education, Inc 67) A toroidal solenoid has a central radius of 0.50 m and a cross-sectional diameter of 10 cm When a current passes through the coil of the solenoid, the magnetic field inside the solenoid at its CENTER has a magnitude of 2.0 μT What is the largest value of the magnetic field inside the solenoid when this current is flowing? (μ0 = 4π × 10-7 T ∙ m/A) A) 3.5 µT B) 1.8 µT C) 2.2 µT D) 0.50 µT E) 2.8 µT Answer: C Var: 68) A 1000-turn toroidal solenoid has a central radius of 4.2 cm and is carrying a current of 1.7 A What is the magnitude of the magnetic field inside the solenoid at the central radius? (μ0 = 4π × 10-7 T ∙ m/A) A) 8.1 mT B) 51 mT C) 16 mT D) 81 mT E) zero Answer: A Var: 43 Copyright © 2016 Pearson Education, Inc