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# Week 5 short assignments 1220

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This 21 page Bundle was uploaded by Dragon Note on Thursday March 24, 2016. The Bundle belongs to 1220 at University of Missouri - Columbia taught by Y Zhang in Spring 2016. Since its upload, it has received 196 views. For similar materials see College Physics II in Physics 2 at University of Missouri - Columbia.

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Date Created: 03/24/16

Short Assignment By 2/26/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/26/2016 Due: 11:00am on Friday, February 26, 2016 To understand how points are awarded, read theading Policy for this assignment. Magnetic Flux through a Coil You hold a wire coil so that the plane of the coil is perpendicular to a magnetic field \texttip{\vec{B}}{B_vec}. Part A If the magnitude of \texttip{\vec{B}}{B_vec} increases while its direction remains unchanged, how will the magnetic flux through the coil change? Check all that apply. Hint 1. How to approach the problem Recall that the magnetic flux depends on the magnetic field magnitude, the area of the coil, and the angle between the magnetic field and the coil's axis. Since the area of the coil and the direction of the magnetic field are unchanged, the flux through the coil can be affected only by the change in the magnitude of the magnetic field. Use the definition of magnetic flux to determine how the flux changes as a function of magnitude of the magnetic field. Hint 2. Magnetic flux The magnetic flux \texttip{\Phi _{\mit B}}{Phi_B} depends on the magnitude of the magnetic field \texttip{B}{B}, the area \texttip{A}{A} of the coil, and the angle \texttip{\phi }{phi} between the magnetic field and the coil's axis. Mathematically, this relationship is expressed as \Phi_B=B A \cos\phi. ANSWER: The flux is unchanged because the position of the coil with respect to \texttip{\vec{B}}{B_vec} is unchanged. The flux increases because the magnitude of \texttip{\vec{B}}{B_vec} increases. The flux decreases because the magnitude of \texttip{\vec{B}}{B_vec} increases. The flux is unchanged because the surface area of the coil is unchanged. Correct The magnetic flux through a coil is directly proportional to the magnitude of the magnetic field. Part B \texttip{\vec{B}}{B_vec} is kept constant but the coil is rotated so that the magnetic field, \texttip{\vec{B}}{B_vec}, is now in the plane of the coil. How will the magnetic flux through the coil change as the rotation occurs? Check all that apply. Hint 1. How to approach the problem Short Assignment By 2/26/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Recall that the magnetic flux depends on the magnitude of the magnetic field, the area of the coil, and the angle between the magnetic field and the coil's axis. Since the area of the coil and the magnitude of the magnetic field are unchanged, the magnetic flux through the coil can be affected only by the change in the angle between the coil's axis and the magnetic field due to the change in orientation of the coil. Use the definition of magnetic flux to determine how the flux changes as a function of this angle. Hint 2. Magnetic flux The magnetic flux \texttip{\Phi _{\mit B}}{Phi_B} depends on the magnitude of the magnetic field \texttip{B}{B}, the area \texttip{A}{A} of the coil, and the angle \texttip{\phi }{phi} between the magnetic field and the coil's axis. Mathematically, this relationship is expressed as \Phi_B=B A \cos\phi. Hint 3. Find the cosines of the angles Let \texttip{\phi _{\rm 1}}{phi_1} denote the angle between the coil's axis and the magnetic field when the coil is perpendicular to the field, and let \texttip{\phi _{\rm 2}}{phi_2} denote the angle between the coil's axis and the magnetic field when the coil is parallel to the field. What are the values of \cos\phi_1 and \cos\phi_2? Enter your answers numerically, separated by a comma. ANSWER: \cos\phi_1, \cos\phi_2 = 1,0 ANSWER: The flux is unchanged because the magnitude of \texttip{\vec{B}}{B_vec} is constant. The flux increases because the angle between \texttip{\vec{B}}{B_vec} and the coil's axis changes. The flux decreases because the angle between \texttip{\vec{B}}{B_vec} and the coil's axis changes. The flux is unchanged because the area of the coil is unchanged. Correct As the orientation of the coils changes, the magnetic flux through the coil decreases. It reaches its minimum value (zero) when the coil is parallel to the field. A Magnet and a Coil When a magnet is plunged into a coil at speed \texttip{v}{v}, as shown in the figure, a voltage is induced in the coil and a current flows in the circuit. Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/26/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Part A If the speed of the magnet is doubled, the induced voltage is ________ . Hint 1. How to approach the problem Recall that the magnitude of the induced emf in a circuit equals the absolute value of the time rate of change of the magnetic flux through the circuit. As the magnet moves toward the coil, the flux through the coil increases because the magnitude of the magnetic field through the center of the coil increases. The faster the magnet moves toward the coil, the faster the flux through the coil increases. ANSWER: twice as great four times as great half as great unchanged Correct Part B The same magnet is plunged into a coil that has twice the number of turns as before. The magent is shown before it enters the coil in the figure. If the speed of the magnet is again \texttip{v}{v}, the induced current in the coil is _______ . Hint 1. How to approach the problem Recall that the current in the coil is proportional to the induced emf and inversely proportional to the resistance of Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/26/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... the coil. Do the induced emf and the resistance of the coil vary when the number of turns in the coil is doubled? Hint 2. Find the induced emf in the coil If the number of turns in the coil is doubled, how does the induced emf \texttip{{\cal{E}}}{EMF} in the coil change? Hint 1. Induced emf In a coil with several identical turns, the induced emf due to the change in magnetic flux is proportional to the number of turns in the coil. ANSWER: \texttip{{\cal{E}}}{EMF} decreases by a factor of 1/2. \texttip{{\cal{E}}}{EMF} increases by a factor of 2. \texttip{{\cal{E}}}{EMF} increases by a factor of 4. \texttip{{\cal{E}}}{EMF} is unchanged. Hint 3. Find the resistance of the coil If the number of turns in the coil is doubled, how does the resistance \texttip{R}{R} of the coil change? Note that the turns in the coil can be thought of as resistors connected in series. Hint 1. Resistors in series Recall that the equivalent resistance of a series connection of resistors is equal to the sum of the resistances of all the resistors. Therefore, if the resistors in the circuit are all identical, if the number of turns doubles, the equivalent resistance doubles as well. ANSWER: The resistance decreases by a factor of 1/2. The resistance increases by a factor of 2. The resistance increases by a factor of 4. The resistance is unchanged. Hint 4. Induced current By Ohm's law, the current in the coil is given by the ratio of the induced emf to the resistance of the coil. When the number of turns in the coil doubles, both the induced emf and the coil's resistance double as well. Therefore, what will their ratio be in this case? ANSWER: Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/26/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... twice as great four times as great half as great unchanged Correct By increasing the number of turns in the coil, the induced emf increases, but so does the resistance of the coil. Since those two quantities increase by the same factor, their ratio remains constant, and the induced current in the circuit is unchanged. Problem 23.3 A magnetic field is oriented at an angle of 43 {\rm ^\circ} to the normal of a rectangular area 5.1 {\rm {\rm cm}} by 7.1 {\rm {\rm cm}} . Part A If the magnetic flux through this surface has a magnitude of 5.0×1{\rm {\rm{T}} \cdot {\rm{m}}^2} , what is the strength of the magnetic field? Express your answer using two significant figures. ANSWER: B = 19 {\rm mT} Correct Score Summary: Your score on this assignment is 100%. You received 1.5 out of a possible total of 1.5 points. Loading [MathJax]/jax/output/HTML-CSS/autoload/maction.js Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/24/2016 Due: 11:00am on Wednesday, February 24, 2016 To understand how points are awarded, read theding Policy for this assignment. Magnetic Force on a Bent Wire Conceptual Question The bent wire circuit shown in the figure is in a region of space with a uniform magnetic field in the +z direction. Current flows through the circuit in the direction indicated. Note that segments 2 and 5 are oriented parallel to the z axis; the other pieces are parallel to either the x or y axis. Part A Determine the direction of the magnetic force along segment 1, which carries current in the -x direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. Hint 1. Magnetic force on a current-carrying wire Electric current, by convention, is considered to be the flow of positively charged particles. Therefore, to determine the direction of the magnetic force on a current-carrying wire, simply determine the direction of the force on a positive charge moving in the direction of the current flow. Hint 2. Magnetic force on segment 1 1. Point the fingers of your right hand in the direction of the current flow (to the left). 2. Rotate your hand until you can curl your fingers in the +z direction (directly out from the computer screen). At this point, is your palm facing the computer screen? ANSWER: yes no ANSWER: Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Part B Determine the direction of the magnetic force along segment 2, which carries current in the -z direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. Hint 1. Magnetic force on segment 2 The magnetic force is proportional to the sine of the angle between the current flow and the magnetic field. What is the angle between the direction of current flow and the magnetic field along segment 2? Express your answer in degrees. ANSWER: -180 ANSWER: Correct Part C Determine the direction of the magnetic force along segment 3, which carries current in the +y direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. Magnetic field on segment 3 1. Point the fingers of your right hand in the direction of the current flow (upward). 2. Rotate your hand until you can curl your fingers in the +z direction (directly out from the computer screen). At this point, is your palm facing the computer screen? ANSWER: yes no ANSWER: Correct Part D Determine the direction of the magnetic force along segment 4, which carries current in the +x direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. ANSWER: Correct Part E Determine the direction of the magnetic force along segment 5, which carries current in the +z direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. ANSWER: Correct Part F Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Determine the direction of the magnetic force along segment 6, which carries current in the +x direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. ANSWER: Correct Part G Determine the direction of the magnetic force along segment 7, which carries current in the -y direction. Enter the direction of the force as a sign (+ or -) followed by a coordinate direction (x, y, or z) without spaces. For instance, if you think that the force points in the positive y direction, enter +y. If there is no magnetic force, enter 0. ANSWER: Correct Direction of the Magnetic Field due to a Wire Conceptual Question Find the direction of the magnetic field at each of the indicated points. For the following two questions consider the wire shown in the figure. . Part A What is the direction of the magnetic fieldat Point A? Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. The magnitude of the magnetic field due to a long, straight, current-carrying wire The magnitude of the field is directly proportional to the currentflowing in the wire and inversely proportional to the distance from the wire: . Hint 2. The direction of the magnetic field due to a long, straight, current-carrying wire The magnetic field surrounding a long, straight wire encircles the wire, as shown in the figure: The direction of the field is determined by a right-hand rule: Grasp the wire with the thumb of your right hand in the direction of the current flow. The direction in which your fingers encircle the wire is the direction in which the magnetic field encircles the wire. ANSWER: is out of the page. is into the page. is neither out of nor into the page and . . Correct Part B What is the direction of the magnetic field at Point B? ANSWER: Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... is out of the page. is into the page. is neither out of nor into the page and . . Correct Now consider the wires shown in this figure. Note that the bottom wire carries a current of magnitude . Part C What is the direction of the magnetic field at Point C? Hint 1. How to approach the problem To determine the direction of the magnetic field at Point C, you must determine the contribution to the field from both of the wires. The field at Point C is the vector sum of these two contributions. Keep in mind that if the magnetic fields are in opposite directions, the larger field will decide the direction of the net magnetic field. If they are the same size, the net magnetic field will be zero. Hint 2. Find the direction of the magnetic field at Point C due to wire 1 Is the magnetic field from wire 1 directed out of or into the screen at Point C? ANSWER: out of into Hint 3. Find the direction of the magnetic field at Point C due to wire 2 Is the magnetic field from wire 2 directed out of or into the screen at Point C? Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: out of into ANSWER: is out of the page. is into the page. is neither out of nor into the page and . . Correct Part D What is the direction of the magnetic field at Point D? Hint 1. Find the direction of the magnetic field at Point D due to wire 1 Is the magnetic field from wire 1 directed out of or into the screen at Point D? ANSWER: out of into Hint 2. Find the direction of the magnetic field at Point D due to wire 2 Is the magnetic field from wire 2 directed out of or into the screen at Point D? ANSWER: out of into ANSWER: Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... is out of the page. is into the page. is neither out of nor into the page and . . Correct Part E What is the direction of the magnetic field at Point E? Hint 1. Find the direction of the magnetic field at Point E due to wire 1 Is the magnetic field from wire 1 directed out of or into the screen at Point E? ANSWER: out of into Hint 2. Find the direction of the magnetic field at Point E due to wire 2 Is the magnetic field from wire 2 directed out of or into the screen at Point E? ANSWER: out of into ANSWER: is out of the page. is into the page. is neither out of nor into the page and . . Correct Short Assignment By 2/24/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Conceptual Exercise 22.55 A loop of wire is connected to the terminals of a battery, as indicated in the figure . Part A If the loop is to attract the bar magnet, which of the terminors, , should be the positive terminal of the battery? ANSWER: terminal terminal Correct Part B Explain. ANSWER: 3582 Character(s) remaining in a magnets the field travels from north to south. In the same sense current travels from negative to positive. With the south end acting like a positive charge it would attract the negative charge the the B terminal. Submitted, grade pending Score Summary: Your score on this assignment is 84.6%. You received 2.75 out of a possible total of 3.25 points. Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Short Assignment By 2/22/2016 Due: 11:00am on Monday, February 22, 2016 To understand how points are awarded, read therading Policy for this assignment. Interaction of a Current Loop with a Magnetic Field The effects due to the interaction of a current-carrying loop with a magnetic field have many applications, some as common as the electric motor. This problem illustrates the basic principles of this interaction. Consider a current that flows in a plane rectangular current loop with height= 4.00 and horizontal sides = 2.00 . The loop is placed into a uniform magnetic field in such a way that the sides of length are perpendicular to , and there is an angle between the sides of length and , as shown in the figures. Part A Will the interaction of the current through the loop with the magnetic field cause the loop to rotate? Hint 1. Find the direction of the forces on the parts of the loop that have length As current is moving through the loop, forces act on its different parts. These result from magnetic forces acting on the charges that move through the wire. What is the direction of the forces on the two pieces of wire of length ? Select the correct diagram from the four options. The forces are symbolized by the red arrows. Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Hint 1. Direction of magnetic force on a straight current-carrying wire: the right-hand rule The direction of the force acting on a straight wire that carries a currein a magnetic field can be determined using the right-hand rule: Point the fingers of your right hand in the direction of the current; then curl your fingers toward the direction o. Your thumb will give you the direction of. ANSWER: A B C D Hint 2. Find the direction of the forces on the parts of the loop that have length As current is moving through the loop, forces act on its different parts. These result from magnetic forces acting on the charges that move through the wire. What can you say about the forces on the two pieces of wire of length ? Hint 1. Direction of magnetic force on a straight current-carrying wire: the right-hand rule The direction of the force acting on a straight wire that carries a currein a magnetic field can be determined using the right-hand rule: Point the fingers of your right hand in the direction of the current; then curl your fingers toward the direction o. Your thumb will give you the direction of. ANSWER: Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... The forces point away from the center of the loop and cancel each other. The forces act as a torque about an axis through the midpoints of the two pieces of length and make the loop turn in the counterclockwise direction. The forces point toward the center of the loop and cancel each other. Both forces point upward perpendicular to and the piece of wire of length . ANSWER: Yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle (clockwise). Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle (counterclockwise). No, the net torque acting on the loop is zero and the loop is in equilibrium. No, the net force acting on the loop is zero and the loop is in equilibrium. Correct Part B Assume that the loop is initially positioned at and the current flowing into the loop is 0.500 . If the magnitude of the magnetic field is 0.300 , what is , the net torque about the vertical axis of the current loop due to the interaction of the current with the magnetic field? Express your answer in newton-meters. Hint 1. Torque on a current-carrying loop The torque acting on a current-carrying loop of area due to the interaction of the currentflowing through the loop with a magnetic field of magnitude is given by , where is the angle between the normal to the loop and the direction of the magnetic field. Hint 2. Find the area of the loop What is the area of a rectangular loop of wire with height 4.00 and horizontal sides 2.00 ? Express your answer in square meters. ANSWER: = 8.00×10 −4 Hint 3. Find the angle between the normal to the loop and the magnetic field Consider the loop described in the introduction of this problem. Recall thatis the angle between the sides of Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... length and . Now consider the normal to the loop. What is the angle between the normal and the magnetic field? Be careful to consider the correct sign f.r ANSWER: ANSWER: = 1.04×10 −4 Correct Part C What happens to the loop when it reaches the position for which , that is, when its horizontal sides of length are perpendicular to (see the figure)? Hint 1. Find the net torque acting on the loop What is , the net torque about the vertical axis of the current loop due to the interaction of the current with the magnetic field? Express your answer in newton-meters. Hint 1. Find the angle between the normal to the loop and the magnetic field What is the angle between the normal to the loop and the magnetic field when the horizontal sides of the loop of length are perpendicular to ? Express your answer in degrees. Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: = 0 ANSWER: = 0 ANSWER: The direction of rotation changes because the net torque acting on the loop causes the loop to rotate in a clockwise direction. The net torque acting on the loop is zero, but the loop continues to rotate in a counterclockwise direction. The net torque acting on the loop is zero; therefore it stops rotating. The net force acting on the loop is zero, so the loop must be in equilibrium. Correct Part D Now suppose that you change the initial angular position of the loop relative, and assume that the loop is placed in such a way that initially the angle between the sides of lenand is , as shown in the figure. Will the interaction of the current through the loop with the magnetic field cause the loop to rotate? Hint 1. Find the direction of the forces on the parts of the loop that have length As current is moving through the loop, forces act on its different parts. These result from magnetic forces acting on the charges that move through the wire. What is the direction of the forces on the two pieces of wire of length ? Select the correct diagram from the four options. The forces are symbolized by the red arrows. Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... ANSWER: A B C D Hint 2. Find the direction of the forces on the parts of the loop that have length As current is moving through the loop, forces act on its different parts. These result from magnetic forces acting on the charges that move through the wire. What can you say about the forces on the two pieces of wire of length ? ANSWER: The forces point away from the center of the loop and cancel each other. The forces act as a torque about an axis through the midpoints of the two pieces of and make the loop turn in the counterclockwise direction. The forces point toward the center of the loop and cancel each other. Both forces point upward perpendicular toand the piece of wire of length . ANSWER: Yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle (clockwise). Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle (counterclockwise). No, the net torque acting on the loop is zero and the loop is in equilibrium. No, the net force acting on the loop is zero and the loop is in equilibrium. Short Assignment By 2/22/2016 https://session.masteringphysics.com/myct/assignmentPrintView?displ... Correct Depending on the initial position of the loop relative to , the direction of rotation of the loop will be different. If initially , then the net torque acting on the loop will cause the loop to rotate in the counterclockwise direction. If instead, , then the net torque will rotate the loop in the opposite direction. Score Summary: Your score on this assignment is 97.2%. You received 0.97 out of a possible total of 1 points.

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