vv d of the electrons. As a result, there is a net current in

[International Campus] Objective Investigate the effects of current, length of wire and magnetic field strength on a magnetic force. Theory ----------------------------- Reference -------------------------- Young & Freedman, University Physics (14 th ed.), Pearson, 2016 25.1 Current (p.841-844) 27.2 Magnetic Field (p.907-911) 27.6 on a Current-Carrying Conductor (p.920-923) ----------------------------------------------------------------------------- 1. Current, Drift Velocity, and Current Density If an electric field EE is established inside a conductor, a free electron is then subjected to a force FF = qqee and accelerated in the direction of FF. But an electron moving in a conductor undergoes frequent collision with the massive stationary ions of the material, so the electron s direction of motion undergoes a random change. The net effect of EE is that in addition to the random motion of the electron, there is also a very slow net motion of drift of moving electrons as a group in the direction of FF. This motion is described in terms of the drift velocity vv d of the electrons. As a result, there is a net current in the conductor. While the random motion of the electrons has a very fast average speed of about 10 6 m/s, the drift speed is very slow, often on the order of 10 4 m/s. A current is any motion of charge from one region to another. Electrons in motion involve currents in conducting materials such as copper wire. In electrostatic situations, the electric field is zero everywhere within the conductor, and there is no current. However, this does not mean that all charges within the conductor are at rest. In an ordinary metal, some of electrons are free to move, as shown in Fig.1. These free electrons move randomly in all direction, so there is no net flow of charge in any direction and hence no current. Fig 1 If there is no electric field inside a conductor, an electron moves randomly from PP 1 to PP 2 in ΔΔΔΔ. If EE is present, FF = qqee imposes a small drift that takes the electron to PP 2, a distance vv d ΔΔΔΔ from PP 2 in the direction of the force. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 1 / 11

We define the conventional current II to be in the direction in which there is a flow of positive charge, even if the actual current is due to electrons. Fig. 2 shows a segment of a conductor in which a current is flowing. We define the current II through the cross-sectional area AA to be the net charge dddd flowing through the area per unit time dddd. If each particle has a charge qq, the charge dddd that flows out of the end of the cylinder during time dddd is and the current is dddd = qq(nnnnvv d dddd) = nnnnvv d AAdddd (2) II = dddd dddd (1) II = dddd dddd = nnnnvv daa (3) The SI unit of current is the ampere. (1 A = 1 C s) The current per unit cross-sectional area is called the current density JJ: We can express current in terms of the drift velocity of the moving charges. In Fig. 2, an electric field EE is directed to right in a conductor with cross-sectional area AA. Assume that the free charges in the conductor are positive; then the drift velocity is in the same direction as the field. Suppose there are nn moving charged particles per unit volume and all the particles move with the same drift velocity with magnitude vv d. We call nn the concentration of particles; its SI unit is m 3. In a time interval dddd, each particle moves a distance vv d dddd. The particles in the shaded cylinder with length vv d dddd flow out of the right end of the cylinder during dddd. The volume of the cylinder is AAvv d dddd, and the number of particles within it is nnnnvv d dddd. JJ = II AA = nnnnvv d (A m 2 ) (4) 2. on a Current-Carrying Conductor The magnetic force FF on a charge qq moving with velocity vv in a magnetic field BB is given by FF = qqvv BB (5) Fig 2 The current II is the time rate of charge transfer through the cross-sectional area AA. The random component of each moving charged particle s motion averages to zero, and the current is in the same direction as EE whether the moving charges are positive (as shown here) or negative. Fig 3 The magnetic force FF acting on a positive charge qq moving with velocity vv is perpendicular to both vv and the magnetic field BB. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 2 / 11

There is a magnetic force on a current-carrying conductor in a magnetic field because charges in the conductor are in motion. We can compute the force on it with equation (5). Figure 4 shows a straight segment of a conducting wire, with length ll and cross-sectional area AA. The wire is in a uniform magnetic field BB, perpendicular to the plane of the diagram and directed into the plane. Let s assume that the moving charges are positive. The drift velocity vv d is upward, perpendicular to BB. The magnitude of the average force on each charge is then FF = qqvv d BB from equation (5). If the BB is not perpendicular to the wire but makes and angle φφ with it, only the component of BB perpendicular to the wire exerts a force; this component is BB = BB sin φφ. The magnetic force on the wire segment is then FF = IIIIBB = IIIIII sin φφ (8) The force is always perpendicular to both the conductor and the field, with the direction determined by the right-hand rule. Hence this force can be expressed as a vector product. We represent the segment of wire a vector ll along the wire in the direction of the current; then the force FF on this segment is We can derive an expression for the total force on all the moving charges in a length ll of conductor with crosssectional area AA using the same language we used in Eqs. (3) and (4). The number of charges per unit volume is nn; a segment of conductor with length ll has volume AAll and contains a number of charges equal to nnnnll. The total force FF on all the moving charges in this segment has magnitude FF = IIll BB (9) Figure 5 and 6 illustrate the direction of BB, ll, and FF for several cases. FF = (nnnnnn)(qqvv d BB) = (nnnnvv d AA)(llll) (6) From Eq. (4) the current density is JJ = nnnnvv d. The product JJJJ is the total current II, so we can rewrite Eq. (6) as FF = IIIIII (7) Fig 5 A straight wire segment of length ll carries a current II in the direction of ll. The magnetic force on this segment is perpendicular to both ll and the magnetic field BB Fig 4 Forces on a moving positive charge in a current-carrying conductor. Fig 6 Magnetic field BB, length ll, and force FF vectors for a straight wire carrying a current II. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 3 / 11

Equipment 1. List Items Qty. Description Conductor Boards set 1 set Includes 6 PC boards with different length of straight conductive foil. Rotatable Conductor Assembly with Goniometer 1 Rotates the direction of conductive wires. Conductor Holder 1 Holds the Conductor Boards or the Rotatable Conductor Assembly. Magnet Assemblies 1 set Produces a magnetic field. Magnet assembly #1: for Conductor Boards Magnet assembly #2: for Rotatable Conductor Ass. Power Supply (Power Cable included) 1 Produces regulated DC power up to 10 A in a voltage range 0 to 30 V. Electronic Balance (DC Adapter included) 1 Measures mass of an object with a precision to 0.01 g. in a range of 0~300g. Ruler 1 Measures length. Patch Cords (with banana plugs) 2 Carry electric current. A-shaped Base Support Rod (300mm) 1 1 Provides stable support for experiment set-ups. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 4 / 11

Procedure Prior to the experiment, measure the length of horizontal conductive foil of the Conductor Boards. Single-sided Double-sided ll ll = ll 1 + ll 2 Experiment 1. Force vs. Current (1) Set up your equipment. 1 Mount the Conductor Holder on an A-shaped Base. (front) (back) 2 Select any Conductor Board, and plug it into the end of the Holder, with the conductive foil extending down. 3 Place the Magnet Assembly on the balance. Position the A-shaped Base so the horizontal position of the conductive foil passes through the pole region of the magnets. The conductive foil shouldn t touch the magnets. Make sure the north poles of the magnets of the Magnet Assembly #1 are all on the same side. You can disassemble the Magnet Assembly if required. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 5 / 11

(2) Turn on the power supply. (3) Zero the electronic balance. Caution Caution Do not touch the Conductor Board or the metal arms of the Conductor Holder while current is flowing through them. The electronic balance is a precision instrument. Subjecting it to impact could cause it to fail. Treat it with care. Before turning on the power supply, rotate the voltage and current adjustment knobs fully counterclockwise for no output settings. Place the Magnet Assembly on the balance. With no current flowing, zero the balance by pressing [ 영점 ] or [ 용기 ] button. Turn on the power supply, and then rotate the voltage adjustment knob fully clockwise. Do not increase the current yet. You can now adjust the current II through the conductor using the current adjustment knob. Note For zeroing the balance, press [ 영점 ] and stand by until the [ZERO] mark lights up on the display. When the initial value is relatively high, [ 영점 ] button will not work. In this case, you can zero it using [ 용기 ] button. ([TARE] mark will light up on the display.) Note If you have any problem zeroing the balance, turn the power off and then on again. If you cannot obtain the desired output current: 1 Check the connections. Make sure the power supply is properly connected to the conductor. 2 Check if the CV lamp is on. It indicates that the DC output is in constant voltage mode, i.e. the voltage level you set is too low. Increase the voltage level by rotating the voltage adjustment knob clockwise. Note If any of [CT], [%], [PCS], [CHK], or [ANI] symbols lights up on the display, press [ 모드 ] repeatedly until all symbols disappear. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 6 / 11

(4) Increase the current and record your results. Experiment 2. Force vs. Length of current-carrying wire Increase the current to 0.5 A, read the mass, and record the force value in the Force column of the table below. Note the actual force is proportional to the mass reading, FF = mmgg. (1) Set up your equipment. Follow the setup of experiment 1. Increase the current in 0.5 A increments to 5.0 A, each time recording the new force value. Current (A) Mass (kg) Force (N) 0.0 0.5 1.0 5.0 (2) Plug the shortest Conductor Board. Select the Conductor Board with the shortest conductive foil, and plug it into the ends of the Conductor Holder. (3) Set the current to 2.0 A, and record the measured value of mass. (4) Repeat the measurements for other length of conductor. (5) Analyze your results. Plot a graph of the magnetic force as a function of the current through the conductor. Before removing the Conductor Board, you should TURN OFF the power supply. Note You can swing the arm of the Conductor Holder up to raise the present Conductor Board out of the magnetic field gap. Q What is the nature of the relationship between these two variables? What does this tell us about how changes in the current will affect the force acting on a wire that is inside a magnetic field? Length (m) Mass (kg) Force (N) A 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 7 / 11

(5) Analyze your results. (4) Zero the balance. Plot a graph of the magnetic force as a function of the length of current-carrying wire. Place the Magnet Assembly on the balance. With no current flowing, zero the balance by pressing [ 영점 ] or [ 용기 ] button. Q A What is the nature of the relationship between these two variables? What does this tell us about how changes in the length of a current-carrying wire will affect the force that it feels when it is in a magnetic field? (5) Set the current to 2.0 A, and record the force. (6) Repeat the measurements for other number of magnets. Add additional magnets, one at a time. Make sure the north poles of the magnets are all on the same side of the Magnet Assembly. Each time you add a magnet, repeat steps (4)-(5). Experiment 3. Force vs. Magnetic Field (1) Set up your equipment. Follow the setup of experiment 1. (2) Plug the shortest Conductor Board. Select the Conductor Board with the shortest conductive foil, and plug it into the ends of the Conductor Holder. (3) Mount a single magnet in the Magnet Assembly. Disassemble the Magnet Assembly and attach a single magnet in the center of the assembly. Number of magnets Mass (kg) Force (N) 1 2 3 4 5 6 Note The magnetic field is varied by changing the number of magnets that are mounted on the Magnet Assembly. The field may not be exactly proportional to the number of the magnets, but it is reasonably close. (7) Analyze your results. Plot a graph of the force as a function of number of magnets. Q What is the relationship between these two variables? How does the number of magnets affect the force between a current carrying wire and a magnetic field? Is it reasonable to assume that the strength of the magnetic field is directly proportional to the number of magnets? A 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 8 / 11

Experiment 4. Force vs. Angle (3) Set the current to 1.0 A, and record the force. Determine how the angle between the current carrying wire and the magnetic field affects the force between them. (1) Set up your equipment. Caution The current through the wire of the Rotatable Conductor Assembly should never exceed 2.0 A. 1 Plug the Rotatable Conductor Assembly into the ends of the Conductor Holder. 2 Set the goniometer dial on the Rotatable Conductor to 0. (4) Repeat the measurements. 3 Place the Magnet Assembly #2 on the balance, and align it so that the magnetic field is parallel with the wires of the coil at the end of the Rotatable Conductor Assembly. Increase the angle in 5 increments up to 90 and then in 5 increments to 90, by rotating the goniometer dial of the Rotatable Conductor Assembly. At each angle, record the force. Angle ( ) Mass (kg) Force (N) Angle ( ) 0 0 5-5 10-10 15-15 90-90 Mass (kg) Force (N) (5) Analyze your results. Plot a graph of the force as a function of the angle. Q What is the relationship between these two variables? How do changes in the angle between the current and the magnetic field affect the force acting between them? What angle produces the greatest force? What angle produces the least force? (2) Zero the balance. A With the current turned off, zero the balance. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 9 / 11

Result & Discussion Your TA will inform you of the guidelines for writing the laboratory report during the lecture. End of LAB Checklist Please put your equipment in order as shown below. Delete all your data files from your lab computer. Turn off your lab Computer. With the voltage and current adjustment knob set at zero, turn off the Power Supply and unplug the power cable. Turn off the Electronic Balance and unplug the dc adaptor. Reassemble the Magnet Assembly #1. (Be careful not to lose any parts of it.) Make sure the north poles of the magnets are all on the same side of the magnet assembly. 85 Songdogwahak-ro, Yeonsu-gu, Incheon 21983, KOREA ( +82 32 749 3430) Page 10 / 11